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1
Meyer, Amelie, Kurt L. Polzin, Bernadette M. Sloyan, and Helen E. Phillips. "Internal Waves and Mixing near the Kerguelen Plateau." Journal of Physical Oceanography 46, no. 2 (February 2015): 417–37. http://dx.doi.org/10.1175/jpo-d-15-0055.1.
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AbstractIn the stratified ocean, turbulent mixing is primarily attributed to the breaking of internal waves. As such, internal waves provide a link between large-scale forcing and small-scale mixing. The internal wave field north of the Kerguelen Plateau is characterized using 914 high-resolution hydrographic profiles from novel Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats. Altogether, 46 coherent features are identified in the EM-APEX velocity profiles and interpreted in terms of internal wave kinematics. The large number of internal waves analyzed provides a quantitative framework for characterizing spatial variations in the internal wave field and for resolving generation versus propagation dynamics. Internal waves observed near the Kerguelen Plateau have a mean vertical wavelength of 200 m, a mean horizontal wavelength of 15 km, a mean period of 16 h, and a mean horizontal group velocity of 3 cm s−1. The internal wave characteristics are dependent on regional dynamics, suggesting that different generation mechanisms of internal waves dominate in different dynamical zones. The wave fields in the Subantarctic/Subtropical Front and the Polar Front Zone are influenced by the local small-scale topography and flow strength. The eddy-wave field is influenced by the large-scale flow structure, while the internal wave field in the Subantarctic Zone is controlled by atmospheric forcing. More importantly, the local generation of internal waves not only drives large-scale dissipation in the frontal region but also downstream from the plateau. Some internal waves in the frontal region are advected away from the plateau, contributing to mixing and stratification budgets elsewhere.
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Morozov, Eugene G. "Semidiurnal internal wave global field." Deep Sea Research Part I: Oceanographic Research Papers 42, no. 1 (January 1995): 135–48. http://dx.doi.org/10.1016/0967-0637(95)92886-c.
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Varma, Dheeraj, Manikandan Mathur, and Thierry Dauxois. "Instabilities in internal gravity waves." Mathematics in Engineering 5, no. 1 (2022): 1–34. http://dx.doi.org/10.3934/mine.2023016.
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<abstract><p>Internal gravity waves are propagating disturbances in stably stratified fluids, and can transport momentum and energy over large spatial extents. From a fundamental viewpoint, internal waves are interesting due to the nature of their dispersion relation, and their linear dynamics are reasonably well-understood. From an oceanographic viewpoint, a qualitative and quantitative understanding of significant internal wave generation in the ocean is emerging, while their dissipation mechanisms are being debated. This paper reviews the current knowledge on instabilities in internal gravity waves, primarily focusing on the growth of small-amplitude disturbances. Historically, wave-wave interactions based on weakly nonlinear expansions have driven progress in this field, to investigate spontaneous energy transfer to various temporal and spatial scales. Recent advances in numerical/experimental modeling and field observations have further revealed noticeable differences between various internal wave spatial forms in terms of their instability characteristics; this in turn has motivated theoretical calculations on appropriately chosen internal wave fields in various settings. After a brief introduction, we present a pedagogical discussion on linear internal waves and their different two-dimensional spatial forms. The general ideas concerning triadic resonance in internal waves are then introduced, before proceeding towards instability characteristics of plane waves, wave beams and modes. Results from various theoretical, experimental and numerical studies are summarized to provide an overall picture of the gaps in our understanding. An ocean perspective is then given, both in terms of the relevant outstanding questions and the various additional factors at play. While the applications in this review are focused on the ocean, several ideas are relevant to atmospheric and astrophysical systems too.</p></abstract>
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Lelong, M. P., and E. Kunze. "Can barotropic tide–eddy interactions excite internal waves?" Journal of Fluid Mechanics 721 (March 13, 2013): 1–27. http://dx.doi.org/10.1017/jfm.2013.1.
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AbstractThe interaction of barotropic tidal currents and baroclinic geostrophic eddies is considered theoretically and numerically to determine whether energy can be transferred to an internal wave field by this process. The eddy field evolves independently of the tide, suggesting that it acts catalytically in facilitating energy transfer from the barotropic tide to the internal wave field, without exchanging energy with the other flow components. The interaction is identically zero and no waves are generated when the barotropic tidal current is horizontally uniform. Optimal internal wave generation occurs when the scales of tide and eddy fields satisfy resonant conditions. The most efficient generation is found if the tidal current horizontal scale is comparable to that of the eddies, with a weak maximum when the scales differ by a factor of two. Thus, this process is not an effective mechanism for internal wave excitation in the deep ocean, where tidal current scales are much larger than those of eddies, but it may provide an additional source of internal waves in coastal areas where horizontal modulation of the tide by topography can be significant.
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Cusack, Jesse M., J. Alexander Brearley, Alberto C. Naveira Garabato, David A. Smeed, Kurt L. Polzin, Nick Velzeboer, and Callum J. Shakespeare. "Observed Eddy–Internal Wave Interactions in the Southern Ocean." Journal of Physical Oceanography 50, no. 10 (October 1, 2020): 3043–62. http://dx.doi.org/10.1175/jpo-d-20-0001.1.
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AbstractThe physical mechanisms that remove energy from the Southern Ocean’s vigorous mesoscale eddy field are not well understood. One proposed mechanism is direct energy transfer to the internal wave field in the ocean interior, via eddy-induced straining and shearing of preexisting internal waves. The magnitude, vertical structure, and temporal variability of the rate of energy transfer between eddies and internal waves is quantified from a 14-month deployment of a mooring cluster in the Scotia Sea. Velocity and buoyancy observations are decomposed into wave and eddy components, and the energy transfer is estimated using the Reynolds-averaged energy equation. We find that eddies gain energy from the internal wave field at a rate of −2.2 ± 0.6 mW m−2, integrated from the bottom to 566 m below the surface. This result can be decomposed into a positive (eddy to wave) component, equal to 0.2 ± 0.1 mW m−2, driven by horizontal straining of internal waves, and a negative (wave to eddy) component, equal to −2.5 ± 0.6 mW m−2, driven by vertical shearing of the wave spectrum. Temporal variability of the transfer rate is much greater than the mean value. Close to topography, large energy transfers are associated with low-frequency buoyancy fluxes, the underpinning physics of which do not conform to linear wave dynamics and are thereby in need of further research. Our work suggests that eddy–internal wave interactions may play a significant role in the energy balance of the Southern Ocean mesoscale eddy and internal wave fields.
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Broutman, D., and R. Grimshaw. "The energetics of the interaction between short small-amplitude internal waves and inertial waves." Journal of Fluid Mechanics 196 (November 1988): 93–106. http://dx.doi.org/10.1017/s0022112088002629.
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The interaction between a wave packet of small-amplitude short internal waves, and a finite-amplitude inertial wave field is described to second order in the short-wave amplitude. The discussion is based on the principle of wave action conservation and the equations for the wave-induced Lagrangian mean flow. It is demonstrated that as the short internal waves propagate through the inertial wave field they generate a wave-induced train of trailing inertial waves. The contribution of this wave-induced mean flow to the total energy balance is described. The results obtained here complement the finding of Broutman & Young (1986) that the short internal waves undergo a net change in energy after their encounter with the inertial wave field.
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MERCIER, MATTHIEU J., DENIS MARTINAND, MANIKANDAN MATHUR, LOUIS GOSTIAUX, THOMAS PEACOCK, and THIERRY DAUXOIS. "New wave generation." Journal of Fluid Mechanics 657 (July 19, 2010): 308–34. http://dx.doi.org/10.1017/s0022112010002454.
