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1

Oh, C. H., and Rosy Teh. "Nonabelian progressive waves." Journal of Mathematical Physics 26, no. 4 (April 1985): 841–44. http://dx.doi.org/10.1063/1.526576.

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2

Utkin, Andrei B. "Mathieu Progressive Waves." Communications in Theoretical Physics 56, no. 4 (October 2011): 733–39. http://dx.doi.org/10.1088/0253-6102/56/4/23.

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3

Becker, Janet M., and John W. Miles. "Progressive radial cross-waves." Journal of Fluid Mechanics 245, no. -1 (December 1992): 29. http://dx.doi.org/10.1017/s0022112092000338.

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4

Miles, John, and Janet Becker. "Parametrically excited, progressive cross-waves." Journal of Fluid Mechanics 186 (January 1988): 129–46. http://dx.doi.org/10.1017/s0022112088000072.

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The variational formulation of the nonlinear wavemaker problem, previously applied (Miles 1988) to cross-waves in a short tank, is extended to allow for slow spatial, as well as slow temporal, variation of cross-waves in a long tank. The resulting evolution equations for the envelope of the cross-waves are equivalent to those derived by Jones (1984) and may be combined to obtain a cubic Schrödinger equation in a semi-infinite domain. The corresponding criterion for the stability of plane waves (i.e. for the temporal decay of cross-waves) agrees with Jones but differs from Mahony (1972). Weak damping is incorporated, and those stationary envelopes that are evanescent at large distances from the wavemaker are determined through analytical approximations and numerical integration and compared with the experimental observations of Barnard & Pritchard (1972) and the numerical calculations of Lichter & Chen (1987). These comparisons suggest that stationary envelopes with either no or one maximum are stable for sufficiently small amplitudes (solutions with multiple maxima may be stable but more difficult to attain) and evolve into limit cycles for somewhat larger amplitudes, but the analytical question of stability remains open.
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5

Peregrine, D. H. "Tables of Progressive Gravity Waves." Applied Ocean Research 9, no. 1 (January 1987): 53. http://dx.doi.org/10.1016/0141-1187(87)90032-0.

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6

Shakhin, Victor M., and Tatiana V. Shakhina. "COMPENSATORY REVERSE FLOW OF PROGRESSIVE WAVES WITH FINITE AMPLITUDE." Coastal Engineering Proceedings, no. 35 (June 23, 2017): 9. http://dx.doi.org/10.9753/icce.v35.waves.9.

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This paper is devoted to problem of mass transport of fluid for the surface progressive waves. Both Stokes and cnoidal waves are considered. New solutions for the transitional current are obtained. It is discovered that the mass transport of fluid in the direction of wave propagation exists only in the top layer. In the underlying layers a compensatory reverse flow is formed. The existence of a compensatory flow was verified experimentally. It is revealed that theoretical results duly conform to experimental data.
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7

Restrepo, Juan M., and Jorge M. Ramirez. "Transport due to Transient Progressive Waves." Journal of Physical Oceanography 49, no. 9 (September 2019): 2323–36. http://dx.doi.org/10.1175/jpo-d-19-0087.1.

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AbstractMaking use of a Lagrangian description, we interpret the kinematics and analyze the mean transport due to numerically generated transient progressive waves, including breaking waves. The waves are packets and are generated with a boundary-forced, air–water, two-phase Navier–Stokes solver. These transient waves produce transient transport, which can sometimes be larger than what would be estimated using estimates developed for translationally invariant progressive waves. We identify the critical assumption that makes our standard notion of the steady Stokes drift inapplicable to the data and explain how and in what sense the transport due to transient waves can be larger than the steady counterpart. A comprehensive analysis of the data in the Lagrangian framework leads us to conclude that much of the transport can be understood using an irrotational approximation of the velocity, even though the simulations use Navier–Stokes fluid simulations with moderately high Reynolds numbers. Armed with this understanding, it is possible to formulate a simple Lagrangian model that captures the mean transport and variance of transport for a large range of wave amplitudes. For large-amplitude waves, the parcel paths in the neighborhood of the free surface exhibit increased dispersion and lingering transport due to the generation of vorticity. We examined the wave-breaking case. For this case, it is possible to characterize the transport very well, away from the wave boundary layer, and approximately using a simple model that captures the unresolved breaking dynamics via a stochastic parameterization.
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8

