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Journal articles on the topic 'Three wave interaction'

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Published: 4 June 2021

Last updated: 10 February 2022

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1

WEBB, G. M., A. R. ZAKHARIAN, M. BRIO, and G. P. ZANK. "Nonlinear and three-wave resonant interactions in magnetohydrodynamics." Journal of Plasma Physics 63, no. 5 (June 2000): 393–445. http://dx.doi.org/10.1017/s0022377800008370.

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Hamiltonian and variational formulations of equations describing weakly nonlinear magnetohydrodynamic (MHD) wave interactions in one Cartesian space dimension are discussed. For wave propagation in uniform media, the wave interactions of interest consist of (a) three-wave resonant interactions in which high-frequency waves may evolve on long space and time scales if the wave phases satisfy the resonance conditions; (b) Burgers self-wave steepening for the magnetoacoustic waves, and (c) mean wave field effects, in which a particular wave interacts with the mean wave field of the other waves. The equations describe four types of resonant triads: slow–fast magnetoacoustic wave interaction, Alfvén–entropy wave interaction, Alfvén–magnetoacoustic wave interaction, and magnetoacoustic–entropy wave interaction. The formalism is restricted to coherent wave interactions. The equations are used to investigate the Alfvén-wave decay instability in which a large-amplitude forward propagating Alfvén wave decays owing to three-wave resonant interaction with a backward-propagating Alfvén wave and a forward-propagating slow magnetoacoustic wave. Exact solutions of the equations for Alfvén–entropy wave interactions are also discussed.

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2

Krafft, C., and A. Volokitin. "Resonant three-wave interaction in the presence of suprathermal electron fluxes." Annales Geophysicae 22, no. 6 (June 14, 2004): 2171–79. http://dx.doi.org/10.5194/angeo-22-2171-2004.

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Abstract. A theoretical and numerical model is presented which describes the nonlinear interaction of lower hybrid waves with a non-equilibrium electron distribution function in a magnetized plasma. The paper presents some relevant examples of numerical simulations which show the nonlinear evolution of a set of three waves interacting at various resonance velocities with a flux of electrons presenting some anisotropy in the parallel velocity distribution (suprathermal tail); in particular, the case when the interactions between the waves are neglected (for sufficiently small waves' amplitudes) is compared to the case when the three waves follow a resonant decay process. A competition between excitation (due to the fan instability with tail electrons or to the bump-in-tail instability at the Landau resonances) and damping processes (involving bulk electrons at the Landau resonances) takes place for each wave, depending on the strength of the wave-wave coupling, on the linear growth rates of the waves and on the modifications of the particles' distribution resulting from the linear and nonlinear wave-particle interactions. It is shown that the energy carried by the suprathermal electron tail is more effectively transfered to lower energy electrons in the presence of wave-wave interactions.

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3

Julien, F., J. M. Lourtioz, and T. A. DeTemple. "Parallel three-wave interaction." Journal de Physique 47, no. 5 (1986): 781–88. http://dx.doi.org/10.1051/jphys:01986004705078100.

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4

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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5

Brodin, G., and L. Stenflo. "Three-wave coupling coefficients for MHD plasmas." Journal of Plasma Physics 39, no. 2 (April 1988): 277–84. http://dx.doi.org/10.1017/s0022377800013027.

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By reconsidering the general theory for the resonant interaction of three waves in a plasma, we find explicit expressions for the coupling coefficients for three MHD waves. In particular we demonstrate that the interaction between two magnetosonic waves and one Alfvén wave, as well as the interaction between two Alfvén waves and one magnetosonic wave, can be described by very simple formulae for the coupling coefficients.

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6

Brodin, G., and L. Stenflo. "Three-wave interaction between transverse and longitudinal waves." Journal of Plasma Physics 42, no. 1 (August 1989): 187–91. http://dx.doi.org/10.1017/s0022377800014264.

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We consider the resonant interaction between two transverse waves and one longitudinal wave in a plasma. In particular, we discuss coupling phenomena involving long-wavelength modes that have been overlooked by previous authors.

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7

Luo, Qinghuan, and D. B. Melrose. "Induced Three-wave Interactions in Eclipsing Pulsars." Publications of the Astronomical Society of Australia 12, no. 1 (April 1995): 71–75. http://dx.doi.org/10.1017/s1323358000020063.

