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.

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.

Reflection of a high-amplitude solitary wave at a vertical wall

1997 ◽  
Vol 342 ◽  
pp. 141-158 ◽  
Author(s):  
M. J. COOKER ◽  
P. D. WEIDMAN ◽  
D. S. BALE
Keyword(s):  
Solitary Wave ◽  
Residence Time ◽  
Vertical Wall ◽  
High Amplitude ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Wave Crest ◽  
Asymptotic Formulae ◽  
Cine Film ◽  
Run Up

The collision of a solitary wave, travelling over a horizontal bed, with a vertical wall is investigated using a boundary-integral method to compute the potential fluid flow described by the Euler equations. We concentrate on reporting new results for that part of the motion when the wave is near the wall. The wall residence time, i.e. the time the wave crest remains attached to the wall, is introduced. It is shown that the wall residence time provides an unambiguous characterization of the phase shift incurred during reflection for waves of both small and large amplitude. Numerically computed attachment and detachment times and amplitudes are compared with asymptotic formulae developed using the perturbation results of Su & Mirie (1980). Other features of the flow, including the maximum run-up and the instantaneous wall force, are also presented. The numerically determined residence times are in good agreement with measurements taken from a cine film of solitary wave reflection experiments conducted by Maxworthy (1976).

scholarly journals Performance of an Array of Oblate Spheroidal Heaving Wave Energy Converters in Front of a Wall

Water ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 188 ◽  
Author(s):  
Eva Loukogeorgaki ◽  
Ifigeneia Boufidi ◽  
Ioannis K. Chatjigeorgiou
Keyword(s):  
Wave Energy ◽  
Vertical Wall ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Power Absorption ◽  
Enhanced Absorption ◽  
Wave Energy Converters ◽  
Oblate Spheroidal ◽  
Specific Frequency ◽  
Energy Converters

In this paper, we investigate the performance of a linear array of five semi-immersed, oblate spheroidal heaving Wave Energy Converters (WECs) in front of a bottom-mounted, finite-length, vertical wall under perpendicular to the wall regular waves. The diffraction and radiation problems are solved in the frequency domain by utilizing the conventional boundary integral equation method. Initially, to demonstrate the enhanced absorption ability of this array, we compare results with the ones corresponding to arrays of cylindrical and hemisphere-shaped WECs. Next, we investigate the effect of the array’s distance from the wall and of the length of the wall on the physical quantities describing the array’s performance. The results illustrate that the array’s placement at successively larger distances from the wall, up to three times the WECs’ radius, induces hydrodynamic interactions that improve the array’s hydrodynamic behavior, and thus its power absorption ability. An increase in the length of the wall does not lead to any significant power absorption improvement. Compared to the isolated array, the presence of the wall affects positively the array’s power absorption ability at specific frequency ranges, depending mainly on the array’s distance from the wall. Finally, characteristic diffracted wave field patterns are presented to interpret physically the occurrence of the local minima of the heave exciting forces.

scholarly journals An open-channel flow meeting a barrier and forming one or two jets

2000 ◽  
Vol 41 (4) ◽  
pp. 458-472 ◽  
Author(s):  
L. H. Wiryanto ◽  
E. O. Tuck
Keyword(s):  
Free Surface ◽  
Open Channel ◽  
Vertical Wall ◽  
Open Channel Flow ◽  
Free Surface Flow ◽  
Integral Equation Method ◽  
Finite Depth ◽  
Surface Flow ◽  
Parameter Measuring ◽  
Two Jets

AbstractA steady two-dimensional free-surface flow in a channel of finite depth is considered. The channel ends abruptly with a barrier in the form of a vertical wall of finite height. Hence the stream, which is uniform far upstream, is forced to go upward and then falls under the effect of gravity. A configuration is examined where the rising stream splits into two jets, one falling backward and the other forward over the wall, in a fountain-like manner. The backward-going jet is assumed to be removed without disturbing the incident stream. This problem is solved numerically by an integral-equation method. Solutions are obtained for various values of a parameter measuring the fraction of the total incoming flux that goes into the forward jet. The limit where this fraction is one is also examined, the water then all passing over the wall, with a 120° corner stagnation point on the upper free surface.