Stiassnie, Michael, and Raphael Stuhlmeier. "Progressive waves on a blunt interface." Discrete & Continuous Dynamical Systems - A 34, no. 8 (2014): 3171–82. http://dx.doi.org/10.3934/dcds.2014.34.3171.

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9

Kalinichenko, V. A., and S. Ya Sekerzh-Zen’kovich. "Excitation of progressive-standing faraday waves." Doklady Physics 56, no. 6 (June 2011): 343–47. http://dx.doi.org/10.1134/s1028335811060024.

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10

Abohadima, Samir, and Masahiko Isobe. "Limiting criteria of permanent progressive waves." Coastal Engineering 44, no. 3 (January 2002): 231–37. http://dx.doi.org/10.1016/s0378-3839(01)00033-3.

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11

Kong, William Chin‐Hwa. "Progressive surface waves in elliptical channels." Journal of the Chinese Institute of Engineers 9, no. 1 (January 1986): 9–17. http://dx.doi.org/10.1080/02533839.1986.9676856.

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12

Andrade, Marco A. B., Flávio Buiochi, and Julio C. Adamowski. "Particle manipulation by ultrasonic progressive waves." Physics Procedia 3, no. 1 (January 2010): 283–88. http://dx.doi.org/10.1016/j.phpro.2010.01.038.

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13

McHugh, John. "Progressive Internal Waves of Permanent Form." SIAM Journal on Applied Mathematics 70, no. 4 (January 2009): 1017–31. http://dx.doi.org/10.1137/08073281x.

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14

Wu, Chung‐Shang, and E. B. Thornton. "Wave Numbers of Linear Progressive Waves." Journal of Waterway, Port, Coastal, and Ocean Engineering 112, no. 4 (July 1986): 536–40. http://dx.doi.org/10.1061/(asce)0733-950x(1986)112:4(536).

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15

Bettess, Peter, and Edmund Chadwick. "Wave envelope examples for progressive waves." International Journal for Numerical Methods in Engineering 38, no. 15 (August 15, 1995): 2487–508. http://dx.doi.org/10.1002/nme.1620381502.

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16

Ambika, K., R. Radha, and V. D. Sharma. "Progressive waves in non-ideal gases." International Journal of Non-Linear Mechanics 67 (December 2014): 285–90. http://dx.doi.org/10.1016/j.ijnonlinmec.2014.09.012.

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17

Ioualalen, Mansour, and Christian Kharif. "On the subharmonic instabilities of steady three-dimensional deep water waves." Journal of Fluid Mechanics 262 (October 3, 1994): 265–91. http://dx.doi.org/10.1017/s0022112094000509.

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A numerical procedure has been developed to study the linear stability of nonlinear three-dimensional progressive gravity waves on deep water. The three-dimensional patterns considered herein are short-crested waves which may be produced by two progressive plane waves propagating at an oblique angle, γ, to each other. It is shown that for moderate wave steepness the dominant resonances are sideband-type instabilities in the direction of propagation and, depending on the value of γ, also in the transverse direction. It is also shown that three-dimensional progressive gravity waves are less unstable than two-dimensional progressive gravity waves.
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18

Hill, D. F., and M. A. Foda. "Subharmonic resonance of short internal standing waves by progressive surface waves." Journal of Fluid Mechanics 321 (August 25, 1996): 217–33. http://dx.doi.org/10.1017/s0022112096007707.