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We present the results of a combined experimental and numerical study of the generation of internal waves using the novel internal wave generator design of Gostiaux et al. (Exp. Fluids, vol. 42, 2007, pp. 123–130). This mechanism, which involves a tunable source composed of oscillating plates, has so far been used for a few fundamental studies of internal waves, but its full potential is yet to be realized. Our study reveals that this approach is capable of producing a wide variety of two-dimensional wave fields, including plane waves, wave beams and discrete vertical modes in finite-depth stratifications. The effects of discretization by a finite number of plates, forcing amplitude and angle of propagation are investigated, and it is found that the method is remarkably efficient at generating a complete wave field despite forcing only one velocity component in a controllable manner. We furthermore find that the nature of the radiated wave field is well predicted using Fourier transforms of the spatial structure of the wave generator.
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Didenkulova, Ekaterina, and Efim Pelinovsky. "Interaction Features of Internal Wave Breathers in a Stratified Ocean." Fluids 5, no. 4 (November 10, 2020): 205. http://dx.doi.org/10.3390/fluids5040205.
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Oscillating wave packets (breathers) are a significant part of the dynamics of internal gravity waves in a stratified ocean. The formation of these waves can be provoked, in particular, by the decay of long internal tidal waves. Breather interactions can significantly change the dynamics of the wave fields. In the present study, a series of numerical experiments on the interaction of breathers in the frameworks of the etalon equation of internal waves—the modified Korteweg–de Vries equation (mKdV)—were conducted. Wave field extrema, spectra, and statistical moments up to the fourth order were calculated.
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Feng, Jiabao, and Yang Song. "Effect of underwater vehicle wake on sound propagation characteristics in stratified medium." Journal of Physics: Conference Series 2718, no. 1 (March 1, 2024): 012077. http://dx.doi.org/10.1088/1742-6596/2718/1/012077.
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Abstract Due to the uneven distribution of seawater temperature and salinity, the density distribution at different depths is different, thus forming a density step layer with a certain gradient. Acquiring the wake internal wave field generated by underwater vehicles passing through this layered structure and mastering its modulation characteristics for the sound field can provide new technical support for the tracking and identification of underwater vehicles. In this paper, the real size model of a certain type of underwater vehicle is taken as the research object to explore the characteristics of its wake internal wave field, and the influence of navigation parameters on the wake field and the change of winning characteristics under the influence of internal waves are simulated and analyzed. The results show that the navigation parameters of underwater vehicles have obvious influence on the wake field, and then have specific influence on the sound field structure in a certain range, especially on the sound signal of the sound field.
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HORN, D. A., L. G. REDEKOPP, J. IMBERGER, and G. N. IVEY. "Internal wave evolution in a space–time varying field." Journal of Fluid Mechanics 424 (November 16, 2000): 279–301. http://dx.doi.org/10.1017/s0022112000001841.
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An extended Korteweg–de Vries (KdV) equation is derived that describes the evolution and propagation of long interfacial gravity waves in the presence of a strong, space–time varying background. Provision is made in the derivation for a spatially varying lower depth so that some topographic effects can also be included. The extended KdV model is applied to some simple scenarios in basins of constant and varying depths, using approximate expressions for the variable coefficients derived for the case when the background field is composed of a moderate-amplitude ultra-long wave. The model shows that energy can be transferred either to or from the evolving wave packet depending on the relative phases of the evolving waves and the background variation. Comparison of the model with laboratory experiments confirms its applicability and usefulness in examining the evolution of weakly nonlinear waves in natural systems where the background state is rarely uniform or steady.
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Abdilghanie, Ammar M., and Peter J. Diamessis. "The internal gravity wave field emitted by a stably stratified turbulent wake." Journal of Fluid Mechanics 720 (February 27, 2013): 104–39. http://dx.doi.org/10.1017/jfm.2012.640.
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AbstractThe internal gravity wave (IGW) field emitted by a stably stratified, initially turbulent, wake of a towed sphere in a linearly stratified fluid is studied using fully nonlinear numerical simulations. A wide range of Reynolds numbers, $\mathit{Re}= UD/ \nu \in [5\times 1{0}^{3} , 1{0}^{5} ] $ and internal Froude numbers, $\mathit{Fr}= 2U/ (ND)\in [4, 16, 64] $ ($U$, $D$ are characteristic body velocity and length scales, and $N$ is the buoyancy frequency) is examined. At the higher $\mathit{Re}$ examined, secondary Kelvin–Helmholtz instabilities and the resulting turbulent events, directly linked to a prolonged non-equilibrium (NEQ) regime in wake evolution, are responsible for IGW emission that persists up to $Nt\approx 100$. In contrast, IGW emission at the lower $\mathit{Re}$ investigated does not continue beyond $Nt\approx 50$ for the three $\mathit{Fr}$ values considered. The horizontal wavelengths of the most energetic IGWs, obtained by continuous wavelet transforms, increase with $\mathit{Fr}$ and appear to be smaller at the higher $\mathit{Re}$, especially at late times. The initial value of these wavelengths is set by the wake height at the beginning of the NEQ regime. At the lower $\mathit{Re}$, consistent with a recently proposed model, the waves propagate over a narrow range of angles that minimize viscous decay along their path. At the higher $\mathit{Re}$, wave motion is much less affected by viscosity, at least initially, and early-time wave propagation angles extend over a broader range of values which are linked to increased efficiency in momentum extraction from the turbulent wake source.
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Zhao, Yiyang, Zhiyin Sun, Donghua Pan, Shengxin Lin, Yinxi Jin, and Liyi Li. "A New Approach to Calculate the Shielding Factor of Magnetic Shields Comprising Nonlinear Ferromagnetic Materials under Arbitrary Disturbances." Energies 12, no. 11 (May 29, 2019): 2048. http://dx.doi.org/10.3390/en12112048.
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To enable the realization of ultra-low magnetic fields for scientific and technological research, magnetic shielding is required to create a space with low residual magnetic field and high shielding factors. The shielding factors of magnetic shields are due to nonlinear material properties, the geometry and structure of the shields, and the external magnetic fields. Magnetic shielding is used in environments full of random realistic disturbances, resulting in an arbitrary and random external magnetic field, and in this case, the shielding effect is hard to define simply by the shielding factors. A new method to simulate and predict a dynamic internal space magnetic field wave is proposed based on the Finite Element method (FEM) combined with the Jiles-Atherton (JA) model. By simulating the hysteresis behavior of the magnetic shields and establishing a dynamic model, the new method can simulate dynamic magnetic field changes inside magnetic shields as long as the external disturbances are known. The shielding factors under an AC external field with a sine wave and certain frequencies are calculated to validate the feasibility of the new method. A real-time wave of internal magnetic flux density under an AC triangular wave external field is simulated directly with the new method versus a method that splits the triangular wave into several sine waves by a Fourier transform, divides the shielding factors, and then adds the quotients together. Moreover, real-time internal waves under some arbitrary fields are measured. Experimental internal magnetic flux density waves of a 4-layer magnetically shielded room (MSR) at the Harbin Institute of Technology (HIT) fit the simulated results well, taking experimental errors into account.
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Perfect, B., N. Kumar, and J. J. Riley. "Energetics of Seamount Wakes. Part II: Wave Fluxes." Journal of Physical Oceanography 50, no. 5 (May 2020): 1383–98. http://dx.doi.org/10.1175/jpo-d-19-0104.1.
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AbstractSeamounts are thought to facilitate ocean mixing through unsteady wake processes, and through the generation of internal waves, which propagate away from the seamount and later break. The relative importance of these processes is examined for idealized, isolated seamounts (with characteristic width D and height H) in uniform barotropic flow U. A range of Coriolis parameters f and buoyancy frequencies N are used such that a broad parameter space of low Froude numbers (U/NH) and low Rossby numbers (U/fD) is considered. Results indicate that eddy processes energetically dominate the internal wave energy flux in this range of parameter space. The internal wave field is specifically examined and partitioned into steady lee waves and unsteady, wake-generated waves. It is found that the lee wave energy flux cannot be explained by existing analytical theories. A lee wave model by Smith is then extended into the low-Froude-number regime and the effect of rotation is included. While strongly stratified experiments have previously indicated that only the top U/N of an obstacle generates internal waves, the effect of rotation appears to modify this wavemaking height. Once the U/N height is revised to account for rotation, the lee wave energy flux can be reasonably accurately reproduced by the extended Smith model.