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AbstractThree-wave interactions involving two high-frequency waves (in the same mode) and a low-frequency wave are discussed and applied to pulsar eclipses. When the magnetic field is taken into account, the low-frequency waves can be the ω-mode (the low-frequency branch of the ordinary mode) or the z-mode (the low-frequency branch of the extraordinary mode). It is shown that in the cold plasma approximation, effective growth of the low-frequency waves due to an anisotropic photon beam can occur only for z-mode waves near the resonance frequency. In the application to pulsar eclipses, the cold plasma approximation may not be adequate and we suggest that when thermal effects are included, three-wave interaction involving low-frequency cyclotron waves (e.g. Bernstein modes) is a plausible candidate for pulsar eclipses

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8

Annenkov, S. Yu, and N. N. Romanova. "Three-wave resonant interaction involving unstable wave packets." Doklady Physics 48, no. 8 (August 2003): 441–46. http://dx.doi.org/10.1134/1.1606760.

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9

Raad, Peter E., and Razvan Bidoae. "Three‐Dimensional Wave Interaction with Solids." Physics of Fluids 11, no. 9 (September 1999): S6. http://dx.doi.org/10.1063/1.4739156.

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10

Giannoulis, Johannes. "Three-wave interaction in discrete lattices." PAMM 6, no. 1 (December 2006): 475–76. http://dx.doi.org/10.1002/pamm.200610218.

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11

Yang, Bo, and Jianke Yang. "General rogue waves in the three-wave resonant interaction systems." IMA Journal of Applied Mathematics 86, no. 2 (March 25, 2021): 378–425. http://dx.doi.org/10.1093/imamat/hxab005.

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Abstract General rogue waves in (1+1)-dimensional three-wave resonant interaction systems are derived by the bilinear method. These solutions are divided into three families, which correspond to a simple root, two simple roots and a double root of a certain quartic equation arising from the dimension reduction, respectively. It is shown that while the first family of solutions associated with a simple root exists for all signs of the nonlinear coefficients in the three-wave interaction equations, the other two families of solutions associated with two simple roots and a double root can only exist in the so-called soliton-exchange case, where the nonlinear coefficients have certain signs. Many of these rogue wave solutions, such as those associated with two simple roots, the ones generated by a $2\times 2$ block determinant in the double-root case, and higher-order solutions associated with a simple root, are new solutions which have not been reported before. Technically, our bilinear derivation of rogue waves for the double-root case is achieved by a generalization to the previous dimension reduction procedure in the bilinear method, and this generalized procedure allows us to treat roots of arbitrary multiplicities. Dynamics of the derived rogue waves is also examined, and new rogue wave patterns are presented. Connection between these bilinear rogue waves and those derived earlier by Darboux transformation is also explained.

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12

Borluk, H., and S. Erbay. "Stability of solitary waves for three-coupled long wave-short wave interaction equations." IMA Journal of Applied Mathematics 76, no. 4 (September 13, 2010): 582–98. http://dx.doi.org/10.1093/imamat/hxq044.

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13

Brodin, G., and L. Stenflo. "Three-wave coupling coefficients for magnetized plasmas with pressure anisotropy." Journal of Plasma Physics 41, no. 1 (February 1989): 199–208. http://dx.doi.org/10.1017/s0022377800013763.

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In order to find the equations for the nonlinear energy exchange between low-frequency waves in magnetized plasmas in the presence of pressure anisotropy, we start from the Chew–Goldberger–Low equations, the isothermal MHD equations, as well as a new hybrid system of equations. The coupling coefficients describing the interaction between two Alfvén waves and one magnetosonic wave as well as the interaction between two magnetosonic waves and one Alfvén wave are deduced.

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14

SCHNEIDER, GUIDO, and C. EUGENE WAYNE. "Estimates for the three-wave interaction of surface water waves." European Journal of Applied Mathematics 14, no. 5 (October 2003): 547–70. http://dx.doi.org/10.1017/s0956792503005163.

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15

Alexey, Doronin, and Erofeev Vladimir. "THREE-WAVE RESONANCE INTERACTION IN ELASTOPLASTIC SOLID." PNRPU Mechanics Bulletin, no. 3 (September 30, 2015): 52–62. http://dx.doi.org/10.15593/perm.mech/2015.3.05.