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Experimental evidence and a theoretical formulation describing the interaction between a progressive surface wave and a nearly standing subharmonic internal wave in a two-layer system are presented. Laboratory investigations into the dynamics of an interface between water and a fluidized sediment bed reveal that progressive surface waves can excite short standing waves at this interface. The corresponding theoretical analysis is second order and specifically considers the case where the internal wave, composed of two oppositely travelling harmonics, is much shorter than the surface wave. Furthermore, the analysis is limited to the case where the internal waves are small, so that only the initial growth is described. Approximate solution to the nonlinear boundary value problem is facilitated through a perturbation expansion in surface wave steepness. When certain resonance conditions are imposed, quadratic interactions between any two of the harmonics are in phase with the third, yielding a resonant triad. At the second order, evolution equations are derived for the internal wave amplitudes. Solution of these equations in the inviscid limit reveals that, at this order, the growth rates for the internal waves are purely imaginary. The introduction of viscosity into the analysis has the effect of modifying the evolution equations so that the growth rates are complex. As a result, the amplitudes of the internal waves are found to grow exponentially in time. Physically, the viscosity has the effect of adjusting the phase of the pressure so that there is net work done on the internal waves. The growth rates are, in addition, shown to be functions of the density ratio of the two fluids, the fluid layer depths, and the surface wave conditions.
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19

Kobayashi, K., and H. Okamoto. "Uniqueness Issues on Permanent Progressive Water-Waves." Journal of Nonlinear Mathematical Physics 11, no. 4 (January 2004): 472–79. http://dx.doi.org/10.2991/jnmp.2004.11.4.4.

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20

Troy, C. D., and J. R. Koseff. "The viscous decay of progressive interfacial waves." Physics of Fluids 18, no. 2 (February 2006): 026602. http://dx.doi.org/10.1063/1.2166849.

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21

Mok, K. M., and Harry Yeh. "On mass transport of progressive edge waves." Physics of Fluids 11, no. 10 (October 1999): 2906–24. http://dx.doi.org/10.1063/1.870149.

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22

FRINGER, OLIVER B., and ROBERT L. STREET. "The dynamics of breaking progressive interfacial waves." Journal of Fluid Mechanics 494 (November 10, 2003): 319–53. http://dx.doi.org/10.1017/s0022112003006189.

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23

Law, Adrian Wing-Keung, Siu-Kui Au, and Jie Song. "Stochastic diffusion by progressive waves in turbulence." Journal of Hydrodynamics 22, S1 (October 2010): 588–93. http://dx.doi.org/10.1016/s1001-6058(10)60001-7.

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24

Ignaczak, Jozef. "Plane Progressive Heat Waves in Metal Films." Journal of Thermal Stresses 35, no. 1-3 (January 2012): 48–60. http://dx.doi.org/10.1080/01495739.2012.637459.

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25

Yeh, Harry H. "Nonlinear progressive edge waves: their instability and evolution." Journal of Fluid Mechanics 152 (March 1985): 479–99. http://dx.doi.org/10.1017/s0022112085000799.

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The fundamental properties of nonlinear progressive edge waves are investigated experimentally in a physical model with a uniformly and mildly sloping beach with a straight shoreline. An evolution equation for the envelope of progressive edge waves is the nonlinear Schrödinger (NLS) equation. It is found that the timescale of viscous-dissipation effects in the experiments is comparable with the timescale of the theoretical evolution process for inviscid progressive edge waves. This lack of timescale separation indicates a major shortcoming of the NLS equation as a model of the laboratory experiments. Even with this limitation, a uniform train of edge waves is found to be unstable to a modulational perturbation as predicted by the NLS equation. However, behaviour of the evolution is both qualitatively and quantitatively different from the theoretical predictions. The evolution of the periodogram for the unstable wavetrain shows an asymmetric development of the sidebands about the fundamental frequency; instability growth is limited to the lower sideband. This behaviour leads to a sequential shift of wave energy to lower frequencies as the waves propagate. It is found that a locally soliton-shaped wave packet is unstable in the laboratory environment. It is estimated that a much-larger-scale experimental facility is required to achieve inviscid experiments for the NLS equation.
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26

Chiriţă, Stan, and Ionel-Dumitrel Ghiba. "Strong ellipticity and progressive waves in elastic materials with voids." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2114 (October 21, 2009): 439–58. http://dx.doi.org/10.1098/rspa.2009.0360.

