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1
Pizzo, Nick E. "Surfing surface gravity waves." Journal of Fluid Mechanics 823 (June 16, 2017): 316–28. http://dx.doi.org/10.1017/jfm.2017.314.
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A simple criterion for water particles to surf an underlying surface gravity wave is presented. It is found that particles travelling near the phase speed of the wave, in a geometrically confined region on the forward face of the crest, increase in speed. The criterion is derived using the equation of John (Commun. Pure Appl. Maths, vol. 6, 1953, pp. 497–503) for the motion of a zero-stress free surface under the action of gravity. As an example, a breaking water wave is theoretically and numerically examined. Implications for upper-ocean processes, for both shallow- and deep-water waves, are discussed.
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Robinson, T. O., I. Eames, and R. Simons. "Dense gravity currents moving beneath progressive free-surface water waves." Journal of Fluid Mechanics 725 (May 23, 2013): 588–610. http://dx.doi.org/10.1017/jfm.2013.112.
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AbstractThe characteristics of dense gravity currents in coastal regions, where free-surface gravity waves are dominant, have yet to be studied in the laboratory. This paper provides a first insight into the dynamics of dense saline gravity currents moving beneath regular progressive free-surface water waves. The gravity currents were generated by releasing a finite volume of saline into a large wave tank with an established periodic wave field. After the initial collapse, the gravity currents propagated horizontally with two fronts, one propagating in the wave direction and the other against the wave direction. The fronts of the gravity currents oscillated with an amplitude and phase that correlated with the orbital velocities within a region close to the bed. To leading order, the overall length of the gravity current was found to be weakly affected by the wave action and the dynamics of the current could be approximated by simply considering the buoyancy of the released fluid. Other characteristics such as the position of the gravity current centre and the shape of the two leading profiles were found to be significantly affected by the wave action. The centre was displaced at constant speed dependent on the second-order wave-induced mean Lagrangian velocity. For long waves, the centre was advected downstream in the direction of wave propagation owing to the dominance of Stokes drift. For short waves, the gravity current centre moved upstream against the wave direction, as under these wave conditions Stokes drift is negligible at the bed. An asymmetry in the shape of the upstream and downstream current heads was observed, with the gravity current front moving against the waves being much thicker and the front steeper, similar to the case of a current moving in a stream.
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Doering, J. C., and A. J. Bowen. "SHOALING SURFACE GRAVITY WAVES: A BISPECTRAL ANALYSIS." Coastal Engineering Proceedings 1, no. 20 (January 29, 1986): 12. http://dx.doi.org/10.9753/icce.v20.12.
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Nonlinearities (wave-wave interactions) play a vital role in many aspects of nearshore dynamics, such as wave shoaling and breaking, wave forces, wave-current interactions, radiation stress effects, and sediment transport. The importance of nonlinearities in the nearshore region cannot be overemphasized. At present, however, there is no wave theory that adequately accounts for these interactions, and field observations are sparse. Herein, the bispectrum is used to investigate the temporal and spatial variation of wave-wave interactions in cross-shore velocity for shoaling surface gravity waves in several nearshore environments. The implications for sediment movement of the sign of the observed wavewave interactions for both the real part of the velocity bispectrum (which is related to the skewness of the horizontal asymmetry) and the imaginary part of the velocity bispectrum (which is related to the skewness of the temporal derivative) are discussed. A parameterization is given for the amplitude and phase evolution of the self-self sum interactions within the wind-wave peak for both planar and barred nearshore topography. The results of this paper underline the potential importance of infragravity wave energy in determining nearshore morphology.
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Mui, R. C. Y., and D. G. Dommermuth. "The Vortical Structure of Parasitic Capillary Waves." Journal of Fluids Engineering 117, no. 3 (September 1, 1995): 355–61. http://dx.doi.org/10.1115/1.2817269.
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A two-dimensional numerical simulation of the parasitic capillary waves that form on a 5 cm gravity-capillary wave is performed. A robust numerical algorithm is developed to simulate flows with complex boundary conditions and topologies. The free-surface boundary layer is resolved at the full-scale Reynolds, Froude, and Weber numbers. Seventeen million grid points are used to resolve the flow to within 6 × 10–4 cm. The numerical method is used to investigate the formation of parasitic capillary waves on the front face of a gravity-capillary wave. The parasitic capillary waves shed vorticity that induces surface currents that exceed twenty-five percent of the phase velocity of the gravity-capillary wave when the steepness of the parasitic capillary waves is approximately 0.8 and the total wave steepness is 1.1. A mean surface current develops in the direction of the wave’s propagation and is concentrated on the front face of the gravity-capillary wave. This current enhances mixing, and remnants of this surface current are probably present in post-breaking waves. Regions of high vorticity occur on the back sides of the troughs of the parasitic capillary waves. The vorticity separates from the free surface in regions where the wave-induced velocities exceed the vorticity-induced velocities. The rate of energy dissipation of the gravity-capillary wave with parasitic capillaries riding on top is twenty-two times greater than that of the gravity-capillary wave alone.
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Longuet-Higgins, M. S. "Eulerian and Lagrangian aspects of surface waves." Journal of Fluid Mechanics 173 (December 1986): 683–707. http://dx.doi.org/10.1017/s0022112086001325.
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Surface waves can be recorded in two kinds of ways, either with a fixed (Eulerian) probe or with a free-floating (Lagrangian) buoy. In steep waves, the differences between corresponding properties can be very marked.By a simple physical model and by accurate calculation it is shown that the Lagrangian wave period may differ from the Eulerian wave period by as much as 38 %. The Lagrangian mean level is also higher than the Eulerian mean, leading to possible discrepancies in remote sensing of the ocean from satellites.Surface accelerations are of interest in relation to the incidence of breaking waves, and for interactions between short (gravity or capillary) waves and longer gravity waves. Eulerian accelerations tend to be very non-sinusoidal, with large downwards peaks, sometimes exceeding - g in magnitude, near to sharp wave crests. Lagrangian accelerations are much smoother; for uniform gravity waves they lie between −0.388g and +0.315g. These values are verified by laboratory experiments. In wind-generated waves the limits are probably wider.In progressive gravity waves in deep water the horizontal accelerations generally exceed the vertical accelerations. In steep waves, the subsurface accelerations can slightly exceed those at the free surface.A novel application is made to the rolling motion of ships. In very steep, irrotational waves it is shown theoretically that the flow near the wave crest can lead to the rotation of the hull through angles up to 120° by a single wave, even if the wave is not breaking. This is confirmed by simple experiments. The efficiency of the keel appears to promote capsizing.
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Balk, Alexander M. "Surface gravity wave turbulence: three wave interaction?" Physics Letters A 314, no. 1-2 (July 2003): 68–71. http://dx.doi.org/10.1016/s0375-9601(03)00795-3.
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Kenyon, Kern E. "On Surface Gravity Wave Energies." Natural Science 12, no. 10 (2020): 667–69. http://dx.doi.org/10.4236/ns.2020.1210057.
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Coleman, Timothy A., and Kevin R. Knupp. "Factors Affecting Surface Wind Speeds in Gravity Waves and Wake Lows." Weather and Forecasting 24, no. 6 (December 1, 2009): 1664–79. http://dx.doi.org/10.1175/2009waf2222248.1.
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Abstract Ducted gravity waves and wake lows have been associated with numerous documented cases of “severe” winds (>25 m s−1) and wind damage. These winds are associated with the pressure perturbations and transient mesoscale pressure gradients occurring in many gravity waves and wake lows. However, not all wake lows and gravity waves produce significant winds nor wind damage. In this paper, the factors that affect the surface winds produced by ducted gravity waves and wake lows are reviewed and examined. It is shown theoretically that the factors most conducive to high surface winds include a large-amplitude pressure disturbance, a slow intrinsic speed of propagation, and an ambient wind with the same sign as the pressure perturbation (i.e., a headwind for a pressure trough). Multiple case studies are presented, contrasting gravity waves and wake lows with varying amplitudes, intrinsic speeds, and background winds. In some cases high winds occurred, while in others they did not. In each case, the factor(s) responsible for significant winds, or the lack thereof, are discussed. It is hoped that operational forecasters will be able to, in some cases, compute these factors in real time, to ascertain in more detail the threat of damaging wind from an approaching ducted gravity wave or wake low.