scholarly journals Do true elevation gravity–capillary solitary waves exist? A numerical investigation

2002 ◽  
Vol 454 ◽  
pp. 403-417 ◽  
Author(s):  
A. R. CHAMPNEYS ◽  
J.-M. VANDEN-BROECK ◽  
G. J. LORD
Keyword(s):  
Solitary Waves ◽  
Finite Depth ◽  
Bond Number ◽  
Boundary Integral ◽  
Numerical Results ◽  
Boundary Integral Method ◽  
Small Function ◽  
Asymptotic Results ◽  
Water Wave Problem ◽  
Strong Conclusion

This paper extends the numerical results of Hunter & Vanden-Broeck (1983) and Vanden-Broeck (1991) which were concerned with studies of solitary waves on the surface of fluids of finite depth under the action of gravity and surface tension. The aim of this paper is to answer the question of whether small-amplitude elevation solitary waves exist. Several analytical results have proved that bifurcating from Froude number F = 1, for Bond number τ between 0 and 1/3, there are families of ‘generalized’ solitary waves with periodic tails whose minimum amplitude is an exponentially small function of F−1. An open problem (which, for τ sufficiently close to 1/3, was recently proved by Sun 1999 to be false) is whether this amplitude can ever be zero, which would give a truly localized solitary wave.The problem is first addressed in terms of model equations taking the form of generalized fifth-order KdV equations, where it is demonstrated that if such a zero-tail-amplitude solution occurs, it does so along codimension-one lines in the parameter plane. Moreover, along solution paths of generalized solitary waves a topological distinction is found between cases where the tail does vanish and those where it does not. This motivates a new set of numerical results for the full problem, formulated using a boundary integral method, namely to probe the size of the tail amplitude as τ varies for fixed F > 1. The strong conclusion from the numerical results is that true solitary waves of elevation do not exist for the steady gravity–capillary water wave problem, at least for 9/50 < τ < 1=3. This finding confirms and explains previous asymptotic results by Yang & Akylas.

scholarly journals Capillary-gravity waves on the interface of two dielectric fluid layers under normal electric fields

2020 ◽  
Vol 73 (3) ◽  
pp. 231-250
Author(s):  
A Doak ◽  
T Gao ◽  
J -M Vanden-Broeck ◽  
J J S Kandola
Keyword(s):  
Electric Fields ◽  
Solitary Waves ◽  
Gravity Waves ◽  
Integral Equation Method ◽  
Travelling Wave ◽  
Boundary Integral ◽  
Dielectric Fluid ◽  
Weakly Nonlinear ◽  
Dielectric Fluids ◽  
Fluid Layers

Summary In this article, we consider capillary-gravity waves propagating on the interface of two dielectric fluids under the influence of normal electric fields. The density of the upper fluid is assumed to be much smaller than the lower one. Linear and weakly nonlinear theories are studied. The connection to the results in other limit configurations is discussed. Fully nonlinear computations for travelling wave solutions are achieved via a boundary integral equation method. Periodic waves, solitary waves and generalised solitary waves are presented. The bifurcation of generalised solitary waves is discussed in detail.

Nonlinear three-dimensional interfacial flows with a free surface

2007 ◽  
Vol 591 ◽  
pp. 481-494 ◽  
Author(s):  
E. I. PĂRĂU ◽  
J.-M. VANDEN-BROECK ◽  
M. J. COOKER
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Solitary Waves ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Interfacial Flows ◽  
Fully Nonlinear Equations ◽  
Weakly Nonlinear ◽  
Integral Equation Methods ◽  
Superposed Fluids

A configuration consisting of two superposed fluids bounded above by a free surface is considered. Steady three-dimensional potential solutions generated by a moving pressure distribution are computed. The pressure can be applied either on the interface or on the free surface. Solutions of the fully nonlinear equations are calculated by boundary-integral equation methods. The results generalize previous linear and weakly nonlinear results. Fully localized gravity–capillary interfacial solitary waves are also computed, when the free surface is replaced by a rigid lid.

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