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In the present paper, we investigate a model for propagating progressive waves associated with the voids within the framework of a linear theory of porous media. Owing to the use of lighter materials in modern buildings and noise concerns in the environment, such models for progressive waves are of much interest to the building industry. The analysis of such waves is also of interest in acoustic microscopy where the identification of material defects is of paramount importance to the industry and medicine. Our analysis is based on the strong ellipticity of the poroelastic materials. We illustrate the model of progressive wave propagation for isotropic and transversely isotropic porous materials. We also study the propagation of harmonic plane waves in porous materials including the thermal effect.
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27

RAVAL, ASHISH, XIANYUN WEN, and MICHAEL H. SMITH. "Numerical simulation of viscous, nonlinear and progressive water waves." Journal of Fluid Mechanics 637 (September 23, 2009): 443–73. http://dx.doi.org/10.1017/s002211200999070x.

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A numerical simulation is performed to study the velocity, streamlines, vorticity and shear stress distributions in viscous water waves with different wave steepness in intermediate and deep water depth when the average wind velocity is zero. The numerical results present evidence of ‘clockwise’ and ‘anticlockwise’ rotation of the fluid at the trough and crest of the water waves. These results show thicker vorticity layers near the surface of water wave than that predicted by the theories of inviscid rotational flow and the low Reynolds number viscous flow. Moreover, the magnitude of vorticity near the free surface is much larger than that predicted by these theories. The analysis of the shear stress under water waves show a thick shear layer near the water surface where large shear stress exists. Negative and positive shear stresses are observed near the surface below the crest and trough of the waves, while the maximum positive shear stress is inside the water and below the crest of the water wave. Comparison of wave energy decay rate in intermediate depth and deep water waves with laboratory and theoretical results are also presented.
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28

Li, Meng, Ze Zhao, Yajat Pandya, Giacomo Iungo, and Di Yang. "Large-Eddy Simulations of Oil Droplet Aerosol Transport in the Marine Atmospheric Boundary Layer." Atmosphere 10, no. 8 (August 12, 2019): 459. http://dx.doi.org/10.3390/atmos10080459.

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In this study, a hybrid large-eddy simulation (LES) model is developed and applied to simulate the transport of oil droplet aerosols in wind over progressive water waves. The LES model employs a hybrid spectral and finite difference method for simulating the wind turbulence and a bounded finite-volume method for modeling the oil aerosol transport. Using a wave-following coordinate system and computational grid, the LES model captures the turbulent flow and oil aerosol fields in the region adjacent to the unsteady wave surface. A flat-surface case with prescribed roughness (representing a pure wind-sea) and a wavy-surface case with regular plane progressive 100 m long waves (representing long-crest long-wavelength ocean swells) are considered to illustrate the capability of the LES model and study the effects of long progressive waves on the transport of oil droplet aerosols with four different droplet diameters. The simulation results and statistical analysis reveal enhanced suspension of oil droplets in wind turbulence due to strong disturbance from the long progressive waves. The spatial distribution of the aerosol concentration also exhibits considerable streamwise variations that correlate with the phase of the long progressive waves.
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29

Shin, JangRyong. "An Analytical Solution for Regular Progressive Water Waves." Journal of Advanced Research in Ocean Engineering 1, no. 3 (September 30, 2015): 157–67. http://dx.doi.org/10.5574/jaroe.2015.1.3.157.

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30

Sobey, Rodney J. "Steep progressive waves in deep and shallow water." Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics 165, no. 3 (September 2012): 181–200. http://dx.doi.org/10.1680/eacm.10.00013.