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16

Pushkina, N. I. "Nonlinear three-wave interaction in marine sediments." Physics of Wave Phenomena 20, no. 3 (July 2012): 204–7. http://dx.doi.org/10.3103/s1541308x12030077.

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17

Tkeshelashvili, L., and K. Busch. "Nonlinear three-wave interaction in photonic crystals." Applied Physics B 81, no. 2-3 (July 2005): 225–29. http://dx.doi.org/10.1007/s00340-005-1815-4.

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18

Lagrange, S., H. R. Jauslin, and A. Picozzi. "Thermalization of the dispersive three-wave interaction." Europhysics Letters (EPL) 79, no. 6 (August 21, 2007): 64001. http://dx.doi.org/10.1209/0295-5075/79/64001.

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19

Maslov, V. P., and G. A. Omel'yanov. "Three-wave interaction including frequency doubling effects." Soviet Physics Journal 29, no. 3 (March 1986): 157–75. http://dx.doi.org/10.1007/bf00891878.

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20

Jurčo, Branislav. "Quantum integrable multiple three-wave interaction models." Physics Letters A 143, no. 1-2 (January 1990): 47–51. http://dx.doi.org/10.1016/0375-9601(90)90796-q.

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21

Kurin, V. V. "Origin and interaction of three-wave solitons." Radiophysics and Quantum Electronics 31, no. 10 (October 1988): 853–60. http://dx.doi.org/10.1007/bf01040017.

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22

WEBB, G. M., A. ZAKHARIAN, M. BRIO, and G. P. ZANK. "Wave interactions in magnetohydrodynamics, and cosmic-ray-modified shocks." Journal of Plasma Physics 61, no. 2 (February 1999): 295–346. http://dx.doi.org/10.1017/s0022377898007399.

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Multiple-scales perturbation methods are used to study wave interactions in magnetohydrodynamics (MHD), in one Cartesian space dimension, with application to cosmic-ray-modified shocks. In particular, the problem of the propagation and interaction of short wavelength MHD waves, in a large-scale background flow, modified by cosmic rays is studied. The wave interaction equations consist of seven coupled evolution equations for the backward and forward Alfvén waves, the backward and forward fast and slow magnetoacoustic waves and the entropy wave. In the linear wave regime, the waves are coupled by wave mixing due to gradients in the background flow, cosmic-ray squeezing instability effects, and damping due to the diffusing cosmic rays. In the most general case, the evolution equations also contain nonlinear wave interaction terms due to Burgers self wave steepening for the magnetoacoustic modes, resonant three wave interactions, and mean wave field interaction terms. The form of the wave interaction equations in the ideal MHD case is also discussed. Numerical simulations of the fully nonlinear cosmic ray MHD model equations are compared with spectral code solutions of the linear wave interaction equations for the case of perpendicular, cosmic-ray-modified shocks. The solutions are used to illustrate how the different wave modes can be generated by wave mixing, and the modification of the cosmic ray squeezing instability due to wave interactions. It is shown that the Alfvén waves are coupled to the magnetoacoustic and entropy waves due to linear wave mixing, only in background flows with non-zero field aligned electric current and/or vorticity (i.e. if B·∇×B≠0 and/or B·∇×u≠0, where B and u are the magnetic field induction and fluid velocity respectively).

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23

Gegenhasi, Jun-Xiao Zhao, Xing-Biao Hu, and Hon-Wah Tam. "Pfaffianization of the discrete three-dimensional three wave interaction equation." Linear Algebra and its Applications 407 (September 2005): 277–95. http://dx.doi.org/10.1016/j.laa.2005.05.012.

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24

de Paula, I. B., W. Würz, M. T. Mendonça, and M. A. F. Medeiros. "Interaction of instability waves and a three-dimensional roughness element in a boundary layer." Journal of Fluid Mechanics 824 (July 6, 2017): 624–60. http://dx.doi.org/10.1017/jfm.2017.362.