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Krasitsky, V. P. "Five-wave kinetic equation for surface gravity waves." Physical Oceanography 5, no. 6 (November 1994): 413–21. http://dx.doi.org/10.1007/bf02198507.
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Raghukumar, Kaustubha, Lindsay Hogan, Christopher Zappa, Frank Spada, and Grace Chang. "Optical detection of ensonified capillary-gravity waves using polarimetric imaging." Journal of the Acoustical Society of America 153, no. 3_supplement (March 1, 2023): A64. http://dx.doi.org/10.1121/10.0018177.
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The optical detection of surface capillary-gravity waves induced by underwater sound has many potential applications that range from the detection of sound-generating underwater objects to airborne bathymetric surveys. While multiple lab-based efforts have measured acoustically generated surface capillary-gravity waves, we report on a recent field-based measurement using polarimetric imaging. A controlled acoustic source was placed 10 m below a lake surface and emitted sound in the 500 Hz to 10000Hz frequency range. The lake surface was imaged using a polarimetric camera mounted 7 m above the lake surface. Measurable short-lived surface capillary-gravity waves (∼3 mm wavelength) were observed in the polarimetric camera images during ensonification of the lake surface. Changes were observed in both the omnidirectional and directional wave spectra. In the omni-directional wavenumber spectrum, enhanced capillary wave activity at high wavenumbers was observed for acoustic source frequencies in the 2–5 kHz range. Additionally, ensonification was observed to result in the amplitude and wavenumber modulation (enhancement/diminution) of existing wind-generated surface gravity-capillary waves. In the directional spectra, while ambient gravity-capillary waves showed a spreading function with stronger downwind versus upwind propagation, the acoustically generated gravity-capillary waves showed minimal impact on the directionality of the wave spectra.
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Lentz, S. J., J. H. Churchill, and K. A. Davis. "Coral Reef Drag Coefficients—Surface Gravity Wave Enhancement." Journal of Physical Oceanography 48, no. 7 (July 2018): 1555–66. http://dx.doi.org/10.1175/jpo-d-17-0231.1.
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AbstractA primary challenge in modeling flow over shallow coral reefs is accurately characterizing the bottom drag. Previous studies over continental shelves and sandy beaches suggest surface gravity waves should enhance the drag on the circulation over coral reefs. The influence of surface gravity waves on drag over four platform reefs in the Red Sea is examined using observations from 6-month deployments of current and pressure sensors burst sampling at 1 Hz for 4–5 min. Depth-average current fluctuations U′ within each burst are dominated by wave orbital velocities uw that account for 80%–90% of the burst variance and have a magnitude of order 10 cm s−1, similar to the lower-frequency depth-average current Uavg. Previous studies have shown that the cross-reef bottom stress balances the pressure gradient over these reefs. A bottom stress estimate that neglects the waves (ρCdaUavg|Uavg|, where ρ is water density and Cda is a drag coefficient) balances the observed pressure gradient when uw is smaller than Uavg but underestimates the pressure gradient when uw is larger than Uavg (by a factor of 3–5 when uw = 2Uavg), indicating the neglected waves enhance the bottom stress. In contrast, a bottom stress estimate that includes the waves [ρCda(Uavg + U′)|Uavg + U′|)] balances the observed pressure gradient independent of the relative size of uw and Uavg, indicating that this estimate accounts for the wave enhancement of the bottom stress. A parameterization proposed by Wright and Thompson provides a reasonable estimate of the total bottom stress (including the waves) given the burst-averaged current and the wave orbital velocity.
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Mukherjee, Animesh, P. R. Sengupta, and Lokenath Debnath. "Surface waves in higher order visco-elastic media under the influence of gravity." Journal of Applied Mathematics and Stochastic Analysis 4, no. 1 (January 1, 1991): 71–82. http://dx.doi.org/10.1155/s1048953391000047.
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Based upon Biot's [1965] theory of initial stresses of hydrostatic nature produced by the effect of gravity, a study is made of surface waves in higher order visco-elastic media under the influence of gravity. The equation for the wave velocity of Stonely waves in the presence of viscous and gravitational effects is obtained. This is followed by particular cases of surface waves including Rayleigh waves and Love waves in the presence of viscous and gravity effects. In all cases the wave-velocity equations are found to be in perfect agreement with the corresponding classical results when the effects of gravity and viscosity are neglected.
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Kadri, Usama. "Time-Reversal Analogy by Nonlinear Acoustic–Gravity Wave Triad Resonance." Fluids 4, no. 2 (May 17, 2019): 91. http://dx.doi.org/10.3390/fluids4020091.
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Time reversal of free-surface water (gravity) waves due to a sudden change in the effective gravity has been extensively studied in recent years. Here, we show that an analogy to time-reversal can be obtained using nonlinear acoustic-gravity wave theory. More specifically, we present a mathematical model for the evolution of a time-reversed gravity wave packet from a nonlinear resonant triad perspective. We show that the sudden appearance of an acoustic mode in analogy to a sudden vertical oscillation of the liquid film, can resonate effectively with the original gravity wave packet causing energy pumping into an oppositely propagating (time-reversed) surface gravity wave of an almost identical shape.
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Melville, W. Kendall, and Alexey V. Fedorov. "The equilibrium dynamics and statistics of gravity–capillary waves." Journal of Fluid Mechanics 767 (February 18, 2015): 449–66. http://dx.doi.org/10.1017/jfm.2014.740.
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AbstractRecent field observations and modelling of breaking surface gravity waves suggest that air-entraining breaking is not sufficiently dissipative of surface gravity waves to balance the dynamics of wind-wave growth and nonlinear interactions with dissipation for the shorter gravity waves of $O(10)$ cm wavelength. Theories of parasitic capillary waves that form at the crest and forward face of shorter steep gravity waves have shown that the dissipative effects of these waves may be one to two orders of magnitude greater than the viscous dissipation of the underlying gravity waves. Thus the parasitic capillaries may provide the required dissipation of the short wind-generated gravity waves. This has been the subject of speculation and conjecture in the literature. Using the nonlinear theory of Fedorov & Melville (J. Fluid Mech., vol. 354, 1998, pp. 1–42), we show that the dissipation due to the parasitic capillaries is sufficient to balance the wind input to the short gravity waves over some range of wave ages and wave slopes. The range of gravity wave lengths on which these parasitic capillary waves are dynamically significant approximately corresponds to the range of short gravity waves that Cox & Munk (J. Mar. Res., vol. 13, 1954, pp. 198–227) found contributed significantly to the mean square slope of the ocean surface, which they measured to be proportional to the wind speed. Here we show that the mean square slope predicted by the theory is proportional to the square of the friction velocity of the wind, ${u_{\ast }}^{2}$, for small wave slopes, and approximately $u_{\ast }$ for larger slopes.
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Krasitskii, Vladimir P. "On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves." Journal of Fluid Mechanics 272 (August 10, 1994): 1–20. http://dx.doi.org/10.1017/s0022112094004350.
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Many studies of weakly nonlinear surface waves are based on so-called reduced integrodifferential equations. One of these is the widely used Zakharov four-wave equation for purely gravity waves. But the reduced equations now in use are not Hamiltonian despite the Hamiltonian structure of exact water wave equations. This is entirely due to shortcomings of their derivation. The classical method of canonical transformations, generalized to the continuous case, leads automatically to reduced equations with Hamiltonian structure. In this paper, attention is primarily paid to the Hamiltonian reduced equation describing the combined effects of four- and five-wave weakly nonlinear interactions of purely gravity waves. In this equation, for brevity called five-wave, the non-resonant quadratic, cubic and fourth-order nonlinear terms are eliminated by suitable canonical transformation. The kernels of this equation and the coefficients of the transformation are expressed in explicit form in terms of expansion coefficients of the gravity-wave Hamiltonian in integral-power series in normal variables. For capillary–gravity waves on a fluid of finite depth, expansion of the Hamiltonian in integral-power series in a normal variable with accuracy up to the fifth-order terms is also given.