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31

Okamoto, Hisashi. "Interfacial progressive water waves---a singularity-theoretic view." Tohoku Mathematical Journal 49, no. 1 (1997): 33–57. http://dx.doi.org/10.2748/tmj/1178225184.

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32

Pei, Zhiyong, Tao Xu, and Weiguo Wu. "Progressive Collapse Test of Ship Structures in Waves." Polish Maritime Research 25, s3 (December 1, 2018): 91–98. http://dx.doi.org/10.2478/pomr-2018-0117.

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Abstract The external loads and structural ultimate strength are two important aspects for the safety of ship hull girder. It may collapse in case the structural capacity is less than the external forces in extreme seas. In the present research, progressive collapse test is performed to investigate the collapse mechanism of ship structure in waves. External load with time history and corresponding structural collapse behavior are measured and discussed to demonstrate the interaction of fluid and structures.
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33

Ishimi, Kosaku, and Sadatoshi Koroyasu. "Gas Absorption into Liquid Flowing with Progressive Waves." JOURNAL OF CHEMICAL ENGINEERING OF JAPAN 31, no. 1 (1998): 138–41. http://dx.doi.org/10.1252/jcej.31.138.

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34

Rendón, Pablo L., Felipe Orduña-Bustamante, Daniela Narezo, Antonio Pérez-López, and Jacques Sorrentini. "Nonlinear progressive waves in a slide trombone resonator." Journal of the Acoustical Society of America 127, no. 2 (February 2010): 1096–103. http://dx.doi.org/10.1121/1.3277221.

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35

Bryant, P. J. "Doubly periodic progressive permanent waves in deep water." Journal of Fluid Mechanics 161, no. -1 (December 1985): 27. http://dx.doi.org/10.1017/s0022112085002804.

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36

Bryant, Peter J. "Nonlinear progressive free waves in a circular basin." Journal of Fluid Mechanics 205, no. -1 (August 1989): 453. http://dx.doi.org/10.1017/s0022112089002107.

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37

Chapalain, Georges, Raymond Cointe, and Andre Temperville. "Observed and modeled resonantly interacting progressive water-waves." Coastal Engineering 16, no. 3 (February 1992): 267–300. http://dx.doi.org/10.1016/0378-3839(92)90045-v.

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38

Chadwick, Edmund, and Peter Bettess. "Modelling of progressive short waves using wave envelopes." International Journal for Numerical Methods in Engineering 40, no. 17 (September 15, 1997): 3229–45. http://dx.doi.org/10.1002/(sici)1097-0207(19970915)40:17<3229::aid-nme209>3.0.co;2-8.

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39

Nejoh, Y. "New spiky solitary waves, explosive modes and periodic progressive waves in a magnetised plasma." Journal of Physics A: Mathematical and General 23, no. 11 (June 7, 1990): 1973–84. http://dx.doi.org/10.1088/0305-4470/23/11/021.

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40

Grimshaw, R. H. J., and D. I. Pullin. "Stability of finite-amplitude interfacial waves. Part 1. Modulational instability for small-amplitude waves." Journal of Fluid Mechanics 160 (November 1985): 297–315. http://dx.doi.org/10.1017/s0022112085003494.

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In two previous papers (Pullin & Grimshaw 1983a, b) we studied the wave profile and other properties of finite-amplitude interfacial progressive waves in a two-layer fluid. In this and the following paper (Pullin & Grimshaw 1985) we discuss the stability of these waves to small perturbations. In this paper we obtain anatytical results for the long-wavelength modulational instability of small-amplitude waves. Using a multiscale expansion, we obtain a nonlinear Schrödinger equation coupled to a wave-induced mean-flow equation to describe slowly modulated waves. From these coupled equations we determine the stability of a plane progressive wave. Our results are expressed by determining the instability bands in the (p, q)-plane, where (p, q) is the modulation wavenumber, and are obtained for a range of values of basic density ratio and undisturbed layer depths.
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41

Yang, Ray-Yeng, and Hwung Hweng Hwung. "Combination Mode of Internal Waves Generated by Surface Wave Propagating over Two Muddy Sea Beds." Advances in Mathematical Physics 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/183503.