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The influence of a single roughness element on the evolution of two-dimensional (2-D) Tollmien–Schlichting (TS) waves is investigated experimentally. Experiments are carried out in a region of zero pressure gradient of an airfoil section. Downstream from the disturbance source, TS waves interact with a cylindrical roughness element with a slowly oscillating height. The oscillation frequency of the roughness was approximately 1500 times lower than the wave frequency and approximately 250 times slower than the characteristic time of flow passing the region of transition development. Therefore, the roughness behaved as a quasi-steady disturbance. The set-up enabled us to perform hot-wire measurements phase locked to the waves and to the roughness movement. Experimental results show a scattering of the 2-D waves into oblique ones and a relatively weak distortion of the mean flow for roughness heights as large as 0.2 times the boundary layer displacement thickness ($\unicode[STIX]{x1D6FF}^{\ast }$). Transfer functions for TS wave scattering at the roughness are obtained. Results show an unexpected coincidence in shape with acoustic receptivity functions found in Würz et al. (J. Fluid Mech., vol. 478, 2003, pp. 135–163) for the problem of excitation of TS waves by scattering of acoustic waves at surface roughness. In the present work, the ratio between the incoming 2-D wave amplitude to the amplitude of the scattered oblique waves scaled linearly with the roughness height only for very shallow roughness. For roughness elements higher than $0.08\unicode[STIX]{x1D6FF}^{\ast }$ and below $0.2\unicode[STIX]{x1D6FF}^{\ast }$, the wave scattering exhibited a quadratic variation with respect to the roughness height. In addition, this feature did not vary significantly with respect to TS wave frequency. An analysis of the weakly nonlinear interactions triggered by the roughness element is also carried out, assisted by numerical solution of nonlinear parabolized stability equations, performed for a two-dimensional Blasius boundary layer. A comparison between experiments and simulations reveals that the weakly nonlinear interactions observed are not substantially affected by mean flow distortions that could be produced in the wake of the small and medium sized roughness elements ($h<0.2\unicode[STIX]{x1D6FF}^{\ast }$). From a practical perspective, results suggest that scattering coefficients might be employed to include the effect of isolated and medium sized roughness elements in transition prediction tools developed for smooth surfaces.

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25

TIMOSHIN, S. N., and F. T. SMITH. "Vortex/inflectional-wave interactions with weakly three-dimensional input." Journal of Fluid Mechanics 348 (October 10, 1997): 247–94. http://dx.doi.org/10.1017/s0022112097006447.

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The subtle impact of the spanwise scaling in nonlinear interactions between oblique instability waves and the induced longitudinal vortex field is considered theoretically for the case of a Rayleigh-unstable boundary-layer flow, at large Reynolds numbers. A classification is given of various flow regimes on the basis of Reynolds-stress mechanisms of mean vorticity generation, and a connection between low-amplitude non-parallel vortex/wave interactions and less-low-amplitude non-equilibrium critical-layer flows is discussed in more detail than in previous studies. Two new regimes of vortex/wave interaction for increased spanwise lengthscales are identified and studied. In the first, with the cross-scale just slightly larger than the boundary-layer thickness, the wave modulation is governed by an amplitude equation with a convolution and an ordinary integral term present due to nonlinear contributions from all three Reynolds-stress components in the cross-momentum balance. In the second regime the cross-scale is larger, and the wave modulation is found to be governed by an integral/partial differential equation. In both cases the main-flow non-parallelism contributes significantly to the coupled wave/vortex development.

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26

Kim, D. J., and M. H. Kim. "Wave-Current Interaction with a Large Three-Dimensional Body by THOBEM." Journal of Ship Research 41, no. 04 (December 1, 1997): 273–85. http://dx.doi.org/10.5957/jsr.1997.41.4.273.

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The effects of uniform steady currents (or small forward velocity) on the interaction of a large three-dimensional body with waves are investigated by a time-domain higher-order boundary element method (THOBEM). The current speed is assumed to be small so that the viscous effects and the steady wave system generated by currents are insignificant. Using regular perturbation with two small parameters є and δ associated with wave slope and current velocity, respectively, the boundary value problem is decomposed into the zeroth-order steady double-body-flow problem at 0(δ) with a rigid-wall free-surface condition and the first-order unsteady wave problem with the modified free-surface and body-boundary conditions expanded up to O(eδ). Higher-order boundary integral equation methods are then used to solve the respective problems with the Rankine sources distributed over the entire boundary. The free surface is integrated at each time step by Adams-Bashforth-Moulton method. The Sommerfeld/Orlanski radiation condition is numerically implemented to absorb all the wave energy at the open boundary. To solve the so-called corner problem, discontinuous elements are used at the intersection of free-surface and radiation boundaries Using the developed numerical method, wave forces, wave field and run-up, mean drift forces and wave drift damping are calculated.

