Discussion of “Stokes Theory for Waves on a Linear Shear Current” by Norisumi Kishida and Rodney J. Sobey (August, 1988, Vol. 114, No. 8)

1990 ◽  
Vol 116 (4) ◽  
pp. 978-978
Author(s):  
Mario Dogliani
Keyword(s):  
Shear Current ◽  
Linear Shear

scholarly journals On the Dynamics of Two-Dimensional Capillary-Gravity Solitary Waves with a Linear Shear Current

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Dali Guo ◽  
Bo Tao ◽  
Xiaohui Zeng
Keyword(s):  
Solitary Waves ◽  
Gravity Waves ◽  
Small Amplitude ◽  
Numerical Study ◽  
Two Dimensional ◽  
Shear Current ◽  
Linear Shear ◽  
The Stability ◽  
Depression Wave ◽  
Elevation Wave

The numerical study of the dynamics of two-dimensional capillary-gravity solitary waves on a linear shear current is presented in this paper. The numerical method is based on the time-dependent conformal mapping. The stability of different kinds of solitary waves is considered. Both depression wave and large amplitude elevation wave are found to be stable, while small amplitude elevation wave is unstable to the small perturbation, and it finally evolves to be a depression wave with tails, which is similar to the irrotational capillary-gravity waves.

scholarly journals Gravity–capillary waves in finite depth on flows of constant vorticity

2016 ◽  
Vol 472 (2195) ◽  
pp. 20160363 ◽  
Author(s):  
Hung-Chu Hsu ◽  
Marc Francius ◽  
Pablo Montalvo ◽  
Christian Kharif
Keyword(s):  
Surface Profile ◽  
Finite Depth ◽  
Bond Number ◽  
Perturbation Series ◽  
Capillary Waves ◽  
Constant Vorticity ◽  
Expansion Procedure ◽  
Shear Current ◽  
Linear Shear

This paper considers two-dimensional periodic gravity–capillary waves propagating steadily in finite depth on a linear shear current (constant vorticity). A perturbation series solution for steady periodic waves, accurate up to the third order, is derived using a classical Stokes expansion procedure, which allows us to include surface tension effects in the analysis of wave–current interactions in the presence of constant vorticity. The analytical results are then compared with numerical computations with the full equations. The main results are (i) the phase velocity is strongly dependent on the value of the vorticity; (ii) the singularities (Wilton singularities) in the Stokes expansion in powers of wave amplitude that correspond to a Bond number of 1/2 and 1/3, which are the consequences of the non-uniformity in the ordering of the Fourier coefficients, are found to be influenced by vorticity; (iii) different surface profiles of capillary–gravity waves are computed and the effect of vorticity on those profiles is shown to be important, in particular that the solutions exhibit type-2-like wave features, characterized by a secondary maximum on the surface profile with a trough between the two maxima.

scholarly journals Parasitic Capillary Waves on Small-Amplitude Gravity Waves with a Linear Shear Current

2021 ◽  
Vol 9 (11) ◽  
pp. 1217
Author(s):  
Sunao Murashige ◽  
Wooyoung Choi
Keyword(s):  
Gravity Waves ◽  
Small Amplitude ◽  
Approximate Model ◽  
Capillary Waves ◽  
Front Face ◽  
Wide Range ◽  
Shear Current ◽  
Linear Shear ◽  
Flow Domain ◽  
Nonlinear Computation

This paper describes a numerical investigation of ripples generated on the front face of deep-water gravity waves progressing on a vertically sheared current with the linearly changing horizontal velocity distribution, namely parasitic capillary waves with a linear shear current. A method of fully nonlinear computation using conformal mapping of the flow domain onto the lower half of a complex plane enables us to obtain highly accurate solutions for this phenomenon with the wide range of parameters. Numerical examples demonstrated that, in the presence of a linear shear current, the curvature of surface of underlying gravity waves depends on the shear strength, the wave energy can be transferred from gravity waves to capillary waves and parasitic capillary waves can be generated even if the wave amplitude is very small. In addition, it is shown that an approximate model valid for small-amplitude gravity waves in a linear shear current can reasonably well reproduce the generation of parasitic capillary waves.

scholarly journals Steady Deep-Water Waves on a Linear Shear Current

1985 ◽  
Vol 73 (1) ◽  
pp. 35-57 ◽  
Author(s):  
J. A. Simmen ◽  
P. G. Saffman
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Shear Current ◽  
Linear Shear ◽  
Deep Water Waves

Steady solution of solitary wave and linear shear current interaction

2018 ◽  
Vol 60 ◽  
pp. 354-369 ◽  
Author(s):  
W.Y. Duan ◽  
Z. Wang ◽  
B.B. Zhao ◽  
R.C. Ertekin ◽  
W.Q. Yang
Keyword(s):  
Solitary Wave ◽  
Steady Solution ◽  
Shear Current ◽  
Linear Shear ◽  
Current Interaction

scholarly journals Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current

2021 ◽  
Vol 927 ◽  
Author(s):  
Curtis Hooper ◽  
Karima Khusnutdinova ◽  
Roger Grimshaw
Keyword(s):  
Plane Waves ◽  
Large Family ◽  
Tangent Plane ◽  
Stratified Fluid ◽  
Internal Ring ◽  
Interfacial Waves ◽  
Homogeneous Fluid ◽  
Modal Structure ◽  
Shear Current ◽  
Linear Shear

We study long surface and internal ring waves propagating in a stratified fluid over a parallel shear current. The far-field modal and amplitude equations for the ring waves are presented in dimensional form. We re-derive the modal equations from the formulation for plane waves tangent to the ring wave, which opens a way to obtaining important characteristics of the ring waves (group speed, wave action conservation law) and to constructing more general ‘hybrid solutions’ consisting of a part of a ring wave and two tangent plane waves. The modal equations constitute a new spectral problem, and are analysed for a number of examples of surface ring waves in a homogeneous fluid and internal ring waves in a stratified fluid. Detailed analysis is developed for the case of a two-layered fluid with a linear shear current where we study their wavefronts and two-dimensional modal structure. Comparisons are made between the modal functions (i.e. eigenfunctions of the relevant spectral problems) for the surface waves in homogeneous and two-layered fluids, as well as the interfacial waves described exactly and in the rigid-lid approximation. We also analyse the wavefronts of surface and interfacial waves for a large family of power-law upper-layer currents, which can be used to model wind generated currents, river inflows and exchange flows in straits. Global and local measures of the deformation of wavefronts are introduced and evaluated.

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