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Yu, Wen, Fenggang Wang, Jianguo Lin, and Dong Li. "Numerical Simulation of the Force Acting on the Riser by Two Internal Solitary Waves." Applied Sciences 12, no. 10 (May 11, 2022): 4873. http://dx.doi.org/10.3390/app12104873.
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An internal wave is a typical dynamic process. As an internal wave, an internal solitary wave usually occurs between two layers of fluids with different densities. Compared with general internal waves, internal solitary waves have large amplitudes, fast propagation speeds, short-wave periods, and often have tremendous energy. The propagation causes strong convergence and divergence of seawater and generates a sudden strong current. Due to its various characteristics, the propagation of internal solitary waves can cause serious harm to offshore engineering structures. Therefore, studying the effects of internal solitary waves on risers is vital in preventing environmental pollution caused by riser damage. Although the research on internal solitary waves has achieved very fruitful results, the research on structures is mostly focused on a single condition, and the occurrence of internal solitary wave, as a complex ocean phenomenon, is often accompanied by many situations. Therefore, this paper constructs a numerical simulation of the interaction between two columns of internal solitary waves and risers. This study explores the force and flow field changes of the riser under the condition of multiple internal solitary waves using the Star-CCM+ software in the simulation. The improved K-epsilon turbulence model was adopted to close the three-dimensional incompressible Navier–Stokes equation, and the solitary wave solution of the eKdV equation was used as the initial and boundary conditions. The interaction between single and double internal solitary waves and a riser was calculated, compared, and analyzed using numerical analysis. The experiment results indicate that the conditions of two internal solitary waves differ from those of a single internal solitary wave. After colliding at the riser, the waves gradually merge into a single wave, and the flow field reaches its minimum velocity. Under the two-wave condition, the horizontal force on the riser as a whole is less than the single-wave condition. As the amplitude difference between the two internal solitary waves gradually decreases, the horizontal opposing force received by the riser first increases and then decreases, while the horizontal positive force gradually decreases.
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Quinn, B., C. Eden, and D. Olbers. "Application of the IDEMIX Concept for Internal Gravity Waves in the Atmosphere." Journal of the Atmospheric Sciences 77, no. 10 (October 1, 2020): 3601–18. http://dx.doi.org/10.1175/jas-d-20-0107.1.
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AbstractThe model Internal Wave Dissipation, Energy and Mixing (IDEMIX) presents a novel way of parameterizing internal gravity waves in the atmosphere. IDEMIX is based on the spectral energy balance of the wave field and has previously been successfully developed as a model for diapycnal diffusivity, induced by internal gravity wave breaking in oceans. Applied here for the first time to atmospheric gravity waves, integration of the energy balance equation for a continuous wave field of a given spectrum, results in prognostic equations for the energy density of eastward and westward gravity waves. It includes their interaction with the mean flow, allowing for an evolving and local description of momentum flux and gravity wave drag. A saturation mechanism maintains the wave field within convective stability limits, and a closure for critical-layer effects controls how much wave flux propagates from the troposphere into the middle atmosphere. Offline comparisons to a traditional parameterization reveal increases in the wave momentum flux in the middle atmosphere due to the mean-flow interaction, resulting in a greater gravity wave drag at lower altitudes. Preliminary validation against observational data show good agreement with momentum fluxes.
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Finette, Steven, Marshall H. Orr, Altan Turgut, John R. Apel, Mohsen Badiey, Ching-sang Chiu, Robert H. Headrick, et al. "Acoustic field variability induced by time evolving internal wave fields." Journal of the Acoustical Society of America 108, no. 3 (2000): 957. http://dx.doi.org/10.1121/1.1288662.
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Yuan, C., R. Grimshaw, E. Johnson, and Z. Wang. "Topographic effect on oblique internal wave–wave interactions." Journal of Fluid Mechanics 856 (September 28, 2018): 36–60. http://dx.doi.org/10.1017/jfm.2018.678.
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Based on a variable-coefficient Kadomtsev–Petviashvili (KP) equation, the topographic effect on the wave interactions between two oblique internal solitary waves is investigated. In the absence of rotation and background shear, the model set-up featuring idealised shoaling topography and continuous stratification is motivated by the large expanse of continental shelf in the South China Sea. When the bottom is flat, the evolution of an initial wave consisting of two branches of internal solitary waves can be categorised into six patterns depending on the respective amplitudes and the oblique angles measured counterclockwise from the transverse axis. Using theoretical multi-soliton solutions of the constant-coefficient KP equation, we select three observed patterns and examine each of them in detail both analytically and numerically. The effect of shoaling topography leads to a complicated structure of the leading waves and the emergence of two types of trailing wave trains. Further, the case when the along-crest width is short compared with the transverse domain of interest is examined and it is found that although the topographic effect can still modulate the wave field, the spreading effect in the transverse direction is dominant.
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Pelinovksy, E., T. Talipova, and V. Ivanov. "Estimations of the nonlinear properties of the internal wave field off the Israel coast." Nonlinear Processes in Geophysics 2, no. 2 (June 30, 1995): 80–88. http://dx.doi.org/10.5194/npg-2-80-1995.
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Abstract. The measurements of the vertical structure of hydrological fields and internal waves on the Levantine Sea's polygon in the Mediterranean, obtained in the 27-th cruise of the RV "Professor Kolesnikov" in 1991, have been used to estimate the kinematic and nonlinear characteristics of the internal wave field. Statistical and spatial distributions of the vertical profiles of the Brunt-Vaisala frequency are described. They have been used to calculate the coefficients of the Korteweg - de Vries equation. This equation forms the main model for nonlinear parameters. It is shown that the variations of the long wave speed propagation and the dispersion parameter are relatively small in comparison with the variation of the nonlinear parameter. Estimations of the nonlinear properties of the internal waves, being measured, based on the calculation of the local Ursell parameter are given. This method can be used for investigation of the internal wave transformation processes in oceanic regions with horizontal variability of the hydrophysical fields (temperature, salinity) and sloped sea floor.
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Baydulov, V. G. "On the Problem of Determining the Position of the Source of Internal Waves." Прикладная математика и механика 87, no. 1 (January 1, 2023): 36–44. http://dx.doi.org/10.31857/s0032823523010046.
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When bodies move in a continuously stratified fluid, the steady wave field moves along with the body and form a field of so-called associated internal waves. The flow incident on the body is usually assumed to be constant; non-stationary waves generated at the initial stage of motion are neglected. In this case, the body is modeled by point mass sources, and the wave field is found using the Green’s function method, followed by the use of asymptotic expansions based on the stationary phase method [1]. The inverse problem of determining the position of the source is solved from the wave field.
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Köhler, Janna, Georg S. Völker, and Maren Walter. "Response of the Internal Wave Field to Remote Wind Forcing by Tropical Cyclones." Journal of Physical Oceanography 48, no. 2 (February 2018): 317–28. http://dx.doi.org/10.1175/jpo-d-17-0112.1.
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AbstractIn the tropical North Atlantic, mean winds introduce relatively little energy into the internal wave field, but hurricanes act as very energetic sources for near-inertial waves. In addition to the eventlike passage of such tropical cyclones, changes in the wind speed north of the trade wind system induce a seasonal cycle in surface swell, with potential implications for the high-frequency part of the internal wave field. Using a 5-yr mooring time series in the interior of the tropical North Atlantic at 16°N, the temporal variability of internal wave energy south of the main hurricane track in different frequency bands is studied, and the magnitude of its variability, along with possible energy transfer mechanisms, is analyzed. The results show that changes in near-inertial energy are dominated by the passage of internal waves generated by hurricanes centered several hundred kilometers north of the mooring. The major role of hurricanes in the generation of near-inertial waves is also seen in an extended slab model that takes the horizontal divergence of the near-inertial current field at the mixed layer base into account. A seasonal cycle is observed in the energy at the high-frequency end (frequencies above 6 cpd) of the internal wave spectrum. It is not in phase with the near-inertial energy variability but covaries with changes in the local surface waves. These high-frequency internal waves are most energetic at times when large-amplitude surface swell with long periods and correspondingly long wavelengths is observed.
