Nonlinear Dispersive Waves and Whitham’s Equations

1997 ◽  
pp. 263-282
Author(s):  
Lokenath Debnath
Keyword(s):  
Dispersive Waves

scholarly journals Dark solitons, dispersive waves and their collision in an optical fiber

2018 ◽  
Author(s):  
T. Marest ◽  
C. Mas Arabí ◽  
M. Conforti ◽  
A. Mussot ◽  
C. Milian ◽  
...  
Keyword(s):  
Optical Fiber ◽  
Dispersive Waves ◽  
Dark Solitons

Axisymmetric internal waves generated by a travelling oscillating body

1969 ◽  
Vol 35 (2) ◽  
pp. 219-224 ◽  
Author(s):  
T. N. Stevenson
Keyword(s):  
Internal Waves ◽  
Salt Solution ◽  
Reynolds Numbers ◽  
Mean Velocity ◽  
Dispersive Waves ◽  
The Mean ◽  
Oscillating Sphere

Experiments are presented in which axisymmetric internal waves are generated by an oscillating sphere moving vertically in a stably stratified salt solution. The Reynolds numbers for the sphere based on the diameter and the mean velocity are between 10 and 200. Lighthill's theory for dispersive waves is used to calculate the phase configuration of the internal waves. The agreement between experiment and theory is reasonably good.

A reduced model for nonlinear dispersive waves in a rotating environment

1999 ◽  
Vol 90 (3-4) ◽  
pp. 139-159 ◽  
Author(s):  
P. A. Milewski ◽  
E. G. Tabak
Keyword(s):  
Reduced Model ◽  
Dispersive Waves

scholarly journals Generation of upstream advancing solitons by moving disturbances

1987 ◽  
Vol 184 ◽  
pp. 75-99 ◽  
Author(s):  
T. Yao-Tsu Wu
Keyword(s):  
Solitary Waves ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Theoretical Models ◽  
Computer Code ◽  
Basic Mechanism ◽  
Stationary Solutions ◽  
Boussinesq Model ◽  
Dispersive Waves ◽  
Fkdv Equation

This study investigates the recently identified phenomenon whereby a forcing disturbance moving steadily with a transcritical velocity in shallow water can generate, periodically, a succession of solitary waves, advancing upstream of the disturbance in procession, while a train of weakly nonlinear and weakly dispersive waves develops downstream of a region of depressed water surface trailing just behind the disturbance. This phenomenon was numerically discovered by Wu & Wu (1982) based on the generalized Boussinesq model for describing two-dimensional long waves generated by moving surface pressure or topography. In a joint theoretical and experimental study, Lee (1985) found a broad agreement between the experiment and two theoretical models, the generalized Boussinesq and the forced Korteweg-de Vries (fKdV) equations, both containing forcing functions. The fKdV model is applied in the present study to explore the basic mechanism underlying the phenomenon.To facilitate the analysis of the stability of solutions of the initial-boundary-value problem of the fKdV equation, a family of forced steady solitary waves is found. Any such solution, if once established, will remain permanent in form in accordance with the uniqueness theorem shown here. One of the simplest of the stationary solutions, which is a one-parameter family and can be scaled into a universal similarity form, is chosen for stability calculations. As a test of the computer code, the initially established stationary solution is found to be numerically permanent in form with fractional uncertainties of less than 2% after the wave has traversed, under forcing, the distance of 600 water depths. The other numerical results show that when the wave is initially so disturbed as to have to rise from the rest state, which is taken as the initial value, the same phenomenon of the generation of upstream-advancing solitons is found to appear, with a definite time period of generation. The result for this similarity family shows that the period of generation, Ts, and the scaled amplitude α of the solitons so generated are related by the formula Ts = const α−3/2. This relation is further found to be in good agreement with the first-principle prediction derived here based on mass, momentum and energy considerations of the fKdV equation.