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When surface wave propagating over the two layer system usually induces internal wave in three different modes: they are external, internal and combination. In the present study, the nonlinear response of an initially flat sea bed, with two muddy sections, to a monochromatic surface progressive wave was investigated. From this theoretical result, it shows that a surface water wave progressing over two different muddy sections, the surface wave will excite two opposite-traveling short interfacial waves, forming a nearly standing wave at the interface of the fresh water and the muddy layer. Meanwhile, two opposite-outgoing “mud” waves each with very long wavelength will be simultaneously induced at the interface of two muddy sections. As a result, the amplitudes of the two short internal waves are found to grow exponentially in time. Furthermore, it will be much difficult to excite the internal waves when surface water wave progressing over two muddy sections with the large density gap.
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42

Wang, Zhan. "A universal bifurcation mechanism arising from progressive hydroelastic waves." Theoretical and Applied Mechanics Letters 12, no. 1 (January 2022): 100315. http://dx.doi.org/10.1016/j.taml.2021.100315.

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43

Sekiguchi, Hideo, Katsutoshi Kita, and Shinji Sassa. "Generation of Nearly Progressive Fluid Waves in a Centrifuge." PROCEEDINGS OF CIVIL ENGINEERING IN THE OCEAN 11 (1995): 7–12. http://dx.doi.org/10.2208/prooe.11.7.

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44

Larsen, Bjarke Eltard, David R. Fuhrman, and Johan Roenby. "Performance of interFoam on the simulation of progressive waves." Coastal Engineering Journal 61, no. 3 (May 9, 2019): 380–400. http://dx.doi.org/10.1080/21664250.2019.1609713.

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45

Chen, Yang-Yih, Bin-Da Yang, Lin-Wu Tang, Shan-Hwei Ou, and John R. C. Hsu. "Transformation of Progressive Waves Propagating Obliquely on Gentle Slope." Journal of Waterway, Port, Coastal, and Ocean Engineering 130, no. 4 (July 2004): 162–69. http://dx.doi.org/10.1061/(asce)0733-950x(2004)130:4(162).

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46

Chaney, RC, KR Demars, H. Sekiguchi, K. Kita, S. Sassa, and T. Shimamura. "Generation of Progressive Fluid Waves in a Geo-Centrifuge." Geotechnical Testing Journal 21, no. 2 (1998): 95. http://dx.doi.org/10.1520/gtj10747j.

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47

Coulouvrat, Francois. "A shock‐fitting method for general nonlinear progressive waves." Journal of the Acoustical Society of America 125, no. 4 (April 2009): 2601. http://dx.doi.org/10.1121/1.4783899.

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48

Callaghan, T. G., and L. K. Forbes. "Computing large-amplitude progressive Rossby waves on a sphere." Journal of Computational Physics 217, no. 2 (September 2006): 845–65. http://dx.doi.org/10.1016/j.jcp.2006.01.035.

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49

KIHARA, Naoto, Hideshi HANAZAKI, Hiromasa UEDA, and Toru MIZUYA. "Turbulence Structure in the Airflow Over Progressive Wind Waves." Transactions of the Japan Society of Mechanical Engineers Series B 71, no. 712 (2005): 2914–21. http://dx.doi.org/10.1299/kikaib.71.2914.

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50

Pujol, Dolors, Teresa Serra, Jordi Colomer, and Xavier Casamitjana. "Flow structure in canopy models dominated by progressive waves." Journal of Hydrology 486 (April 2013): 281–92. http://dx.doi.org/10.1016/j.jhydrol.2013.01.024.

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