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Naeser, Harald. "The Capillary Waves’ Contribution to Wind-Wave Generation." Fluids 7, no. 2 (February 10, 2022): 73. http://dx.doi.org/10.3390/fluids7020073.
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Published theories and observations have shown that dissipation of gravity waves implies frequency downshifting of wave energy. Hence, for wind-waves, the wind energy input to the highest frequencies is of special interest. Here it is shown that this input is vital, because the direct wind energy input obtained by the air-pressure’s work on most gravity waves is slightly less than what the waves need to grow. Further, the wind’s input of the angular momentum that waves need to grow is found to be absent at most gravity wave frequencies. The capillary waves that appear at the surface of the sea when the wind is blowing solve these problems. To demonstrate this, an extension of linear wave theory is established to study possibilities and limitations for transfer of energy and angular momentum from the wind to waves through these frequencies. The theory describes regular, gravity–capillary waves with constant amplitude under laminar conditions. It includes surface tensions, viscosity, gravity and a wind-generated shear current, and shows that these waves—contrary to most gravity waves—receive more energy from the wind than they dissipate and angular momentum they cannot keep. Hence, the problem of the missing input of energy and angular momentum from wind to gravity waves is solved by transfers through the capillary waves. This implies that capillary waves are vital to obtain growing gravity waves.
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MONISMITH, S. G., E. A. COWEN, H. M. NEPF, J. MAGNAUDET, and L. THAIS. "Laboratory observations of mean flows under surface gravity waves." Journal of Fluid Mechanics 573 (February 2007): 131–47. http://dx.doi.org/10.1017/s0022112006003594.
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In this paper we present mean velocity distributions measured in several different wave flumes. The flows shown involve different types of mechanical wavemakers, channels of differing sizes, and two different end conditions. In all cases, when surface waves, nominally deep-water Stokes waves, are generated, counterflowing Eulerian flows appear that act to cancel locally, i.e. not in an integral sense, the mass transport associated with the Stokes drift. No existing theory of wave–current interactions explains this behaviour, although it is symptomatic of Gerstner waves, rotational waves that are exact solutions to the Euler equations. In shallow water (kH ≈ 1), this cancellation of the Stokes drift does not hold, suggesting that interactions between wave motions and the bottom boundary layer may also come into play.
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Su, Tao, and Guoqing Zhai. "The Role of Convectively Generated Gravity Waves on Convective Initiation: A Case Study." Monthly Weather Review 145, no. 1 (January 1, 2017): 335–59. http://dx.doi.org/10.1175/mwr-d-16-0196.1.
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Abstract A case study of a convection initiation (CI) event involving a mesoscale gravity wave is presented. This severe convection event occurred in east China on 5 June 2009. High-frequency automatic weather station (AWS) data, visible satellite data, and Doppler radar data were combined to depict the features of the gravity wave and the development of several convection centers. The gravity wave was manifested by a surface pressure dip and surface wind shift propagating westward away from the early convection. The pressure dip propagated at a speed of >30 m s−1, which is comparable with that in previous observational studies of convectively generated gravity waves. A special focus is on the initiation of a deep convection cell in Anhui Province, which resulted in 25 deaths. Surface observations showed two precursors before CI, including a convergence line and wind shift at the eastern end of the convergence line. High-resolution numerical simulations with the Weather Research and Forecasting (WRF) Model were used to examine the structure of the gravity waves and forecast CI processes. The model reproduced the observed features of the gravity wave and the precursors before CI. Three-dimensional model results showed that CI occurred at the intersection between a convergence line and the gravity wave. The relationships between the wind shift and the pressure drop are consistent with polarization relation in ducted gravity waves. As the updraft of the gravity wave intersected with the convergence line, the low-level updraft strengthened and led to CI. The gravity wave, which had stronger updraft than downdraft, suggested a positive contribution to CI.
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DECONINCK, BERNARD, and KATIE OLIVERAS. "The instability of periodic surface gravity waves." Journal of Fluid Mechanics 675 (March 17, 2011): 141–67. http://dx.doi.org/10.1017/s0022112011000073.
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Euler's equations describe the dynamics of gravity waves on the surface of an ideal fluid with arbitrary depth. In this paper, we discuss the stability of periodic travelling wave solutions to the full set of nonlinear equations via a non-local formulation of the water wave problem, modified from that of Ablowitz, Fokas & Musslimani (J. Fluid Mech., vol. 562, 2006, p. 313), restricted to a one-dimensional surface. Transforming the non-local formulation to a travelling coordinate frame, we obtain a new formulation for the stationary solutions in the travelling reference frame as a single equation for the surface in physical coordinates. We demonstrate that this equation can be used to numerically determine non-trivial travelling wave solutions by exploiting the bifurcation structure of this new equation. Specifically, we use the continuous dependence of the amplitude of the solutions on their propagation speed. Finally, we numerically examine the spectral stability of the periodic travelling wave solutions by extending Fourier–Floquet analysis to apply to the associated linear non-local problem. In addition to presenting the full spectrum of this linear stability problem, we recover past well-known results such as the Benjamin–Feir instability for waves in deep water. In shallow water, we find different instabilities. These shallow water instabilities are critically related to the wavelength of the perturbation and are difficult to find numerically. To address this problem, we propose a strategy to estimate a priori the location in the complex plane of the eigenvalues associated with the instability.
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Marechal, Gwendal, and Charly de Marez. "Variability of surface gravity wave field over a realistic cyclonic eddy." Ocean Science 18, no. 5 (September 7, 2022): 1275–92. http://dx.doi.org/10.5194/os-18-1275-2022.
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Abstract. Recent remote sensing measurements and numerical studies have shown that surface gravity waves interact strongly with small-scale open ocean currents. Through these interactions, the significant wave height, the wave frequency, and the wave direction are modified. In the present paper, we investigate the interactions of surface gravity waves with a large and isolated realistic cyclonic eddy. This eddy is subject to instabilities, leading to the generation of specific features at both the mesoscale and submesoscale ranges. We use the WAVEWATCH III numerical framework to force surface gravity waves in the eddy before and after its destabilization. In the wave simulations the source terms are deactivated, and waves are initialized with different wave intrinsic frequencies. The study of these simulations illustrates how waves respond to the numerous kinds of instabilities in the large cyclonic eddy from a few hundred to a few tens of kilometres. Our findings show that the spatial variability of the wave direction, the mean period, and the significant wave height is very sensitive to the presence of submesoscale structures resulting from the eddy destabilization. The intrinsic frequency of the incident waves is key in the change of the wave direction resulting from the current-induced refraction and in the location, from the boundary where waves are generated, of the maximum values of significant wave height. However, for a given current forcing, the maximum values of the significant wave height are similar regardless of the frequency of the incident waves. In this idealized study it has been shown that the spatial gradients of wave parameters are sharper for simulations forced with the destabilized eddy. Because the signature of currents on waves encodes important information of currents, our findings suggest that the vertical vorticity of the current could be statistically estimated from the significant wave height gradients down to a very fine spatial scale. Furthermore, this paper shows the necessity to include currents in parametric models of sea-state bias; using a coarse-resolution eddy field may severely underestimate the sea-state-induced noise in radar altimeter measurements.
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Haney, S., and W. R. Young. "Radiation of internal waves from groups of surface gravity waves." Journal of Fluid Mechanics 829 (September 15, 2017): 280–303. http://dx.doi.org/10.1017/jfm.2017.536.