General soliton solutions for nonlinear dispersive waves in convective type instabilities

2006 ◽  
Vol 74 (3) ◽  
pp. 384-393 ◽  
Author(s):  
A H Khater ◽  
D K Callebaut ◽  
A R Seadawy
Keyword(s):  
Soliton Solutions ◽  
Dispersive Waves

A new mechanism for generating a bolus within a double layer following Scott Russell

2021 ◽  
Author(s):  
Johan Fourdrinoy ◽  
Julien Dambrine ◽  
Madalina Petcu ◽  
Morgan Pierre ◽  
Germain Rousseaux
Keyword(s):  
Surface Deformation ◽  
Wave Train ◽  
Surrounding Medium ◽  
Negative Polarity ◽  
National Academy Of Sciences ◽  
Dispersive Waves ◽  
Dual Nature ◽  
Free Surface Deformation ◽  
Academy Of Sciences ◽  
Dead Water

<p>While seeking to revisit an old experiment of John Scott Russell, we discovered a new mechanism for generating a non-shoaling bolus (an ovoid coherent mass of recirculating mixed fluids immerged in a surrounding medium/a of different density/ies) propagating along a pycnocline. In a study about dead-water (Fourdrinoy et al. 2020), a wave resistance phenomenon induced by internal waves formation at the interface between waters of different densities, we modified the setup used by Scott Russell. The Scottish engineer studied the formation and propagation of dispersive waves when an object is removed from a laterally confined open channel with a shallow layer of water. The “vacuum” created by the mass removal generates a linear dispersive free surface deformation with a front of negative polarity followed by a wave train. If we extend this configuration to a two-layers stratification, we can observe a linear dispersive wave with negative polarity à la Scott Russell, propagating along the interface. In addition, the removal of the object generates under certain conditions a bolus which induces a mixing zone and a gradient transition layer. We will present this new method of boluses creation, as well as an experimental characterization with space-time diagrams thanks to a subpixel detection procedure.</p><p>The dual nature of the dead-water phenomenology: Nansen versus Ekman wave-making drags.<br>Johan Fourdrinoy, Julien Dambrine, Madalina Petcu, Morgan Pierre and Germain Rousseaux.<br>Proceedings of the National Academy of Sciences, Volume 117, Issue 29, p. 16739-16742, July 2020.</p>

scholarly journals The fully nonlinear stratified geostrophic adjustment problem

2017 ◽  
Vol 24 (1) ◽  
pp. 61-75 ◽  
Author(s):  
Aaron Coutino ◽  
Marek Stastna
Keyword(s):  
Stokes Equations ◽  
Wave Train ◽  
Shallow Water Equation ◽  
Classical Problem ◽  
Point Of View ◽  
Rossby Number ◽  
Adjustment Problem ◽  
Inertial Oscillations ◽  
Dispersive Waves ◽  
Fully Nonlinear

Abstract. The study of the adjustment to equilibrium by a stratified fluid in a rotating reference frame is a classical problem in geophysical fluid dynamics. We consider the fully nonlinear, stratified adjustment problem from a numerical point of view. We present results of smoothed dam break simulations based on experiments in the published literature, with a focus on both the wave trains that propagate away from the nascent geostrophic state and the geostrophic state itself. We demonstrate that for Rossby numbers in excess of roughly 2 the wave train cannot be interpreted in terms of linear theory. This wave train consists of a leading solitary-like packet and a trailing tail of dispersive waves. However, it is found that the leading wave packet never completely separates from the trailing tail. Somewhat surprisingly, the inertial oscillations associated with the geostrophic state exhibit evidence of nonlinearity even when the Rossby number falls below 1. We vary the width of the initial disturbance and the rotation rate so as to keep the Rossby number fixed, and find that while the qualitative response remains consistent, the Froude number varies, and these variations are manifested in the form of the emanating wave train. For wider initial disturbances we find clear evidence of a wave train that initially propagates toward the near wall, reflects, and propagates away from the geostrophic state behind the leading wave train. We compare kinetic energy inside and outside of the geostrophic state, finding that for long times a Rossby number of around one-quarter yields an equal split between the two, with lower (higher) Rossby numbers yielding more energy in the geostrophic state (wave train). Finally we compare the energetics of the geostrophic state as the Rossby number varies, finding long-lived inertial oscillations in the majority of the cases and a general agreement with the past literature that employed either hydrostatic, shallow-water equation-based theory or stratified Navier–Stokes equations with a linear stratification.

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