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27

Larsson, Jonas. "Hamiltonian Theory for Waves and the Resonant Three-Wave Interaction Process." Physica Scripta T75, no. 1 (1998): 173. http://dx.doi.org/10.1238/physica.topical.075a00173.

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28

Schifino, A. C. Sicardi, and R. Montagne. "Nonlinear three-wave interaction description for a global drift wave turbulence." Physica Scripta 47, no. 2 (February 1, 1993): 244–49. http://dx.doi.org/10.1088/0031-8949/47/2/021.

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29

Huang, Guoxiang. "Exact solitary wave solutions of three-wave interaction equations with dispersion." Journal of Physics A: Mathematical and General 33, no. 47 (November 17, 2000): 8477–82. http://dx.doi.org/10.1088/0305-4470/33/47/310.

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30

Williamson, C. H. K., and A. Prasad. "A new mechanism for oblique wave resonance in the ‘natural’ far wake." Journal of Fluid Mechanics 256 (November 1993): 269–313. http://dx.doi.org/10.1017/s0022112093002794.

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There has been some debate recently on whether the far-wake structure downstream of a cylinder is dependent on, or ‘connected’ with, the precise details of the near-wake structure. Indeed, it has previously been suggested that the far-wake scale and frequency are unconnected with those of the near wake. In the present paper, we demonstrate that both the far-wake scale and frequency are dependent on the near wake. Surprisingly, the characteristic that actually forges a ‘connection’ between the near and far wakes is the sensitivity to free-stream disturbances. It is these disturbances that are also responsible for the regular three-dimensional patterns that may be visualized. Observations of a regular ‘honeycomb’-like three-dimensional pattern in the far wake is found to be caused by an interaction between oblique shedding waves from upstream and large-scale two-dimensional waves, amplified from the free-stream disturbances. The symmetry and spanwise wavelength of Cimbala, Nagib & Roshko's (1988) three-dimensional pattern are precisely consistent with such wave interactions. In the presence of parallel shedding, the lack of a honeycomb pattern shows that such a three-dimensional pattern is clearly dependent on upstream oblique vortex shedding.With the deductions above as a starting point, we describe a new mechanism for the resonance of oblique waves, as follows. In the case of two-dimensional waves, corresponding to a very small spectral peak in the free stream (fT) interacting (quadratically) with the oblique shedding waves frequency (fK), it appears that the most amplified or resonant frequency in the far wake is a combination frequency fFW = (fK–fT), which corresponds physically with ‘oblique resonance waves’ at a large oblique angle. The large scatter in (fFW/fK) from previous studies is principally caused by the broad response of the far wake to a range of free-stream spectral peaks (fT). We present clear visualization of the oblique wave phenomenon, coupled with velocity measurements which demonstrate that the secondary oblique wave energy can far exceed the secondary two-dimensional wave energy by up to two orders of magnitude. Further experiments show that, in the absence of an influential free-stream spectral peak, the far wake does not resonate, but instead has a low-amplitude broad spectral response. The present phenomena are due to nonlinear instabilities in the far wake, and are not related to vortex pairing. There would appear to be distinct differences between this oblique wave resonance and the subharmonic resonances that have been previously studied in channel flow, boundary layers, mixing layers and airfoil wakes.

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31

PORTER, R., and D. PORTER. "Interaction of water waves with three-dimensional periodic topography." Journal of Fluid Mechanics 434 (May 10, 2001): 301–35. http://dx.doi.org/10.1017/s0022112001003676.