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Groups of surface gravity waves induce horizontally varying Stokes drift that drives convergence of water ahead of the group and divergence behind. The mass flux divergence associated with spatially variable Stokes drift pumps water downwards in front of the group and upwards in the rear. This ‘Stokes pumping’ creates a deep Eulerian return flow that sets the isopycnals below the wave group in motion and generates a trailing wake of internal gravity waves. We compute the energy flux from surface to internal waves by finding solutions of the wave-averaged Boussinesq equations in two and three dimensions forced by Stokes pumping at the surface. The two-dimensional (2-D) case is distinct from the 3-D case in that the stratification must be very strong, or the surface waves very slow for any internal wave (IW) radiation at all. On the other hand, in three dimensions, IW radiation always occurs, but with a larger energy flux as the stratification and surface wave (SW) amplitude increase or as the SW period is shorter. Specifically, the energy flux from SWs to IWs varies as the fourth power of the SW amplitude and of the buoyancy frequency, and is inversely proportional to the fifth power of the SW period. Using parameters typical of short period swell (e.g. 8 s SW period with 1 m amplitude) we find that the energy flux is small compared to both the total energy in a typical SW group and compared to the total IW energy. Therefore this coupling between SWs and IWs is not a significant sink of energy for the SWs nor a source for IWs. In an extreme case (e.g. 4 m amplitude 20 s period SWs) this coupling is a significant source of energy for IWs with frequency close to the buoyancy frequency.
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Thais, L., and J. Magnaudet. "Turbulent structure beneath surface gravity waves sheared by the wind." Journal of Fluid Mechanics 328 (December 10, 1996): 313–44. http://dx.doi.org/10.1017/s0022112096008749.
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New experiments have been carried out in a large laboratory channel to explore the structure of turbulent motion in the water layer beneath surface gravity waves. These experiments involve pure wind waves as well as wind-ruffled mechanically generated waves. A submersible two-component LDV system has been used to obtain the three components of the instantaneous velocity field along the vertical direction at a single fetch of 26 m. The displacement of the free surface has been determined simultaneously at the same downstream location by means of wave gauges. For both types of waves, suitable separation techniques have been used to split the total fluctuating motion into an orbital contribution (i.e. a motion induced by the displacement of the surface) and a turbulent contribution. Based on these experimental results, the present paper focuses on the structure of the water turbulence. The most prominent feature revealed by the two sets of experiments is the enhancement of both the turbulent kinetic energy and its dissipation rate with respect to values found near solid walls. Spectral analysis provides clear indications that wave–turbulence interactions greatly affect energy transfers over a significant frequency range by imposing a constant timescale related to the wave-induced strain. For mechanical waves we discuss several turbulent statistics and their modulation with respect to the wave phase, showing that the turbulence we observed was deeply affected at both large and small scales by the wave motion. An analysis of the phase variability of the bursting suggests that there is a direct interaction between the waves and the underlying turbulence, mainly at the wave crests. Turbulence budgets show that production essentially takes place in the wavy region of the flow, i.e. above the wave troughs. These results are finally used to address the nature of the basic mechanisms governing wave–turbulence interactions.
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Kim, Young-Ha, Hye-Yeong Chun, Sang-Hun Park, In-Sun Song, and Hyun-Joo Choi. "Characteristics of gravity waves generated in the jet-front system in a baroclinic instability simulation." Atmospheric Chemistry and Physics 16, no. 8 (April 19, 2016): 4799–815. http://dx.doi.org/10.5194/acp-16-4799-2016.
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Abstract. An idealized baroclinic instability case is simulated using a ∼ 10 km resolution global model to investigate the characteristics of gravity waves generated in the baroclinic life cycle. Three groups of gravity waves appear around the high-latitude surface trough at the mature stage of the baroclinic wave. They have horizontal and vertical wavelengths of 40–400 and 2.9–9.8 km, respectively, in the upper troposphere. The two-dimensional phase-velocity spectrum of the waves is arc shaped with a peak at 17 m s−1 eastward. These waves have difficulty in propagating upward through the tropospheric westerly jet. At the breaking stage of the baroclinic wave, a midlatitude surface low is isolated from the higher-latitude trough, and two groups of quasi-stationary gravity waves appear near the surface low. These waves have horizontal and vertical wavelengths of 60–400 and 4.9–14 km, respectively, and are able to propagate vertically for long distances. The simulated gravity waves seem to be generated by surface fronts, given that the structures and speeds of wave phases are coherent with those of the fronts.
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CHEN, ZHAO, PETER D. BROMIRSKI, PETER GERSTOFT, RALPH A. STEPHEN, DOUGLAS A. WIENS, RICHARD C. ASTER, and ANDREW A. NYBLADE. "Ocean-excited plate waves in the Ross and Pine Island Glacier ice shelves." Journal of Glaciology 64, no. 247 (September 12, 2018): 730–44. http://dx.doi.org/10.1017/jog.2018.66.
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AbstractIce shelves play an important role in buttressing land ice from reaching the sea, thus restraining the rate of grounded ice loss. Long-period gravity-wave impacts excite vibrations in ice shelves that can expand pre-existing fractures and trigger iceberg calving. To investigate the spatial amplitude variability and propagation characteristics of these vibrations, a 34-station broadband seismic array was deployed on the Ross Ice Shelf (RIS) from November 2014 to November 2016. Two types of ice-shelf plate waves were identified with beamforming: flexural-gravity waves and extensional Lamb waves. Below 20 mHz, flexural-gravity waves dominate coherent signals across the array and propagate landward from the ice front at close to shallow-water gravity-wave speeds (~70 m s−1). In the 20–100 mHz band, extensional Lamb waves dominate and propagate at phase speeds ~3 km s−1. Flexural-gravity and extensional Lamb waves were also observed by a 5-station broadband seismic array deployed on the Pine Island Glacier (PIG) ice shelf from January 2012 to December 2013, with flexural wave energy, also detected at the PIG in the 20–100 mHz band. Considering the ubiquitous presence of storm activity in the Southern Ocean and the similar observations at both the RIS and the PIG ice shelves, it is likely that most, if not all, West Antarctic ice shelves are subjected to similar gravity-wave excitation.
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Akers, Benjamin F., David M. Ambrose, and J. Douglas Wright. "Gravity perturbed Crapper waves." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2161 (January 8, 2014): 20130526. http://dx.doi.org/10.1098/rspa.2013.0526.
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Crapper waves are a family of exact periodic travelling wave solutions of the free-surface irrotational incompressible Euler equations; these are pure capillary waves, meaning that surface tension is accounted for, but gravity is neglected. For certain parameter values, Crapper waves are known to have multi-valued height. Using the implicit function theorem, we prove that any of the Crapper waves can be perturbed by the effect of gravity, yielding the existence of gravity–capillary waves nearby to the Crapper waves. This result implies the existence of travelling gravity–capillary waves with multi-valued height. The solutions we prove to exist include waves with both positive and negative values of the gravity coefficient. We also compute these gravity perturbed Crapper waves by means of a quasi-Newton iterative scheme (again, using both positive and negative values of the gravity coefficient). A phase diagram is generated, which depicts the existence of single-valued and multi-valued travelling waves in the gravity–amplitude plane. A new largest water wave is computed, which is composed of a string of bubbles at the interface.
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Preston, Leiph, Christian Poppeliers, and David J. Schodt. "Seismic Characterization of the Nevada National Security Site Using Joint Body Wave, Surface Wave, and Gravity Inversion." Bulletin of the Seismological Society of America 110, no. 1 (November 19, 2019): 110–26. http://dx.doi.org/10.1785/0120190151.