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Chunchuzov, I. P. "On the nonlinear shaping mechanism for gravity wave spectrum in the atmosphere." Annales Geophysicae 27, no. 11 (November 2, 2009): 4105–24. http://dx.doi.org/10.5194/angeo-27-4105-2009.
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Abstract. The nonlinear mechanism of shaping of a high vertical wave number spectral tail in the field of a few discrete internal gravity waves in the atmosphere is studied in this paper. The effects of advection of fluid parcels by interacting gravity waves are taken strictly into account by calculating wave field in Lagrangian variables, and performing a variable transformation from Lagrangian to Eulerian frame. The vertical profiles and vertical wave number spectra of the Eulerian displacement field are obtained for both the case of resonant and non-resonant wave-wave interactions. The evolution of these spectra with growing parameter of nonlinearity of the internal wave field is studied and compared to that of a broad band spectrum of gravity waves with randomly independent amplitudes and phases. The calculated vertical wave number spectra of the vertical displacements or relative temperature fluctuations are found to be consistent with the observed spectra in the middle atmosphere.
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Макаренко, Николай Иванович, Валерий Юрьевич Ляпидевский, Данила Сергеевич Денисенко, and Дмитрий Евгеньевич Кукушкин. "Nonlinear internal wave packets in shelf zone." Вычислительные технологии, no. 2(24) (April 17, 2019): 90–98. http://dx.doi.org/10.25743/ict.2019.24.2.008.
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В рамках модели невязкой слабостратифицированной жидкости рассматривается длинноволновое приближение, описывающее нелинейные волновые пакеты типа кноидальных волн. Построены семейства асимптотических решений, одновременно описывающие периодические последовательности приповерхностных волн в форме впадин и придонных волн типа возвышений. Показано, что картины расчетных профилей качественно согласуются со структурами внутренних волн, наблюдавшихся авторами в натурных экспериментах в шельфовой зоне моря. The problem on nonlinear internal waves propagating permanently in shallow fluid is studied semi-analytically in comparison with the field data measured on the sea shelf. At present, the most studied in this context are nonlinear solitary-type waves generated due to the tidal activity over continental slope. This paper deals with periodic cnoidaltype wave packets considered in the framework of mathematical model of continuously stratified fluid. Basic model involves the Dubreil-Jacotin-Long equation for a stream function that results from stationary fully non-linear 2D Euler equations. The longwave approximate equation describing periodic non-harmonic waves is derived by means of scaling procedure using small Boussinesq parameter. This parameter characterizes slight stratification of the fluid layer with the density profile being close to the linear stratification. The fine-scale density plays important role here because it determines the non-linearity rate of model equation, so it permits to consider strongly non-linear dispersive waves of large amplitude. As a result, constructed asymptotic solutions can simulate periodic wave-trains of sub-surface depression coupled with near-bottom wavetrains of isopycnal elevation. It is demonstrated that calculated wave profiles are in good qualitative agreement with internal wave structures observed by the authors in the field experiments performed annually during 2011-2018 in expeditions on the shelf of the Japanese sea.
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Olbers, Dirk, and Carsten Eden. "Revisiting the Generation of Internal Waves by Resonant Interaction with Surface Waves." Journal of Physical Oceanography 46, no. 8 (August 2016): 2335–50. http://dx.doi.org/10.1175/jpo-d-15-0064.1.
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AbstractTwo surface waves can interact to produce an internal gravity wave by nonlinear resonant coupling. The process has been called spontaneous creation (SC) because it operates without internal waves being initially present. Previous studies have shown that the generated internal waves have high frequency close to the local Brunt–Väisälä frequency and wavelengths that are much larger than those of the participating surface waves, and that the spectral transfer rate of energy to the internal wave field is small compared to other generation processes. The aim of the present analysis is to provide a global map of the energy transfer into the internal wave field by surface–internal wave interaction, which is found to be about 10−3 TW in total, based on a realistic wind-sea spectrum (depending on wind speed), mixed layer depths, and stratification below the mixed layer taken from a state-of-the-art numerical ocean model. Unlike previous calculations of the spectral transfer rate based on a vertical mode decomposition, the authors use an analytical framework that directly derives the energy flux of generated internal waves radiating downward from the mixed layer base. Since the radiated waves are of high frequency, they are trapped and dissipated in the upper ocean. The radiative flux thus feeds only a small portion of the water column, unlike in cases of wind-driven near-inertial waves that spread over the entire ocean depth before dissipating. The authors also give an estimate of the interior dissipation and implied vertical diffusivities due to this process. In an extended appendix, they review the modal description of the SC interaction process, completed by the corresponding counterpart, the modulation interaction process (MI), where a preexisting internal wave is modulated by a surface wave and interacts with another one. MI establishes a damping of the internal wave field, thus acting against SC. The authors show that SC overcomes MI for wind speeds exceeding about 10 m s−1.
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Pinkel, Robert. "Vortical and Internal Wave Shear and Strain." Journal of Physical Oceanography 44, no. 8 (August 1, 2014): 2070–92. http://dx.doi.org/10.1175/jpo-d-13-090.1.
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Abstract Depth–time records of isopycnal vertical strain have been collected from intensive CTD profiling programs on the research platform (R/P) Floating Instrument Platform (FLIP). The associated vertical wavenumber frequency spectrum of strain, when viewed in an isopycnal-following frame, displays a clear spectral gap at low vertical wavenumber, separating the quasigeostrophic (vortical) strain field and the superinertial internal wave continuum. This gap enables both model and linear-filter-based methods for separating the submesoscale and internal wave strain fields. These fields are examined independently in six field programs spanning the period 1983–2002. Vortical and internal wave strain variances are often comparable in the upper thermocline, of order 0.2. However, vortical strain tends to decrease with increasing depth (decreasing buoyancy frequency as ~(N2)1/2, while internal wave strain variance increases as ~(N2)−1/2, exceeding vortical variance by a factor of 5–10 at depths below 500 m. In contrast to strain, the low-frequency spectral gap in the shear spectrum is largely obscured by Doppler-smeared near-inertial motions. The vertical wavenumber spectrum of anticyclonic shear exceeds the cyclonic shear and strain spectra at all scales greater than 10 m. The frequency spectrum of anticyclonic shear exceeds that of both cyclonic shear and strain to frequencies of 0.5 cph, emphasizing the importance of lateral Doppler shifting of near-inertial shear. The limited Doppler shifting of the vortical strain field implies surprisingly small submesoscale aspect ratios: kH/kz ~ 0.001, Burger numbers Br = kH N/kzf ~ 0.1. Submesoscale potential vorticity is dominated by vertical straining rather than the vertical component of relative vorticity. The inferred rms fluctuation of fluid vorticity is far less for the vortical field than for the internal wavefield.
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Shakespeare, Callum J., and Andrew McC Hogg. "Spontaneous Surface Generation and Interior Amplification of Internal Waves in a Regional-Scale Ocean Model." Journal of Physical Oceanography 47, no. 4 (April 2017): 811–26. http://dx.doi.org/10.1175/jpo-d-16-0188.1.
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AbstractRecent theories, models, and observations have suggested the presence of significant spontaneous internal wave generation at density fronts near the ocean surface. Spontaneous generation is the emission of waves by unbalanced, large Rossby number flows in the absence of direct forcing. Here, spontaneous generation is investigated in a zonally reentrant channel model using parameter values typical of the Southern Ocean. The model is carefully equilibrated to obtain a steady-state wave field for which a closed energy budget is formulated. There are two main results: First, waves are spontaneously generated at sharp fronts in the top 50 m of the model. The magnitude of the energy flux to the wave field at these fronts is comparable to that from other mechanisms of wave generation. Second, the surface-generated wave field is amplified in the model interior through interaction with horizontal density gradients within the main zonal current. The magnitude of the mean-to-wave conversion in the model interior is comparable to recent observational estimates and is the dominant source of wave energy in the model, exceeding the initial spontaneous generation. This second result suggests that internal amplification of the wave field may contribute to the ocean’s internal wave energy budget at a rate commensurate with known generation mechanisms.