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The scattering and trapping of water waves by three-dimensional submerged topography, infinite and periodic in one horizontal coordinate and of finite extent in the other, is considered under the assumptions of linearized theory. The mild-slope approximation is used to reduce the governing boundary value problem to one involving a form of the Helmholtz equation in which the coefficient depends on the topography and is therefore spatially varying.Two problems are considered: the scattering by the topography of parallel-crested obliquely incident waves and the propagation of trapping modes along the periodic topography. Both problems are formulated in terms of ‘domain’ integral equations which are solved numerically.Trapped waves are found to exist over any periodic topography which is ‘sufficiently’ elevated above the unperturbed bed level. In particular, every periodic topography wholly elevated above that level supports trapped waves. Fundamental differences are shown to exist between these trapped waves and the analogous Rayleigh–Bloch waves which exist on periodic gratings in acoustic theory.Results computed for the scattering problem show that, remarkably, there exist zeros of transmission at discrete wavenumbers for any periodic bed elevation and for all incident wave angles. One implication of this property is that total reflection of an incident wave of a particular frequency will occur in a channel with a single symmetric elevation on the bed. The zeros of transmission in the scattering problem are shown to be related to the presence of a ‘nearly trapped’ mode in the corresponding homogeneous problem.The scattering of waves by multiple rows of periodic topography is also considered and it is shown how Bragg resonance – well-established in scattering of waves by two-dimensional ripple beds – occurs in modes other than the input mode.

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32

Lindgren, T., L. Stenflo, N. Kostov, and I. Zhelyazkov. "Three-wave interaction in a cold plasma column." Journal of Plasma Physics 34, no. 3 (December 1985): 427–34. http://dx.doi.org/10.1017/s0022377800002981.

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We derive the coupled-mode equations for the non-resonant interaction of three high-frequency surface waves propagating along a cold plasma column with sharp movable boundary. The plasma is then supposed to be surrounded by vacuum. Our boundary conditions take into account the effects of the presence of surface charges, as well as the movements of the boundary. The coupling coefficients are expressed in explicit forms and compared with previous results.

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33

Hughes, David W., and Michael R. E. Proctor. "Nonlinear three-wave interaction with non-conservative coupling." Journal of Fluid Mechanics 244, no. -1 (November 1992): 583. http://dx.doi.org/10.1017/s0022112092003203.

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34

Škorić, M. M., T. Sato, A. Maluckov, and M. S. Jovanović. "Self-organization in a dissipative three-wave interaction." Physical Review E 60, no. 6 (December 1, 1999): 7426–34. http://dx.doi.org/10.1103/physreve.60.7426.

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35

Ibragimov, E., A. A. Struthers, D. J. Kaup, J. D. Khaydarov, and K. D. Singer. "Three-wave interaction solitons in optical parametric amplification." Physical Review E 59, no. 5 (May 1, 1999): 6122–37. http://dx.doi.org/10.1103/physreve.59.6122.

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36

Ohkuma, Kenji. "Thermodynamics of the Quantum Three Wave Interaction Model." Journal of the Physical Society of Japan 54, no. 8 (August 15, 1985): 2817–28. http://dx.doi.org/10.1143/jpsj.54.2817.

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37

ZHAO, HONGWEI, WU-MING LIU, YUPENG WANG, and FU-CHO PU. "EXACT SOLUTIONS FOR QUANTUM THREE WAVE INTERACTION SYSTEM." International Journal of Modern Physics B 10, no. 21 (September 30, 1996): 2639–50. http://dx.doi.org/10.1142/s021797929600115x.

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The exact eigenstates of the Hamiltonian for a quantum three wave interaction system are constructed by using the Bethe ansatz. The Bethe-ansatz equations are obtained from the periodic boundary conditions.

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38

Chow, Carson C., A. Bers, and A. K. Ram. "Spatiotemporal chaos in the nonlinear three-wave interaction." Physical Review Letters 68, no. 23 (June 8, 1992): 3379–82. http://dx.doi.org/10.1103/physrevlett.68.3379.

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39

Ibragimov, Edem. "All-optical switching using three-wave-interaction solitons." Journal of the Optical Society of America B 15, no. 1 (January 1, 1998): 97. http://dx.doi.org/10.1364/josab.15.000097.

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40

Mondal, R., and T. Sahoo. "Wave structure interaction problems in three-layer fluid." Zeitschrift für angewandte Mathematik und Physik 65, no. 2 (October 6, 2013): 349–75. http://dx.doi.org/10.1007/s00033-013-0368-3.

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41

Kaup, D. J., and Boris A. Malomed. "Three-wave resonant interaction in a thin layer." Physics Letters A 183, no. 4 (December 1993): 283–88. http://dx.doi.org/10.1016/0375-9601(93)90457-b.