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ABSTRACT As a part of the series of Source Physics Experiments (SPE) conducted on the Nevada National Security Site in southern Nevada, we have developed a local-to-regional scale seismic velocity model of the site and surrounding area. Accurate earth models are critical for modeling sources like the SPE to investigate the role of earth structure on the propagation and scattering of seismic waves. We combine seismic body waves, surface waves, and gravity data in a joint inversion procedure to solve for the optimal 3D seismic compressional and shear-wave velocity structures and earthquake locations subject to model smoothness constraints. Earthquakes, which are relocated as part of the inversion, provide P- and S-body-wave absolute and differential travel times. Active source experiments in the region augment this dataset with P-body-wave absolute times and surface-wave dispersion data. Dense ground-based gravity observations and surface-wave dispersion derived from ambient noise in the region fill in many areas where body-wave data are sparse. In general, the top 1–2 km of the surface is relatively poorly sampled by the body waves alone. However, the addition of gravity and surface waves to the body-wave dataset greatly enhances structural resolvability in the near surface. We discuss the methodology we developed for simultaneous inversion of these disparate data types and briefly describe results of the inversion in the context of previous work in the region.
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Chen, Xuekun, Hongjuan Yang, Zhe Lyu, and Changjun Yu. "Chaotic Properties of Gravity Waves during Typhoons Observed by HFSWR." Remote Sensing 15, no. 21 (November 3, 2023): 5235. http://dx.doi.org/10.3390/rs15215235.
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The gravity wave produced by typhoons has been an essential subject of study that concerns numerous researchers. The damage to human beings and infrastructure in coastal regions caused by typhoon disasters annually is very severe, and analyzing gravity wave variation is a reliable approach to research typhoons. High-frequency surface wave radar (HFSWR) as an over-the-horizon radar can achieve real-time monitoring of an extensive sea area and space. This paper derived the gravity wave perturbation spectrum by handling high-frequency surface wave radar data during typhoons. The gravity wave spectrum data were examined by applying the chaos examination approaches of the Lyapunov exponent and phase-space reconstruction to the gravity wave spectrum data after processing and extraction. The reconstructed phase space had a specific shape in a certain direction, with the maximum Lyapunov exponent greater than zero. The gravity wave spectrum data are suggested to have chaotic properties through two chaos examination approaches. This paper demonstrated that the gravity waves observed by a radar have chaotic properties through the measurement data of HFSWR. While the chaotic properties suggest that observed gravity wave data are predictable in the short term, they are unpredictable in the long term. Predicting gravity wave data is important for understanding the chaotic properties of the atmosphere and for future gravity wave prediction.
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Stuhlmeier, Raphael, and Michael Stiassnie. "Nonlinear dispersion for ocean surface waves." Journal of Fluid Mechanics 859 (November 16, 2018): 49–58. http://dx.doi.org/10.1017/jfm.2018.818.
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Two expressions for the nonlinear dispersion relation for gravity waves on water of constant depth are derived, one for wave fields with discrete amplitude spectra, the other for wave fields with continuous wavenumber energy spectra. Numerical examples for wave quartets and for two-dimensional Pierson–Moskowitz spectra are given, and an important possible application is discussed.
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LONGUET-HIGGINS, MICHAEL S. "Viscous dissipation in steep capillary–gravity waves." Journal of Fluid Mechanics 344 (August 10, 1997): 271–89. http://dx.doi.org/10.1017/s0022112097006046.
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Some simple but exact general expressions are derived for the viscous stresses required at the surface of irrotational capillary–gravity waves of periodic or solitary type on deep water in order to maintain them in steady motion. These expressions are applied to nonlinear capillary waves, and to capillary–gravity waves of solitary type on deep water. In the case of pure capillary waves some algebraic expressions are found for the work done by the surface stresses, from which it is possible to infer the viscous rate of decay of free, nonlinear capillary waves.Similar calculations are carried out for capillary–gravity waves of solitary type on deep water. It is shown that the limiting rate of decay of a solitary wave at low amplitudes is just twice that for linear, periodic waves. This is due to the spreading out of the wave envelope at low wave steepnesses. At large wave steepnesses the dissipation increases by an order of magnitude, owing to the sharply increased curvature in the wave troughs. The calculated rates of decay are in agreement with recent observations.
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Longuet-Higgins, Michael S. "Parasitic capillary waves: a direct calculation." Journal of Fluid Mechanics 301 (October 25, 1995): 79–107. http://dx.doi.org/10.1017/s0022112095003818.
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As in a previous theory (Longuet-Higgins 1963) parasitic capillary waves are considered as a perturbation due to the local action of surface tension forces on an otherwise pure progressive gravity wave. Here the theory is improved by: (i) making use of our more accurate knowledge of the profile of a steep Stokes wave; (ii) taking account of the influence of gravity on the capillary waves themselves, through the effective gravitational acceleration g* for short waves riding on longer waves.Nonlinearity in the capillary waves themselves is not included, and certain other approximations are made. Nevertheless, the theory is shown to be in essential agreement with experiments by Cox (1958), Ebuchi, Kawamura & Toba (1987) and Perlin, Lin & Ting (1993).A principal result is that for gravity waves of a given length L > 5 cm there is a critical steepness parameter (AK)c at which the surface velocity (in a frame of reference moving with the phase-speed) equals the minimum (local) speed of capillary-gravity waves. On subcritical gravity waves, with steepness AK < (AK)c, capillary waves may be generated at all points of the wave surface. On supercritical waves, with AK > (AK)c, capillary waves can only be generated in the wave troughs; they are trapped between two caustics near the crests. Generally, the amplitude of the parasitic capillaries is greatest on gravity waves of near critical (but not maximum) steepness.
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Rozenman, Georgi Gary, Shenhe Fu, Ady Arie, and Lev Shemer. "Quantum Mechanical and Optical Analogies in Surface Gravity Water Waves." Fluids 4, no. 2 (May 27, 2019): 96. http://dx.doi.org/10.3390/fluids4020096.
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We present the theoretical models and review the most recent results of a class of experiments in the field of surface gravity waves. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In particular, experiments involving Airy water-wave packets were carried out. The Airy wave packets have attracted tremendous attention in optics and quantum mechanics owing to their unique properties, spanning from an ability to propagate along parabolic trajectories without spreading, and to accumulating a phase that scales with the cubic power of time. Non-dispersive Cosine-Gauss wave packets and self-similar Hermite-Gauss wave packets, also well known in the field of optics and quantum mechanics, were recently studied using surface gravity waves as well. These wave packets demonstrated self-healing properties in water wave pulses as well, preserving their width despite being dispersive. Finally, this new approach also allows to observe diffractive focusing from a temporal slit with finite width.
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FEDOROV, ALEXEY V., and W. KENDALL MELVILLE. "Nonlinear gravity–capillary waves with forcing and dissipation." Journal of Fluid Mechanics 354 (January 10, 1998): 1–42. http://dx.doi.org/10.1017/s0022112097007453.
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We present a study of nonlinear gravity–capillary waves with surface forcing and viscous dissipation. Based on a viscous boundary layer approximation near the water surface, the theory permits the efficient calculation of steady gravity–capillary waves with parasitic capillary ripples. To balance the viscous dissipation and thus achieve steady solutions, wind forcing is applied by adding a surface pressure distribution. For a given wavelength the properties of the solutions depend upon two independent parameters: the amplitude of the dominant wave and the amplitude of the pressure forcing. We find two main classes of waves for relatively weak forcing: Class 1 and Class 2. (A third class of solution requires strong forcing and is qualitatively different.) For Class 1 waves the maximum surface pressure occurs near the wave trough, while for Class 2 it is near the crest. The Class 1 waves are associated with Miles' (1957, 1959) mechanism of wind-wave generation, while the Class 2 waves may be related to instabilities of the subsurface shear current. For both classes of waves, steady solutions are possible only for forcing amplitudes greater than a certain threshold. We demonstrate how parasitic capillary ripples affect the dissipative and dispersive properties of the solutions. In particular, there may be a significant deviation from the linear phase speed for gravity–capillary waves. Also, wave damping is strongly enhanced by the parasitic capillaries (by as much as two orders of magnitude when compared to the case with no capillary waves). Preliminary experimental results from a wind-wave channel give good agreement with the theory. We find a sharp cut-off in the wavenumber spectra of the solutions which is similar to that observed in laboratory measurements of short gravity–capillary waves. Finally, for large wave amplitudes we find a sharp corner in the wave profile which may separate an overhanging wave crest from a train of parasitic capillaries.