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Shmelev, Alexey, Ying-Tsong Lin, and James Lynch. "Low-Frequency Acoustic Propagation Through Crossing Internal Waves in Shallow Water." Journal of Theoretical and Computational Acoustics 28, no. 03 (February 3, 2020): 1950013. http://dx.doi.org/10.1142/s2591728519500130.
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Crossing internal wave trains are commonly observed in continental shelf shallow water. In this paper, we study the effects of crossing internal wave structures on three-dimensional acoustic ducts with both theoretical and numerical approaches. We show that, depending on the crossing angle, acoustic energy, which is trapped laterally between internal waves of one train, can be either scattered, cross-ducted or reflected by the internal waves in the crossing train. We describe the governing physics of these effects and illustrate them for selected internal wave scenarios using full-field numerical simulations.
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Coyle, Angus J., Md Ayub, Daniel Boettger, Manuel Cervera, and Andrew Mackinnon. "Impact of internal waves on underwater acoustic propagation." Journal of the Acoustical Society of America 154, no. 4_supplement (October 1, 2023): A81. http://dx.doi.org/10.1121/10.0022867.
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The propagation of internal waves in the ocean can produce significant fluctuations in the local sound speed field. Understanding how these fluctuations affect acoustic propagation is an area of considerable interest in underwater acoustics. Previous studies have indicated that large fluctuations (of the order of 20 dB) in transmission loss (TL) of acoustic waves can occur due to focusing and defocusing effects as the acoustic waves propagate through an internal wave. This work looks to extend some of these studies by exploring the frequency and directional dependence of these fluctuations through the implementation of a 3D acoustic model (FOR3D) suitable for modelling low frequency (<1 kHz) acoustic propagation. The study utilises sound speed data produced using the non-hydrostatic model MITgcm, simulating a nonlinear three-dimensional internal wave field that was verified using in situ mooring observations. By also considering results from a study utilising an acoustic ray model (Bellhop3D) on the same data, this work gives a comprehensive picture of the internal wave induced TL fluctuations across a range of acoustic frequencies.
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Dosser, Hayley V., and Luc Rainville. "Dynamics of the Changing Near-Inertial Internal Wave Field in the Arctic Ocean." Journal of Physical Oceanography 46, no. 2 (February 2016): 395–415. http://dx.doi.org/10.1175/jpo-d-15-0056.1.
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ABSTRACTThe dynamics of the wind-generated near-inertial internal wave field in the Canada Basin of the Arctic Ocean are investigated using the drifting Ice-Tethered Profiler dataset for the years 2005 to 2014, during a decade when sea ice extent and thickness decreased dramatically. This time series, with nearly 10 years of measurements and broad spatial coverage, is used to quantify a seasonal cycle and interannual trend for internal waves in the Arctic, using estimates of the amplitude of near-inertial waves derived from isopycnal displacements. The internal wave field is found to be most energetic in summer when sea ice is at a minimum, with a second maximum in early winter during the period of maximum wind speed. Amplitude distributions for the near-inertial waves are quantifiably different during summer and winter, due primarily to seasonal changes in sea ice properties that affect how the ice responds to the wind, which can be expressed through the “wind factor”—the ratio of sea ice drift speed to wind speed. A small positive interannual trend in near-inertial wave energy is linked to pronounced sea ice decline during the last decade. Overall variability in the internal wave field increases significantly over the second half of the record, with an increased probability of larger-than-average waves in both summer and winter. This change is linked to an overall increase in variability in the wind factor and sea ice drift speeds, and reflects a shift in year-round sea ice characteristics in the Arctic, with potential implications for dissipation and mixing associated with internal waves.
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Wagner, G. L., G. Ferrando, and W. R. Young. "An asymptotic model for the propagation of oceanic internal tides through quasi-geostrophic flow." Journal of Fluid Mechanics 828 (September 12, 2017): 779–811. http://dx.doi.org/10.1017/jfm.2017.509.
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We derive a time-averaged ‘hydrostatic wave equation’ from the hydrostatic Boussinesq equations that describes the propagation of inertia–gravity internal waves through quasi-geostrophic flow. The derivation uses a multiple-scale asymptotic method to isolate wave field evolution over intervals much longer than a wave period, assumes the wave field has a well-defined non-inertial frequency such as that of the mid-latitude semi-diurnal lunar tide, assumes that the wave field and quasi-geostrophic flow have comparable spatial scales and neglects nonlinear wave–wave dynamics. As a result the hydrostatic wave equation is a reduced model applicable to the propagation of large-scale internal tides through the inhomogeneous and moving ocean. A numerical comparison with the linearized and hydrostatic Boussinesq equations demonstrates the validity of the hydrostatic wave equation model and illustrates how the model fails when the quasi-geostrophic flow is too strong and the wave frequency is too close to inertial. The hydrostatic wave equation provides a first step toward a coupled model for energy transfer between oceanic internal tides and quasi-geostrophic eddies and currents.
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Budanov, S. P., A. S. Tibilov, and V. A. Yakovlev. "Cauchy internal wave scattering by density field inhomogeneities." Journal of Applied Mechanics and Technical Physics 28, no. 2 (1987): 246–49. http://dx.doi.org/10.1007/bf00918727.
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Flamarion, Marcelo V., and Efim Pelinovsky. "Evolution and Statistical Analysis of Internal Random Wave Fields within the Benjamin–Ono Equation." Journal of Marine Science and Engineering 11, no. 10 (September 23, 2023): 1853. http://dx.doi.org/10.3390/jmse11101853.
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This study investigates the numerical evolution of an initially internal random wave field characterized by a Gaussian spectrum shape using the Benjamin–Ono (BO) equation. The research focuses on analyzing various properties associated with the random wave field, including the transition to a steady state of the spectra, statistical moments, and the distribution functions of wave amplitudes. Numerical simulations are conducted across different Ursell parameters, revealing intriguing findings. Notably, it is observed that the spectra of the wave field converge to a stationary state in a statistical sense, while exhibiting statistical characteristics that deviate from a Gaussian distribution. Moreover, as the Ursell parameter increases, the positive skewness of the wave field intensifies, and the kurtosis increases. The investigation also involves the computation of the probability of rogue wave formation, revealing deviations from the Rayleigh distribution. Notably, the study uncovers distinct types of internal rogue waves, specifically referred to as the “two sisters” and “three sisters” phenomena.
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Klaassen, G. P. "Testing Lagrangian Theories of Internal Wave Spectra. Part I: Varying the Amplitude and Wavenumbers." Journal of the Atmospheric Sciences 66, no. 5 (May 1, 2009): 1077–100. http://dx.doi.org/10.1175/2008jas2666.1.
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Abstract A growing body of literature has been built on the premise that kinematic advection produced by linear superpositions of sinusoidal Lagrangian gravity waves confined to lower vertical wavenumbers can provide an explanation for quasi-universal Eulerian spectral tails commonly found in the oceans and the atmosphere. Recently, Hines has established criteria delineating the circumstances in which Eulerian and Lagrangian spectra differ. For conditions in which Hines claims Lagrangian linearity and the production of quasi-universal Eulerian m−3 spectra, a kinematic advection model based on ensembles of seven nonstanding Lagrangian waves reveals the presence of gross violations of continuity and adiabaticity as well as severe departures from hydrostatic balance. Similar infractions are found for other seven-wave ensembles having a broad range of amplitudes and wavenumbers typical of saturated wave fields in the middle atmosphere. Furthermore, m−3 spectra are found only as the Lagrangian wave field approaches a singular state. The singularities in the Lagrangian to Eulerian transformation are induced by stretching deformation fields that form during the superposition of sinusoidal waves with nonparallel wave vectors. Such deformation fields are known to be unstable with respect to three-dimensional vortices. The results strongly suggest that saturated middle atmosphere wave fields are frequently accompanied by small-scale turbulent eddies.