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42

Leo, M., R. A. Leo, G. Soliani, and L. Martina. "Prolongation theory of the three-wave resonant interaction." Il Nuovo Cimento B Series 11 88, no. 2 (August 1985): 81–101. http://dx.doi.org/10.1007/bf02728892.

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43

Bandilla, A., G. Drobný, and I. Jex. "Phase-space motion in parametric three-wave interaction." Optics Communications 128, no. 4-6 (July 1996): 353–62. http://dx.doi.org/10.1016/0030-4018(96)00136-8.

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44

Grue, John. "Nonlinear interfacial wave formation in three dimensions." Journal of Fluid Mechanics 767 (February 23, 2015): 735–62. http://dx.doi.org/10.1017/jfm.2015.42.

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AbstractA three-dimensional two-layer, fully dispersive and strongly nonlinear interfacial wave model, including the interaction with a time-varying bottom topography, is developed. The method is based on a set of integral equations. The source and dipole terms are developed in series expansions in the vertical excursions of the interface and bottom topography, obtaining explicit inversion by Fourier transform. Calculations of strongly nonlinear interfacial waves with excursions comparable to the thinner layer depth show that the quadratic approximation of the method contains the essential dynamics, while the additional cubic terms always are small. Computations confirm the onset of wave train formation driven by topography, observed in experiments (Maxworthy, J. Geophys. Res., vol. 84(C1), 1979, pp. 338–346), depending on the Froude number and the topography height. Simulations of tidally driven three-dimensional internal wave formation show the formation of two wave trains per half tidal cycle for strong forcing and one wave train for weak forcing. Waves of both backward and forward curvature are calculated.

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45

Cheng, Chong-Dong, Bo Tian, Cong-Cong Hu, and Xin Zhao. "Hybrid solutions of a (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation in an incompressible fluid." International Journal of Modern Physics B 35, no. 17 (July 10, 2021): 2150126. http://dx.doi.org/10.1142/s0217979221501265.

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Incompressible fluids are studied in such disciplines as ocean engineering, astrophysics and aerodynamics. Under investigation in this paper is a [Formula: see text]-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation in an incompressible fluid. Based on the known bilinear form, BLMP hybrid solutions comprising a lump wave, a periodic wave and two kink waves, and hybrid solutions comprising a breather wave and multi-kink waves are derived. We observe the interaction among a lump wave, a periodic wave and two kink waves. Fission of a kink wave is observed: A kink wave divides into a breather wave and three kink waves. On the contrary, we see the fusion among a breather wave and three kink waves: The breather wave and three kink waves merge into a kink wave. Finally, we observe the interaction among a breather wave and four kink waves.

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Gegenhasi and Zhaowen Yan. "Discrete three-dimensional three wave interaction equation with self-consistent sources." Frontiers of Mathematics in China 11, no. 6 (April 12, 2016): 1501–13. http://dx.doi.org/10.1007/s11464-016-0522-2.

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VOITENKO, Yu M. "Three-wave coupling and weak turbulence of kinetic Alfvén waves." Journal of Plasma Physics 60, no. 3 (October 1998): 515–27. http://dx.doi.org/10.1017/s0022377898007107.

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The nonlinear dynamics of kinetic-Alfvén–wave (KAW) turbulence is studied. Weak KAW turbulence induced by three-wave interaction among parallel-propagating KAWs has a direct energy cascade in the wavenumber domain ks⊥>ρ−1i and an inverse cascade in the domain ks⊥<ρ−1i, resulting in Kolmogorov-type spectra, Wk∼(kz) −1/2(k⊥)−p, with exponents p=4 and p=3.5 respectively. The interaction including antiparallel-propagating KAWs, usually most effective, results in an inverse energy cascade over the whole k⊥ range and p=2 (at k⊥<ρ−1i) and p=3.5 (for k⊥>ρ−1i) spectra. Three applications concerning KAW turbulence in flaring loops, in the Earth's magnetosphere and in tokamaks are considered. It is suggested that turbulent KAW spectra are common in space plasmas.

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VOITENKO, Yu M. "Three-wave coupling and parametric decay of kinetic Alfvén waves." Journal of Plasma Physics 60, no. 3 (October 1998): 497–514. http://dx.doi.org/10.1017/s0022377898007090.

