scholarly journals Hydroelastic solitary waves with constant vorticity

Wave Motion ◽  
2019 ◽  
Vol 85 ◽  
pp. 84-97 ◽  
Author(s):  
Tao Gao ◽  
Paul Milewski ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Solitary Waves ◽  
Constant Vorticity

scholarly journals Transverse instability of gravity–capillary solitary waves on deep water in the presence of constant vorticity

2019 ◽  
Vol 871 ◽  
pp. 1028-1043
Author(s):  
M. Abid ◽  
C. Kharif ◽  
H.-C. Hsu ◽  
Y.-Y. Chen
Keyword(s):  
Growth Rate ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Deep Water ◽  
Capillary Waves ◽  
Two Dimensional ◽  
Transverse Instability ◽  
Constant Vorticity ◽  
Dimensional Gravity ◽  
Wave Properties

The bifurcation of two-dimensional gravity–capillary waves into solitary waves when the phase velocity and group velocity are nearly equal is investigated in the presence of constant vorticity. We found that gravity–capillary solitary waves with decaying oscillatory tails exist in deep water in the presence of vorticity. Furthermore we found that the presence of vorticity influences strongly (i) the solitary wave properties and (ii) the growth rate of unstable transverse perturbations. The growth rate and bandwidth instability are given numerically and analytically as a function of the vorticity.

Atmospheric solitary waves: some applications to the morning glory of the Gulf of Carpentaria

1996 ◽  
Vol 321 ◽  
pp. 137-155 ◽  
Author(s):  
Lawrence K. Forbes ◽  
Shaun R. Belward
Keyword(s):  
Solitary Waves ◽  
Lower Layer ◽  
Sea Breeze ◽  
Boundary Integral ◽  
Morning Glory ◽  
Boundary Integral Method ◽  
Far North ◽  
Constant Vorticity ◽  
Shallow Layer ◽  
Meteorological Phenomenon

A mathematical model is proposed to describe atmospheric solitary waves at the interface between a ‘shallow’ layer of fluid near the ground and a stationary upper layer of compressible air. The lower layer is in motion relative to the ground, perhaps as a result of a distant thunderstorm or a sea breeze, and possesses constant vorticity. The upper fluid is compressible and isothermal, so that its density and pressure both decrease exponentially with height. The profile and speed of the solitary wave are determined, for a wave of given amplitude, using a boundary-integral method. Results are discussed in relation to the ‘morning glory’, which is a remarkable meteorological phenomenon evident in the far north of Australia.

scholarly journals Solitary waves on constant vorticity flows with an interior stagnation point

2020 ◽  
Vol 904 ◽  
Author(s):  
V. Kozlov ◽  
N. Kuznetsov ◽  
E. Lokharu
Keyword(s):  
Stagnation Point ◽  
Solitary Waves ◽  
Constant Vorticity

Abstract

scholarly journals On bounds for steady waves with negative vorticity

2021 ◽  
Vol 23 (2) ◽  
Author(s):  
Evgeniy Lokharu
Keyword(s):  
Froude Number ◽  
Solitary Waves ◽  
Upper Bound ◽  
Critical Value ◽  
Two Dimensional ◽  
Absolute Value ◽  
Constant Vorticity ◽  
Negative Constant

AbstractWe prove that no two-dimensional Stokes and solitary waves exist when the vorticity function is negative and the Bernoulli constant is greater than a certain critical value given explicitly. In particular, we obtain an upper bound $$F \le \sqrt{2} + \epsilon $$ F ≤ 2 + ϵ for the Froude number of solitary waves with a negative constant vorticity, sufficiently large in absolute value.

scholarly journals Nonlinear hydroelastic waves on a linear shear current at finite depth

2019 ◽  
Vol 876 ◽  
pp. 55-86 ◽  
Author(s):  
T. Gao ◽  
Z. Wang ◽  
P. A. Milewski
Keyword(s):  
Solitary Waves ◽  
Small Amplitude ◽  
Modulational Instability ◽  
Finite Depth ◽  
Time Dependent ◽  
Mapping Technique ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Constant Vorticity

This work is concerned with waves propagating on water of finite depth with a constant-vorticity current under a deformable flexible sheet. The pressure exerted by the sheet is modelled by using the Cosserat thin shell theory. By means of multi-scale analysis, small amplitude nonlinear modulation equations in several regimes are considered, including the nonlinear Schrödinger equation (NLS) which is used to predict the existence of small-amplitude wavepacket solitary waves in the full Euler equations and to study the modulational instability of quasi-monochromatic wavetrains. Guided by these weakly nonlinear results, fully nonlinear steady and time-dependent computations are performed by employing a conformal mapping technique. Bifurcation mechanisms and typical profiles of solitary waves for different underlying shear currents are presented in detail. It is shown that even when small-amplitude solitary waves are not predicted by the weakly nonlinear theory, we can numerically find large-amplitude solitary waves in the fully nonlinear equations. Time-dependent simulations are carried out to confirm the modulational stability results and illustrate possible outcomes of the nonlinear evolution in unstable cases.

Steep solitary waves in water of finite depth with constant vorticity

1994 ◽  
Vol 274 ◽  
pp. 339-348 ◽  
Author(s):  
J.-M. Vanden-Broeck
Keyword(s):  
Integral Equation ◽  
Solitary Waves ◽  
Numerical Scheme ◽  
Integral Equation Method ◽  
Finite Depth ◽  
Boundary Integral ◽  
Constant Vorticity ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
Shear Current

Solitary waves with constant vorticity in water of finite depth are calculated numerically by a boundary integral equation method. Previous calculations are confirmed and extended. It is shown that there are branches of solutions which bifurcate from a uniform shear current. Some of these branches are characterized by a limiting configuration with a 120° angle at the crest of the wave. Other branches extend for arbitrary large values of the amplitude of the wave. The corresponding solutions ultimately approach closed regions of constant vorticity in contact with the bottom of the channel. A numerical scheme is presented to calculate directly these closed regions of constant vorticity. In addition, it is shown that there are branches of solutions which do not bifurcate from a uniform shear flow.

Stability of solitary waves on deep water with constant vorticity

2021 ◽  
Author(s):  
Alexander Dosaev ◽  
Maria Shishina ◽  
Yuliya Troitskaya
Keyword(s):  
Solitary Waves ◽  
Deep Water ◽  
Equations Of Motion ◽  
Soliton Solutions ◽  
Finite Amplitude ◽  
Weakly Nonlinear ◽  
Constant Vorticity ◽  
Rfbr Grant ◽  
Stability Of Solitary Waves ◽  
Wave Limit

<p>Waves on deep water with constant vorticity propagating in the direction of the shear are known to be weakly dispersive in the long wave limit. Weakly-nonlinear evolution of such waves can be described by the Benjamin-Ono equation, which is integrable and has stable soliton solutions. In the present study we investigate behaviour of finite-amplitude counterparts of Benjamin-Ono solitons by modelling their dynamics within exact equations of motion (Euler equations). Due to the solitons having a near-Lorentzian shape with slowly decaying tails, we need to approach them by examining periodic waves, whose crests, indeed, become more and more localised as the period increases. We perform a parameter space study and analyse how stability of very long waves depends on their amplitude and period. We show that large-amplitude solitary waves are unstable.<br>This research was supported by RFBR (grant No. 16-05-00839) and by the President of Russian Federation (grant No. MK-2041.2017.5). Numerical experiments were supported by RSF grant No. 14-17-00667, data processing was supported by RSF grant No. 15-17-20009.</p>

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