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Hoitink, A. J. F., H. C. Peters, and M. Schroevers. "Field Verification of ADCP Surface Gravity Wave Elevation Spectra." Journal of Atmospheric and Oceanic Technology 24, no. 5 (May 1, 2007): 912–22. http://dx.doi.org/10.1175/jtech2000.1.
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Abstract Acoustic Doppler current profilers (ADCPs) can measure orbital velocities induced by surface gravity waves, yet the ADCP estimates of these velocities are subject to a relatively high noise level. The present paper introduces a linear filtration technique to significantly reduce the influence of noise and turbulence from energy spectra of combined orbital velocity measurements. Data were collected in 13-m-deep water with a 1.2-MHz ADCP sampling in mode 12, where a collocated wave buoy was used for verification. The surface elevation spectra derived from the filtrated and nonfiltrated measurements were compared with corresponding wave buoy spectra. In the frequency range between 0.12 and 0.5 Hz, ADCP- and wave-buoy-derived spectral estimates matched very well, even without applying the filtration technique. At frequencies below 0.12 Hz, the ADCP-derived surface elevation spectra are biased, caused by a depth-varying excess of spectral energy density in the measured orbital velocities, peaking at middepth. Internal waves may provide an explanation for the energy excess, as the experiment was conducted in the region of influence of the Rhine freshwater plume. Alternatively, infragravity waves may be the cause of the depth variation of low-frequency spectral energy density.
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Allaerts, Dries, and Johan Meyers. "Sensitivity and feedback of wind-farm-induced gravity waves." Journal of Fluid Mechanics 862 (January 16, 2019): 990–1028. http://dx.doi.org/10.1017/jfm.2018.969.
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Flow blockage by large wind farms leads to an upward displacement of the boundary layer, which may excite atmospheric gravity waves in the free atmosphere and on the interface between the boundary layer and the free atmosphere. In the current study, we assess the sensitivity of wind-farm gravity-wave excitation to important dimensionless groups and investigate the feedback of gravity-wave-induced pressure fields to wind-farm energy extraction. The sensitivity analysis is performed using a fast boundary-layer model that is developed to this end. It is based on a three-layer representation of the atmosphere in an idealised barotropic environment, and is coupled with an analytical wake model to account for turbine wake interactions. We first validate the model in two-dimensional mode with data from previous large-eddy simulations of ‘infinitely’ wide wind farms, and then use the model to investigate the sensitivity of wind-farm-induced gravity waves to atmospheric state and wind-farm configuration. We find that the inversion layer induces flow physics similar to shallow-water flow and that the corresponding Froude number plays a crucial role. Gravity-wave excitation is maximal at a critical Froude number equal to one, but the feedback on energy extraction is highest when the Froude number is slightly below one due to a trade-off between amplitude and upstream impact of gravity waves. The effect of surface friction and internal gravity waves is to reduce the flow perturbation and the related power loss by dissipating or dispersing perturbation energy. With respect to the wind-farm configuration, we find that gravity-wave-induced power loss increases with wind-farm size and turbine height. Moreover, we find that gravity-wave effects are small for very wide or very long wind farms and attain a maximum at a width-to-depth ratio of approximately $3/2$.
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Czeschel, Lars, and Carsten Eden. "Internal Wave Radiation through Surface Mixed Layer Turbulence." Journal of Physical Oceanography 49, no. 7 (July 2019): 1827–44. http://dx.doi.org/10.1175/jpo-d-18-0214.1.
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AbstractIn a series of large-eddy simulations with different forcing, we study the generation of internal gravity waves at the base of the surface mixed layer. If turbulent eddies act as obstacles and undulate the base of the mixed layer, horizontal velocities associated with inertial oscillations and Ekman dynamics can move the obstacles relative to the stratified interior, exciting internal gravity waves similar to lee waves. We find strong evidence that the “obstacle mechanism” is able to excite large parts of the internal wave spectrum, including near inertial waves. The high-frequency part of the excited wave spectrum is filtered by the increased stratification in the transition layer between the mixed layer and lower stratified interior, but a substantial part of the wave spectrum is able to overcome this barrier, hence contributing to interior mixing. The magnitude of the downward-radiated energy below the transition layer depends on the source of turbulence, but we show that the obstacle mechanism, especially under destabilizing heat fluxes, has the potential to contribute considerably to the internal wave energy in the interior ocean.
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Milinazzo, F. A., and P. G. Saffman. "Effect of a surface shear layer on gravity and gravity–capillary waves of permanent form." Journal of Fluid Mechanics 216 (July 1990): 93–101. http://dx.doi.org/10.1017/s0022112090000350.
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Calculations are carried out of the shape of gravity and gravity–capillary waves on deep water in the presence of a thin sheet of uniform vorticity which models the effect of a wind drift layer. The dependence of the fluid speed at the wave crest is determined and compared for gravity waves with the theory of Banner & Phillips (1974). It is found that this theory underestimates the retardation due to drift and tendency to break. The retardation disappears when capillary forces are significant, but in this case it is found that there can be a significant alteration of the wave shape.
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Ardhuin, Fabrice, and T. H. C. Herbers. "Noise generation in the solid Earth, oceans and atmosphere, from nonlinear interacting surface gravity waves in finite depth." Journal of Fluid Mechanics 716 (January 25, 2013): 316–48. http://dx.doi.org/10.1017/jfm.2012.548.
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AbstractOceanic pressure measurements, even in very deep water, and atmospheric pressure or seismic records, from anywhere on Earth, contain noise with dominant periods between 3 and 10 s, which is believed to be excited by ocean surface gravity waves. Most of this noise is explained by a nonlinear wave–wave interaction mechanism, and takes the form of surface gravity waves, acoustic or seismic waves. Previous theoretical work on seismic noise focused on surface (Rayleigh) waves, and did not consider finite-depth effects on the generating wave kinematics. These finite-depth effects are introduced here, which requires the consideration of the direct wave-induced pressure at the ocean bottom, a contribution previously overlooked in the context of seismic noise. That contribution can lead to a considerable reduction of the seismic noise source, which is particularly relevant for noise periods larger than 10 s. The theory is applied to acoustic waves in the atmosphere, extending previous theories that were limited to vertical propagation only. Finally, the noise generation theory is also extended beyond the domain of Rayleigh waves, giving the first quantitative expression for sources of seismic body waves. In the limit of slow phase speeds in the ocean wave forcing, the known and well-verified gravity wave result is obtained, which was previously derived for an incompressible ocean. The noise source of acoustic, acoustic-gravity and seismic modes are given by a mode-specific amplification of the same wave-induced pressure field near zero wavenumber.
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Longuet-Higgins, M. S. "The propagation of short surface waves on longer gravity waves." Journal of Fluid Mechanics 177 (April 1987): 293–306. http://dx.doi.org/10.1017/s002211208700096x.
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To understand the imaging of the sea surface by radar, it is useful to know the theoretical variations in the wavelength and steepness of short gravity waves propagated over the surface of a train of longer gravity waves of finite amplitude. Such variations may be calculated once the orbital accelerations and surface velocities in the longer waves have been accurately determined – a non-trivial computational task.The results show that the linearized theory used previously for the longer waves is generally inadequate. The fully nonlinear theory used here indicates that for longer waves having a steepness parameter AK = 0.4, for example, the short-wave steepness can be increased at the crests of the longer waves by a factor of order 8, compared with its value at the mean level. (Linear theory gives a factor less than 2.)The calculations so far reported are for free, irrotational gravity waves travelling in the same or directly opposite sense to the longer waves. However, the method of calculation could be extended without essential difficulty so as to include effects of surface tension, energy dissipation due to short-wave breaking, surface wind-drift currents, and to arbitrary angles of wave propagation.
