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.

New solutions for periodic interfacial gravity waves

2021 ◽  
Vol 928 ◽  
Author(s):  
X. Guan ◽  
J.-M. Vanden-Broeck ◽  
Z. Wang
Keyword(s):  
Integral Equation ◽  
Excellent Agreement ◽  
Gravity Waves ◽  
Global Bifurcation ◽  
Integral Equation Method ◽  
Finite Depth ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Fourier Expansions ◽  
Wave Profiles

Two-dimensional periodic interfacial gravity waves travelling between two homogeneous fluids of finite depth are considered. A boundary-integral-equation method coupled with Fourier expansions of the unknown functions is used to obtain highly accurate solutions. Our numerical results show excellent agreement with those already obtained by Maklakov & Sharipov using a different scheme (J. Fluid Mech., vol. 856, 2018, pp. 673–708). We explore the global bifurcation mechanism of periodic interfacial waves and find three types of limiting wave profiles. The new families of solutions appear either as isolated branches or as secondary branches bifurcating from the primary branch of solutions.

scholarly journals Head-on collision of two solitary waves and residual falling jet formation

2009 ◽  
Vol 16 (1) ◽  
pp. 111-122 ◽  
Author(s):  
J. Chambarel ◽  
C. Kharif ◽  
J. Touboul
Keyword(s):  
Residence Time ◽  
Solitary Waves ◽  
Vertical Wall ◽  
Integral Equation Method ◽  
Threshold Value ◽  
Finite Depth ◽  
Boundary Integral ◽  
Jet Formation ◽  
Fully Nonlinear Equations ◽  
Time Calculation

Abstract. The head-on collision of two equal and two unequal steep solitary waves is investigated numerically. The former case is equivalent to the reflection of one solitary wave by a vertical wall when viscosity is neglected. We have performed a series of numerical simulations based on a Boundary Integral Equation Method (BIEM) on finite depth to investigate during the collision the maximum runup, phase shift, wall residence time and acceleration field for arbitrary values of the non-linearity parameter a/h, where a is the amplitude of initial solitary waves and h the constant water depth. The initial solitary waves are calculated numerically from the fully nonlinear equations. The present work extends previous results on the runup and wall residence time calculation to the collision of very steep counter propagating solitary waves. Furthermore, a new phenomenon corresponding to the occurrence of a residual jet is found for wave amplitudes larger than a threshold value.

scholarly journals Free-surface flows emerging from beneath a semi-infinite plate with constant vorticity

2002 ◽  
Vol 461 ◽  
pp. 387-407 ◽  
Author(s):  
SCOTT W. McCUE ◽  
LAWRENCE K. FORBES
Keyword(s):  
Free Surface ◽  
Shear Flow ◽  
Infinite Plate ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Constant Vorticity ◽  
Uniform Shear ◽  
Uniform Shear Flow

The free-surface flow past a semi-infinite horizontal plate in a finite-depth fluid is considered. It is assumed that the fluid is incompressible and inviscid and that the flow approaches a uniform shear flow downstream. Exact relations are derived using conservation of mass and momentum for the case where the downstream free surface is flat. The complete nonlinear problem is solved numerically using a boundary-integral method and these waveless solutions are shown to exist only when the height of the plate above the bottom is greater than the height of the uniform shear flow. Interesting results are found for various values of the constant vorticity. Solutions with downstream surface waves are also considered, and nonlinear results of this type are compared with linear results found previously. These solutions can be used to model the flow near the stern of a (two-dimensional) ship.

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