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The dynamic equation and coupling coefficient of the three-wave interaction among kinetic Alfvén waves (KAWs) are derived by use of plasma kinetic theory. Linear and nonlinear effects of finite ion Larmor radius are kept for arbitrary value of the ‘kinetic variable’ κ=k⊥ρi. The parametric decay KAW→KAW+KAWis investigated and the threshold amplitude for decay instability in a Maxwellian plasma is calculated. The growth rate of decay instability varies as k2⊥ in both limits κ2[Lt ]1 and κ2[Gt ]1. The main tendency of KAWs is towards nonlinear destabilization at very low wave amplitudes Bk/B0[lsim ]10−3. Two applications concerning KAW dynamics in the magnetosphere and in the solar corona show that three-wave resonant interaction among KAWs may be responsible for the turbulent character of their behaviour, often observed in space plasmas.

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Li, Zhisong, Kirti Ghia, Ye Li, Zhun Fan, and Lian Shen. "Unsteady Reynolds-averaged Navier–Stokes investigation of free surface wave impact on tidal turbine wake." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2246 (February 2021): 20200703. http://dx.doi.org/10.1098/rspa.2020.0703.

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Tidal current is a promising renewable energy source. Previous studies have investigated the influence of surface waves on tidal turbines in many aspects. However, the turbine wake development in a surface wave environment, which is crucial for power extraction in a turbine array, remains elusive. In this study, we focus on the wake evolution behind a single turbine and its interaction with surface waves. A numerical solver is developed to study the effects of surface waves on an industrial-size turbine. A case without surface wave and two cases with waves and different rotor depths are investigated. We obtain three-dimensional flow field descriptions near the free surface, around the rotor, and in the near- and far-wake. In a comparative analysis, the time-averaged and instantaneous flow fields are examined for various flow characteristics, including momentum restoration, power output, free surface elevation and vorticity dynamics. A model reduction technique is employed to identify the coherent flow structures and investigate the spatial and temporal characteristics of the wave–wake interactions. The results indicate the effect of surface waves in augmenting wake restoration and reveal the interactions between the surface waves and the wake structure, through a series of dynamic processes and the Kelvin–Helmholtz instability.

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Usui, H., H. Matsumoto, and R. Gendrin. "Numerical simulations of a three-wave coupling occurring in the ionospheric plasma." Nonlinear Processes in Geophysics 9, no. 1 (February 28, 2002): 1–10. http://dx.doi.org/10.5194/npg-9-1-2002.

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Abstract. We studied a three-wave coupling process occurring in an active experiment of microwave power transmission (MPT) in the ionospheric plasma by performing one-dimensional electromagnetic PIC (Particle-In-Cell) simulations. In order to examine the spatial variation of the coupling process, we continuously emitted intense electromagnetic waves from an antenna located at a simulation boundary. In the three-wave coupling, a low-frequency electrostatic wave is excited as the result of a nonlinear interaction between the forward propagating pump wave and backscattered wave. In the simulations, low-frequency electrostatic bursts are discontinuously observed in space. The discontinuity of the electrostatic bursts is accounted for by the local electron heating due to the bursts and the associated modification of the wave dispersion relation. In a case where the pump wave propagates along the geomagnetic field Bext , several bursts of Langmuir waves are observed. Since the first burst consumes a part of the pump wave energy, the pump wave is weakened and cannot trigger the three-wave coupling beyond the region where the burst occurs. Since the dispersion relation of the Langmuir wave is variable, due to the local electron heating by the burst, the coupling condition eventually becomes unsatisfied and the first interaction becomes weak. Another burst of Langmuir waves is observed at a different region beyond the location of the first burst. In the case of perpendicular propagation, the upper hybrid wave, one of the mode branches of the electron cyclotron harmonic waves, is excited. Since the dispersion relation of the upper hybrid wave is less sensitive to the electron temperature, the coupling condition is not easily violated by the temperature increase. As a result, the three-wave coupling periodically takes place in time and eventually, the transmission ratio of the microwaves becomes approximately 20%, while almost no attenuation of the pump waves is observed after the first electrostatic burst in the parallel case. We also examined the dependency of the temporal growth rate for the electrostatic waves on the amplitude of the pump wave.

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