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Young, W. R., and C. L. Wolfe. "Generation of surface waves by shear-flow instability." Journal of Fluid Mechanics 739 (December 18, 2013): 276–307. http://dx.doi.org/10.1017/jfm.2013.617.
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AbstractWe consider the linear stability of an inviscid parallel shear flow of air over water with gravity and capillarity. The velocity profile in the air is monotonically increasing upwards from the sea surface and is convex, while the velocity in the water is monotonically decreasing from the surface and is concave. An archetypical example, the ‘double-exponential’ profile, is solved analytically and studied in detail. We show that there are two types of unstable mode which can, in some cases, co-exist. The first type is the ‘Miles mode’ resulting from a resonant interaction between a surface gravity wave and a critical level in the air. The second unstable mode is an interaction between surface gravity waves and a critical level in the water, resulting in the growth of ripples. The gravity–capillary waves participating in this second resonance have negative intrinsic phase speed, but are Doppler shifted so that their actual phase speed is positive, and matches the speed of the base-state current at the critical level. In both cases, the Reynolds stresses of an exponentially growing wave transfer momentum from the vicinity of the critical level to the zone between the crests and troughs of a surface wave.
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ARDHUIN, FABRICE, and RUDY MAGNE. "Scattering of surface gravity waves by bottom topography with a current." Journal of Fluid Mechanics 576 (March 28, 2007): 235–64. http://dx.doi.org/10.1017/s0022112006004484.
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A theory is presented that describes the scattering of random surface gravity waves by small-amplitude topography, with horizontal scales of the order of the wavelength, in the presence of an irrotational and almost uniform current. A perturbation expansion of the wave action to order η2 yields an evolution equation for the wave action spectrum, where η = max(h)/H is the small-scale bottom amplitude normalized by the mean water depth. Spectral wave evolution is proportional to the bottom elevation variance at the resonant wavenumbers, representing a Bragg scattering approximation. With a current, scattering results from a direct effect of the bottom topography, and an indirect effect of the bottom through the modulations of the surface current and mean surface elevation. For Froude numbers of the order of 0.6 or less, the bottom topography effects dominate. For all Froude numbers, the reflection coefficients for the wave amplitudes that are inferred from the wave action source term are asymptotically identical, as η goes to zero, to previous theoretical results for monochromatic waves propagating in one dimension over sinusoidal bars. In particular, the frequency of the most reflected wave components is shifted by the current, and wave action conservation results in amplified reflected wave energies for following currents. Application of the theory to waves over current-generated sandwaves suggests that forward scattering can be significant, resulting in a broadening of the directional wave spectrum, while back-scattering should be generally weaker.
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Adams-Selin, Rebecca D., and Richard H. Johnson. "Examination of Gravity Waves Associated with the 13 March 2003 Bow Echo." Monthly Weather Review 141, no. 11 (October 25, 2013): 3735–56. http://dx.doi.org/10.1175/mwr-d-12-00343.1.
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Abstract Numerical simulations of the 13 March 2003 bow echo over Oklahoma are used to evaluate bow echo development and its relationship with gravity wave generation. Multiple fast-moving (with speeds of 30–35 m s−1) gravity waves are generated in association with fluctuations in the first vertical mode of heating in the convective line. The surface impacts of four such waves are observed in Oklahoma Mesonet data during this case. Observations of surface pressure surges ahead of convective lines prior to the bowing process are reproduced; a slower gravity wave produced in the simulation is responsible for a prebowing pressure surge. This slower gravity wave, moving at approximately 11 m s−1, is generated by an increase in low-level microphysical cooling associated with an increase in rear-to-front flow and low-level downdrafts shortly before bowing. The wave moves ahead of the convective line and is manifested at the surface by a positive pressure surge. The pattern of low-level vertical motion associated with this wave, in conjunction with higher-frequency gravity waves generated by multicellularity of the convective line, increases the immediate presystem CAPE by approximately 250 J kg−1 just ahead of the bowing segment of the convective line. Increased presystem CAPE aids convective updraft strength in that segment despite amplified updraft tilt due to a stronger cold pool and surface-based rear-to-front flow, compared to updraft strength in other, nonbowing segments of the convective line.
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Fan, Yalin, and Zhitao Yu. "Surface Gravity Wave Effect on Hurricane Energetics." Atmosphere 13, no. 2 (February 7, 2022): 279. http://dx.doi.org/10.3390/atmos13020279.
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Theoretical researches have established that the energy dynamics of a mature tropical cyclone may be idealized to be very similar to a theoretical Carnot heat engine. Assuming the dissipative heating of the atmospheric boundary layer and the net production of mechanical energy in the cyclone dominate the energy budget of the storm, the potential maximum wind speed of the cyclone can be approximated as a function of the air–sea temperature difference (Ts − T0) and specific enthalpy (k0*−k) difference: |Vmax|2≈CkCDTs−T0T0(k0*−k). Although this theory gives a straighforward estimate of maximum tropical cyclone intensity, studies found that few real storms achieve this theoretical maximum estimated using climatological atmospheric conditions and sea surface temperatures. The discrepancies were attributed to a lack of knowledge of the values of the drag coefficient (CD) and surface exchange coefficient for enthalpy (Ck), and on insufficient upper ocean thermal measurements under hurricanes. Recent observational and numerical studies have unearthed another possible factor for these discrepancies by showing that the energy flux into surface gravity waves under extreme wind conditions can be an order of magnitude greater than formerly believed, and thus may play an important role in the energy budget of tropical cyclones. In this study, numerical experiments are performed to investigate the effect of surface gravity waves under a range of idealized tropical cyclone winds. The wave fields are simulated using the WAVEWATCH III model. Our results demonstrate that by considering the energy flux to surface gravity waves, the potential maximum wind speed can be reduced by up to 12% and this ratio varies with the storm size, intensity, and translation speed.
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Lin, Yuchun, and Leo Oey. "Global Trends of Sea Surface Gravity Wave, Wind, and Coastal Wave Setup." Journal of Climate 33, no. 3 (February 1, 2020): 769–85. http://dx.doi.org/10.1175/jcli-d-19-0347.1.
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AbstractAssessing trends of sea surface wave, wind, and coastal wave setup is of considerable scientific and practical importance in view of recent and projected long-term sea level rise due to global warming. Here we analyze global significant wave height (SWH) and wind data from 1993 to 2015 and a wave model to (i) calculate wave age and explain the causal, or the lack thereof, relationship between wave and wind trends; and (ii) estimate trends of coastal wave setup and its contributions to secular trends of relative sea level at coastal locations around the world. We show in-phase, increasing SWH and wind trends in regions dominated by younger waves, and decreasing SWH trends where older waves dominate and are unrelated to the local wind trends. In the central North Pacific where wave age is transitional, in-phase decreasing wave and wind trends are found over the west-northwestern region, but wave and wind trends are insignificantly correlated in the south-southeastern region; here, a reversed, upward momentum flux from wave to wind is postulated. We show that coastal wave setup depends primarily on open-ocean SWH but only weakly on wind, varying approximately like SWH/(wind speed)1/5. The wave-setup trends are shown to be increasing along many coastlines where the local relative sea level trends are also increasing: the North and Irish Seas, Mediterranean Sea, East and South Asian seas, and eastern United States, exacerbating the potential for increased floods along these populated coastlines.
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Sepúlveda, Nicasio. "Solitary waves in the resonant phenomenon between a surface gravity wave packet and an internal gravity wave." Physics of Fluids 30, no. 7 (1987): 1984. http://dx.doi.org/10.1063/1.866212.
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Fujimoto, Wataru, and Takuji Waseda. "Ensemble-Based Variational Method for Nonlinear Inversion of Surface Gravity Waves." Journal of Atmospheric and Oceanic Technology 37, no. 1 (January 2020): 17–31. http://dx.doi.org/10.1175/jtech-d-19-0072.1.