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Chen, Bang-Fuh, and Yi-Jei Huang. "The Close Relationship between Internal Wave and Ocean Free Surface Wave." Journal of Marine Science and Engineering 9, no. 12 (November 25, 2021): 1330. http://dx.doi.org/10.3390/jmse9121330.
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A numerical model was used to simulate the propagation of internal waves (IW) along the surface layer. The results show that strong water exchange during IW propagation results in strong free surface flow and produces small but distinct free surface waves. We found a close relationship between the internal and ocean surface waves. Our intuitive reaction is that by training the relationship between the water surface wave height and the internal wave waveform, the internal wave waveform can be reversed from the water surface wave height value. This paper intends to validate our intuition. The artificial neural network (ANN) method was used to train the Fluent simulated results, and then the trained ANN model was used to predict the inner waves below by the free surface wave signal. In addition, two linear internal wave equations (I and II) were derived, one based on the Archimedes principle and the other based on the long wave and Boussinesq approximation. The prediction by equation (II) was superior to the prediction of equation (I), which is independent of depth. The predicted IW of the proposed ANN method was in good agreement with the simulated results, and the predicted quality was much better than the two linear wave formulas. The proposed simple method can help researchers infer the magnitude of IW from the free surface wave signal. In the future, the spatial distribution of IW below the sea surface might be obtained by the proposed method without costly field investigation.
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Bonneton, P., J. M. Chomaz, and E. J. Hopfinger. "Internal waves produced by the turbulent wake of a sphere moving horizontally in a stratified fluid." Journal of Fluid Mechanics 254 (September 1993): 23–40. http://dx.doi.org/10.1017/s0022112093002010.
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The internal gravity wave field generated by a sphere towed in a stratified fluid was studied in the Froude number range 1.5 ≤ F ≤ 12.7, where F is defined with the radius of the sphere. The Reynolds number was sufficiently large for the wake to be turbulent (Re∈[380, 30000]). A fluorescent dye technique was used to differentiate waves generated by the sphere, called lee waves, from the internal waves, called random waves, emitted by the turbulent wake. We demonstrate that the lee waves are well predicted by linear theory and that the random waves due to the turbulence are related to the coherent structures of the wake. The Strouhal number of these structures depends on F when F [lsim ] 4.5. Locally, these waves behave like transient internal waves emitted by impulsively moving bodies.
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Savva, Miles A. C., and Jacques Vanneste. "Scattering of internal tides by barotropic quasigeostrophic flows." Journal of Fluid Mechanics 856 (October 5, 2018): 504–30. http://dx.doi.org/10.1017/jfm.2018.694.
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Oceanic internal tides and other inertia–gravity waves propagate in an energetic turbulent flow whose length scales are similar to the wavelengths. Advection and refraction by this flow cause the scattering of the waves, redistributing their energy in wavevector space. As a result, initially plane waves radiated from a source such as a topographic ridge become spatially incoherent away from the source. To examine this process, we derive a kinetic equation which describes the statistics of the scattering under the assumptions that the flow is quasigeostrophic, barotropic and well represented by a stationary homogeneous random field. Energy transfers are quantified by computing a scattering cross-section and shown to be restricted to waves with the same frequency and identical vertical structure, hence the same horizontal wavelength. For isotropic flows, scattering leads to an isotropic wave field. We estimate the characteristic time and length scales of this isotropisation, and study their dependence on parameters including the energy spectrum of the flow. Simulations of internal tides generated by a planar wavemaker carried out for the linearised shallow-water model confirm the pertinence of these scales. A comparison with the numerical solution of the kinetic equation demonstrates the validity of the latter and illustrates how the interplay between wave scattering and transport shapes the wave statistics.
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Appleby, J. C., and D. G. Crighton. "Internal gravity waves generated by oscillations of a sphere." Journal of Fluid Mechanics 183 (October 1987): 439–50. http://dx.doi.org/10.1017/s0022112087002714.
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We consider the radiation of internal gravity waves from a spherical body oscillating vertically in a stratified incompressible fluid. A near-field solution (under the Boussinesq approximation) is obtained by separation of variables in an elliptic problem, followed by analytic continuation to the frequencies ω < N of internal wave radiation. Matched expansions are used to relate this solution to a far-field solution in which non-Boussinesq terms are retained. In the outer near field there are parallel conical wavefronts between characteristic cones tangent to the body, but with a wavelength found to be shorter than that for oscillations of a circular cylinder. It is also found that there are caustic pressure singularities above and below the body where the characteristics intersect. Far from the source, non-Boussinesq effects cause a diffraction of energy out of the cones. The far-field wave-fronts are hyperboloidal, with horizontal axes. The case of horizontal oscillations of the sphere is also examined and is shown to give rise to the same basic wave structure.The related problem of a pulsating sphere is then considered, and it is concluded that certain features of the wave pattern, including the caustic singularities near the source, are common to a more general class of oscillating sources.
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Waterman, Stephanie, Alberto C. Naveira Garabato, and Kurt L. Polzin. "Internal Waves and Turbulence in the Antarctic Circumpolar Current." Journal of Physical Oceanography 43, no. 2 (February 1, 2013): 259–82. http://dx.doi.org/10.1175/jpo-d-11-0194.1.
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Abstract This study reports on observations of turbulent dissipation and internal wave-scale flow properties in a standing meander of the Antarctic Circumpolar Current (ACC) north of the Kerguelen Plateau. The authors characterize the intensity and spatial distribution of the observed turbulent dissipation and the derived turbulent mixing, and consider underpinning mechanisms in the context of the internal wave field and the processes governing the waves’ generation and evolution. The turbulent dissipation rate and the derived diapycnal diffusivity are highly variable with systematic depth dependence. The dissipation rate is generally enhanced in the upper 1000–1500 m of the water column, and both the dissipation rate and diapycnal diffusivity are enhanced in some places near the seafloor, commonly in regions of rough topography and in the vicinity of strong bottom flows associated with the ACC jets. Turbulent dissipation is high in regions where internal wave energy is high, consistent with the idea that interior dissipation is related to a breaking internal wave field. Elevated turbulence occurs in association with downward-propagating near-inertial waves within 1–2 km of the surface, as well as with upward-propagating, relatively high-frequency waves within 1–2 km of the seafloor. While an interpretation of these near-bottom waves as lee waves generated by ACC jets flowing over small-scale topographic roughness is supported by the qualitative match between the spatial patterns in predicted lee wave radiation and observed near-bottom dissipation, the observed dissipation is found to be only a small percentage of the energy flux predicted by theory. The mismatch suggests an alternative fate to local dissipation for a significant fraction of the radiated energy.
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Olbers, Dirk, and Carsten Eden. "A Global Model for the Diapycnal Diffusivity Induced by Internal Gravity Waves." Journal of Physical Oceanography 43, no. 8 (August 1, 2013): 1759–79. http://dx.doi.org/10.1175/jpo-d-12-0207.1.
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Abstract An energetically consistent model for the diapycnal diffusivity induced by breaking of internal gravity waves is proposed and tested in local and global settings. The model [Internal Wave Dissipation, Energy and Mixing (IDEMIX)] is based on the spectral radiation balance of the wave field, reduced by integration over the wavenumber space, which yields a set of balances for energy density variables in physical space. A further simplification results in a single partial differential equation for the total energy density of the wave field. The flux of energy to high vertical wavenumbers is parameterized by a functional derived from the wave–wave scattering integral of resonant wave triad interactions, which also forms the basis for estimates of dissipation rates and related diffusivities of ADCP and hydrography fine-structure data. In the current version of IDEMIX, the wave energy is forced by wind-driven near-inertial motions and baroclinic tides, radiating waves from the respective boundary layers at the surface and the bottom into the ocean interior. The model predicts plausible magnitudes and three-dimensional structures of internal wave energy, dissipation rates, and diapycnal diffusivities in rough agreement to observational estimates. IDEMIX is ready for use as a mixing module in ocean circulation models and can be extended with more spectral components.