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ABSTRACTFreak/rogue waves are considered to be the causes of marine accidents and their generation mechanism is closely related to the formation of wave groups. However, observations that capture the spatiotemporal evolution of coherent wave groups in directional windsea are rather limited. The paper presents a new technique known as the surface wave reconstruction by ensemble adjoint-free data assimilation (SWEAD) method that enables reconstruction of a spatiotemporal wave field covering a large area from wave records limited in observational density and spatial extent. We reconstructed spatiotemporal profiles of nonlinear surface gravity waves from virtual observational data using the adjoint-free four-dimensional variational data assimilation (a4DVar) scheme. The higher-order spectral method (HOSM) is used as a forward deep-water nonlinear wave model in a realistic sea state. The a4DVar scheme uses perturbed ensemble simulations to calculate the cost function gradient and Hessian; thus, construction of an adjoint model is not needed. A few extensions of the a4DVar scheme are proposed in this study. For efficient wave reconstruction, perturbed ensemble simulation results are reused by increasing the searching direction dimension at each iteration while assuring conformity to the perturbed model’s linearity. For regularization, Fourier coefficient magnitudes are constrained by a known power spectrum from the phase-averaged wave model. Twin experiments were conducted for a unidirectional wave with virtual wave gauge data and a multidirectional wave with virtual stereo camera imaging data. For both unidirectional and multidirectional cases, nonlinear freak wave–related wave groups were well reproduced, which is impossible using a linear model.
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Smith, Jerome A. "Revisiting Oceanic Acoustic Gravity Surface Waves." Journal of Physical Oceanography 45, no. 12 (December 2015): 2953–58. http://dx.doi.org/10.1175/jpo-d-14-0256.1.
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AbstractThe reintroduction of compressibility into the equations for surface gravity waves can permit mixed acoustic–gravity modes that are periodic in the vertical as well as horizontal directions. These modes interact with the bottom even in deep water, so bottom motion can excite them. Because they propagate rapidly, it has been suggested they may be useful as precursors of tsunamis. Here the equations are revisited, and, using some robust approximations, some physical understanding and interpretation of the phenomena are presented. It is posed that these new modes can alternatively be thought of as acoustic modes slightly modified by a gravity wave boundary condition at the surface, rather than as surface waves dramatically modified by compressibility. Their potential use is not diminished; indeed, this alternative perspective should help make implementation more practical.
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Kang, Youn J., and Yeunwoo Cho. "Gravity–capillary jet-like surface waves generated by an underwater bubble." Journal of Fluid Mechanics 866 (March 18, 2019): 841–64. http://dx.doi.org/10.1017/jfm.2019.135.
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Jet-like surface waves generated by an electric-spark-generated underwater bubble are experimentally studied. Three different motions of jet-like surface waves are observed depending on the inception position of the bubble ($d$: 0.28–7 mm) below the free surface and the maximum radius of the bubble ($R_{m}$: 1.5–3.6 mm). When $d/R_{m}>1.3$, the surface wave shows a simple smooth hump (case 1). When $0.82<d/R_{m}<1.3$, a single droplet or multiple droplets are pinched off sequentially or simultaneously at the tip or from some points of the jet-like surface wave (case 2). Finally, when $d/R_{m}<0.82$, a series of squirting and jetting phenomena are observed at the top of the jet-like surface wave (case 3). For case 1, a proportional relationship is found between $\unicode[STIX]{x1D70C}gh/\unicode[STIX]{x0394}p$ and $(d/R_{m})^{-4.4}$, where $\unicode[STIX]{x1D70C}$ is the density of the fluid, $g$ is the gravitational acceleration and $\unicode[STIX]{x0394}p$ is the difference between the reference atmospheric pressure and the vapour pressure inside a bubble. This proportional relationship is explained semi-analytically using a scaling argument and conservation of momentum and energy, with the help of the Kelvin impulse theory. In addition, we solve the relevant axisymmetric Cauchy–Poisson problem where the initial condition is a jet-like surface wave near its maximum height. By comparing the analytical wave solution with the observed surface wave pattern, it is found that the resultant surface waves are indeed gravity–capillary waves where both the gravity and the surface tension are equally important.
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Hsu, H. C., C. Kharif, M. Abid, and Y. Y. Chen. "A nonlinear Schrödinger equation for gravity–capillary water waves on arbitrary depth with constant vorticity. Part 1." Journal of Fluid Mechanics 854 (September 3, 2018): 146–63. http://dx.doi.org/10.1017/jfm.2018.627.
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A nonlinear Schrödinger equation for the envelope of two-dimensional gravity–capillary waves propagating at the free surface of a vertically sheared current of constant vorticity is derived. In this paper we extend to gravity–capillary wave trains the results of Thomas et al. (Phys. Fluids, 2012, 127102) and complete the stability analysis and stability diagram of Djordjevic & Redekopp (J. Fluid Mech., vol. 79, 1977, pp. 703–714) in the presence of vorticity. The vorticity effect on the modulational instability of weakly nonlinear gravity–capillary wave packets is investigated. It is shown that the vorticity modifies significantly the modulational instability of gravity–capillary wave trains, namely the growth rate and instability bandwidth. It is found that the rate of growth of modulational instability of short gravity waves influenced by surface tension behaves like pure gravity waves: (i) in infinite depth, the growth rate is reduced in the presence of positive vorticity and amplified in the presence of negative vorticity; (ii) in finite depth, it is reduced when the vorticity is positive and amplified and finally reduced when the vorticity is negative. The combined effect of vorticity and surface tension is to increase the rate of growth of modulational instability of short gravity waves influenced by surface tension, namely when the vorticity is negative. The rate of growth of modulational instability of capillary waves is amplified by negative vorticity and attenuated by positive vorticity. Stability diagrams are plotted and it is shown that they are significantly modified by the introduction of the vorticity.
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Deike, Luc, Stephane Popinet, and W. Kendall Melville. "Capillary effects on wave breaking." Journal of Fluid Mechanics 769 (March 25, 2015): 541–69. http://dx.doi.org/10.1017/jfm.2015.103.
Full textAbstract:
We investigate the influence of capillary effects on wave breaking through direct numerical simulations of the Navier–Stokes equations for a two-phase air–water flow. A parametric study in terms of the Bond number, $\mathit{Bo}$, and the initial wave steepness, ${\it\epsilon}$, is performed at a relatively high Reynolds number. The onset of wave breaking as a function of these two parameters is determined and a phase diagram in terms of $({\it\epsilon},\mathit{Bo})$ is presented that distinguishes between non-breaking gravity waves, parasitic capillaries on a gravity wave, spilling breakers and plunging breakers. At high Bond number, a critical steepness ${\it\epsilon}_{c}$ defines the onset of wave breaking. At low Bond number, the influence of surface tension is quantified through two boundaries separating, first gravity–capillary waves and breakers, and second spilling and plunging breakers; both boundaries scaling as ${\it\epsilon}\sim (1+\mathit{Bo})^{-1/3}$. Finally the wave energy dissipation is estimated for each wave regime and the influence of steepness and surface tension effects on the total wave dissipation is discussed. The breaking parameter $b$ is estimated and is found to be in good agreement with experimental results for breaking waves. Moreover, the enhanced dissipation by parasitic capillaries is consistent with the dissipation due to breaking waves.
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Beya, Jose, William Peirson, and Michael Banner. "ATTENUATION OF GRAVITY WAVES BY TURBULENCE." Coastal Engineering Proceedings 1, no. 32 (February 2, 2011): 3. http://dx.doi.org/10.9753/icce.v32.waves.3.
Full textAbstract:
We report new laboratory measurements of the interaction between mechanically-generated gravity waves and turbulence generated by simulated rain. Wave attenuation coefficients and vertical profiles of turbulent velocity fluctuations were measured. Observations are in broad agreement with Teixeira and Belcher (2002) despite substantial differences between assumed and measured turbulence profiles. Wave attenuation due to surface turbulence appears to be stronger than theoretical estimates. These finding could have significant implications for the next generation of spectral wave models and the understanding of wave dissipation processes.