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Bulatov, V. V., and Yu V. Vladimirov. "Asymptotics of the Far Fields of Internal Gravity Waves Excited by a Source of Radial Symmetry." Fluid Dynamics 56, no. 5 (September 2021): 672–77. http://dx.doi.org/10.1134/s0015462821050013.
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Abstract— The problem of the far field of internal gravity waves generated by a perturbation source of radial symmetry aroused at an initial instant of time is solved. The constant model distribution of the buoyancy frequency is considered and, using the Fourier–Hankel transform, an analytical solution to the problem is obtained in the form of the sum of wave modes. Asymptotics of the solutions that describe the spatial-temporal characteristics of elevation of the isopycnic lines and the vertical and horizontal velocity components far from the perturbation source are obtained. The asymptotics of the components of the wave field are expressed in terms of the square of the Airy function and its derivatives in the neighborhood of the wave fronts of an individual wave mode. The exact and asymptotic results are compared and it is shown that the asymptotic method makes it possible to calculate effectively the far wave fields at times of the order of ten and more of the Brunt–Väisälä periods.
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Bourgault, Daniel, David C. Janes, and Peter S. Galbraith. "Observations of a Large-Amplitude Internal Wave Train and Its Reflection off a Steep Slope." Journal of Physical Oceanography 41, no. 3 (March 1, 2011): 586–600. http://dx.doi.org/10.1175/2010jpo4464.1.
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Abstract Remote and in situ field observations documenting the reflection of a normally incident, short, and large-amplitude internal wave train off a steep slope are presented and interpreted with the help of the Dubreil–Jacotin–Long theory. Of the seven remotely observed waves that composed the incoming wave train, five were observed to reflect. It is estimated that the incoming wave train carried Ei = (24 ± 4) × 104 J m−1 to the boundary. The reflection coefficient, defined as the ratio of reflected to incoming wave train energies, is estimated to be R = 0.5 ± 0.2. This is about 0.4 lower than parameterizations in the literature, which are based on reflections of single solitary waves, would suggest. It is also shown that the characteristics of the wave-boundary situation observed in the field are outside the parameter space examined in previous laboratory and numerical experiments on internal solitary wave reflectance. This casts doubts on extrapolating current laboratory-based knowledge to fjord-like systems and calls for more research on internal solitary wave reflectance.
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AGHSAEE, PAYAM, LEON BOEGMAN, and KEVIN G. LAMB. "Breaking of shoaling internal solitary waves." Journal of Fluid Mechanics 659 (July 15, 2010): 289–317. http://dx.doi.org/10.1017/s002211201000248x.
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The breaking of fully nonlinear internal solitary waves of depression shoaling upon a uniformly sloping boundary in a smoothed two-layer density field was investigated using high-resolution two-dimensional simulations. Our simulations were limited to narrow-crested waves, which are more common than broad-crested waves in geophysical flows. The simulations were performed for a wide range of boundary slopes S ∈ [0.01, 0.3] and wave slopes extending the parameter range to weaker slopes than considered in previous laboratory and numerical studies. Over steep slopes (S ≥ 0.1), three distinct breaking processes were observed: surging, plunging and collapsing breakers which are associated with reflection, convective instability and boundary-layer separation, respectively. Over mild slopes (S ≤ 0.05), nonlinearity varies gradually and the wave fissions into a train of waves of elevation as it passes through the turning point where solitary waves reverse polarity. The dynamics of each breaker type were investigated and the predominance of a particular mechanism was associated with a relative developmental time scale. The breaking location was modelled as a function of wave amplitude (a), characteristic wave length and the isopycnal length along the slope. The breaker type was characterized in wave slope (Sw = a/Lw, where Lw is a measure of half of the wavelength) versus S space, and the reflection coefficient (R), modelled as a function of the internal Iribarren number, was in agreement with other studies. The effects of grid resolution and wave Reynolds number (Rew) on R, boundary-layer separation and the evolution of global instability were studied. High Reynolds numbers (Rew ~ 104) were found to trigger a global instability, which modifies the breaking process relative to the lower Rew case, but not necessarily the breaking location, and results in a ~ 10 % increase in R, relative to the Rew ~ 103 case.
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JAVAM, A., J. IMBERGER, and S. W. ARMFIELD. "Numerical study of internal wave reflection from sloping boundaries." Journal of Fluid Mechanics 396 (October 10, 1999): 183–201. http://dx.doi.org/10.1017/s0022112099005996.
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The breaking of internal waves propagating in a stratified fluid of constant buoyancy frequency on a sloping boundary was investigated numerically. It was found that at the boundary, nonlinear non-resonant interactions between the incident and reflected waves produced higher-mode waves. These modes had frequencies greater than the local buoyancy frequency and so could not radiate from the interaction region. The energy level of trapped waves increased with time and subsequently led to overturning of the density field. At the critical frequency, when the reflected wave propagated in a direction parallel to the slope, wave overturning occurred near the wall, but the point of overturning moved off the bottom as the propagation angle changed away from that of the bottom slope as the waves became increasingly supercritical. The internal wave reflection coefficient generally increased as the effects of nonlinearity and viscosity decreased, but depended strongly on the forcing frequency and the angle of the sloping boundary.
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Davis, Géraldine, Thierry Dauxois, Timothée Jamin, and Sylvain Joubaud. "Energy budget in internal wave attractor experiments." Journal of Fluid Mechanics 880 (October 15, 2019): 743–63. http://dx.doi.org/10.1017/jfm.2019.741.
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The current paper presents an experimental study of the energy budget of a two-dimensional internal wave attractor in a trapezoidal domain filled with uniformly stratified fluid. The injected energy flux and the dissipation rate are simultaneously measured from a two-dimensional, two-component, experimental velocity field. The pressure perturbation field needed to quantify the injected energy is determined from the linear inviscid theory. The dissipation rate in the bulk of the domain is directly computed from the measurements, while the energy sink occurring in the boundary layers is estimated using the theoretical expression for the velocity field in the boundary layers, derived recently by Beckebanze et al. (J. Fluid Mech., vol. 841, 2018, pp. 614–635). In the linear regime, we show that the energy budget is closed, in the steady state and also in the transient regime, by taking into account the bulk dissipation and, more importantly, the dissipation in the boundary layers, without any adjustable parameters. The dependence of the different sources on the thickness of the experimental set-up is also discussed. In the nonlinear regime, the analysis is extended by estimating the dissipation due to the secondary waves generated by triadic resonant instabilities, showing the importance of the energy transfer from large scales to small scales. The method tested here on internal wave attractors can be generalized straightforwardly to any quasi-two-dimensional stratified flow.
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Ma, H., and M. P. Tulin. "Experimental Study of Ship Internal Waves—The Supersonic Case." Journal of Offshore Mechanics and Arctic Engineering 115, no. 1 (February 1, 1993): 16–22. http://dx.doi.org/10.1115/1.2920081.
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Internal waves produced by a ship traveling faster than the fastest internal waves (supersonic case) were investigated experimentally in our laboratory in a wide tank using averaging conductivity wave gages developed for this investigation. The wave gage is similar to the conductivity probe, but has space-averaging electrodes. An array of seven such gages was used in a wave tank with dimensions 12 ft length, 8 ft width, 2 ft depth. The water in the tank was stratified with salt to obtain desired density distributions. A spheroid, split vertically, was towed against and along a sidewall to simulate a moving ship. Simultaneous wave profiles at various distances normal to the track of the ship were obtained for different Froude numbers and density distributions. The internal wave patterns were calculated from the measured data and compared with theoretical results. The amplitude on the first crest of the internal wave field is also plotted against the distance from the ship, and a limited comparison with theory is made. The experimental method developed for this study is sensitive, simple and reliable. It may serve to obtain a data base for ship-generated internal waves under a variety of conditions.
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AKYLAS, T. R., R. H. J. GRIMSHAW, S. R. CLARKE, and ALI TABAEI. "Reflecting tidal wave beams and local generation of solitary waves in the ocean thermocline." Journal of Fluid Mechanics 593 (November 23, 2007): 297–313. http://dx.doi.org/10.1017/s0022112007008786.
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It is generally accepted that ocean internal solitary waves can arise from the interaction of the barotropic tide with the continental shelf, which generates an internal tide that in turn steepens and forms solitary waves as it propagates shorewards. Some field observations, however, reveal large-amplitude internal solitary waves in deep water, hundreds of kilometres away from the continental shelf, suggesting an alternative generation mechanism: tidal flow over steep topography forces a propagating beam of internal tidal wave energy which impacts the thermocline at a considerable distance from the forcing site and gives rise to internal solitary waves there. Motivated by this possibility, a simple nonlinear long-wave model is proposed for the interaction of a tidal wave beam with the thermocline and the ensuing local generation of solitary waves. The thermocline is modelled as a density jump across the interface of a shallow homogeneous fluid layer on top of a deep uniformly stratified fluid, and a finite-amplitude propagating internal wave beam of tidal frequency in the lower fluid is assumed to be incident and reflected at the interface. The induced weakly nonlinear long-wave disturbance on the interface is governed in the far field by an integral-differential equation which accounts for nonlinear and dispersive effects as well as energy loss owing to radiation into the lower fluid. Depending on the strength of the thermocline and the intensity of the incident beam, nonlinear wave steepening can overcome radiation damping so a series of solitary waves may arise in the thermocline. Sample numerical solutions of the governing evolution equation suggest that this mechanism is quite robust for typical oceanic conditions.
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Shalimov, S. L., V. I. Zakharov, M. S. Solov’eva, P. K. Sigachev, M. Yu Nekrasova, and G. M. Korkina. "Wave Perturbations of the Lower and Upper Ionosphere during the 2019 Faxai Tropical Typhoon." Геомагнетизм и аэрономия 63, no. 2 (March 1, 2023): 216–26. http://dx.doi.org/10.31857/s0016794022600442.
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In this paper, we studied the response of the lower and upper ionosphere to the passage of TyphoonFaxai 2019 using the regional network of ultralong-wave radio translucence stations in the Far East region ofRussia and measurements of electron density perturbations using the SWARM mission satellites. The presentedexperimental data clearly demonstrate wave perturbations of the amplitude and phase of the ULW signal,as well as the electron density during the active stage of the typhoon. The parameters of wave perturbationscorrespond to atmospheric internal gravity waves. The maximum spectral density of wave perturbations in thelower ionosphere corresponds to 16–20 min. A mechanism for the impact of internal waves on the ionosphere,which is due to polarization fields arising from the wave motion of plasma in the lower part of the F-region, isproposed. These fields projected along the geomagnetic field lines make it possible to interpret the observedvariations in the phase of the ULW signal and variations in the electron density in the upper ionosphere
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Bondur, V. G., Yu V. Grebenyuk, E. V. Ezhova, V. I. Kazakov, D. A. Sergeev, I. A. Soustova, and Yu I. Troitskaya. "Surface manifestations of internal waves investigated by a subsurface buoyant jet: Part 2. Internal wave field." Izvestiya, Atmospheric and Oceanic Physics 46, no. 3 (June 2010): 347–59. http://dx.doi.org/10.1134/s0001433810030084.
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Serebryany, Andrey, Elizaveta Khimchenko, Viktor Zamshin, and Oleg Popov. "Features of the Field of Internal Waves on the Abkhazian Shelf of the Black Sea according to Remote Sensing Data and In Situ Measurements." Journal of Marine Science and Engineering 10, no. 10 (September 21, 2022): 1342. http://dx.doi.org/10.3390/jmse10101342.
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The field of internal waves in the Black Sea is quite significant. The Black Sea shelf is of particular interest, but it has not been studied enough in some specific regions. For example, a narrow and steep shelf of Abkhazia has been poorly explored. Particularly unexplored are the actual parameters and causes of the generation of internal waves in this area. In this article, we have attempted to fill this gap by analyzing remote sensing data and in situ data. An analysis of a set of optical multispectral satellite images (Sentinel-2, Landsat-8) and a collection of sea-truth data of the shelf zone of Abkhazia was carried out to identify features of internal wave fields of this region. In situ data were acquired over 9 years using ADCP, CTD, and SVP probes and moored stations with point and line temperature sensors. It is shown that internal waves are widespread on the Abkhazian shelf. They appear as trains of short-period waves (as a rule, soliton-like). The quantitative parameters and features of internal waves are shown and analyzed. The form of manifestation and direction of internal wave trains’ travel depend on the mechanisms of their origin, among which are the transformations of inertial internal waves, generation by river plumes, and submesoscale structures. In general, the article is the most complete and relevant study of the field of internal waves on the shelf of Abkhazia.
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Pollmann, Friederike, Jonas Nycander, Carsten Eden, and Dirk Olbers. "Resolving the horizontal direction of internal tide generation." Journal of Fluid Mechanics 864 (February 7, 2019): 381–407. http://dx.doi.org/10.1017/jfm.2019.9.
Full textAbstract:
The mixing induced by breaking internal gravity waves is an important contributor to the ocean’s energy budget, shaping, inter alia, nutrient supply, water mass transformation and the large-scale overturning circulation. Much of the energy input into the internal wave field is supplied by the conversion of barotropic tides at rough bottom topography, which hence needs to be described realistically in internal gravity wave models and mixing parametrisations based thereon. A new semi-analytical method to describe this internal wave forcing, calculating not only the total conversion but also the direction of this energy flux, is presented. It is based on linear theory for variable stratification and finite depth, that is, it computes the energy flux into the different vertical modes for two-dimensional, subcritical, small-amplitude topography and small tidal excursion. A practical advantage over earlier semi-analytical approaches is that the new one gives a positive definite conversion field. Sensitivity studies using both idealised and realistic topography allow the identification of suitable numerical parameter settings and corroborate the accuracy of the method. This motivates the application to the global ocean in order to better account for the geographical distribution of diapycnal mixing induced by low-mode internal gravity waves, which can propagate over large distances before breaking. The first results highlight the significant differences of energy flux magnitudes with direction, confirming the relevance of this more detailed approach for energetically consistent mixing parametrisations in ocean models. The method used here should be applicable to any physical system that is described by the standard wave equation with a very wide field of sources.
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Lvov, Yuri V., Kurt L. Polzin, Esteban G. Tabak, and Naoto Yokoyama. "Oceanic Internal-Wave Field: Theory of Scale-Invariant Spectra." Journal of Physical Oceanography 40, no. 12 (December 1, 2010): 2605–23. http://dx.doi.org/10.1175/2010jpo4132.1.
Full textAbstract:
Abstract Steady scale-invariant solutions of a kinetic equation describing the statistics of oceanic internal gravity waves based on wave turbulence theory are investigated. It is shown in the nonrotating scale-invariant limit that the collision integral in the kinetic equation diverges for almost all spectral power-law exponents. These divergences come from resonant interactions with the smallest horizontal wavenumbers and/or the largest horizontal wavenumbers with extreme scale separations. A small domain is identified in which the scale-invariant collision integral converges and numerically find a convergent power-law solution. This numerical solution is close to the Garrett–Munk spectrum. Power-law exponents that potentially permit a balance between the infrared and ultraviolet divergences are investigated. The balanced exponents are generalizations of an exact solution of the scale-invariant kinetic equation, the Pelinovsky–Raevsky spectrum. A small but finite Coriolis parameter representing the effects of rotation is introduced into the kinetic equation to determine solutions over the divergent part of the domain using rigorous asymptotic arguments. This gives rise to the induced diffusion regime. The derivation of the kinetic equation is based on an assumption of weak nonlinearity. Dominance of the nonlocal interactions puts the self-consistency of the kinetic equation at risk. However, these weakly nonlinear stationary states are consistent with much of the observational evidence.