scholarly journals Analytical Study of the Head-On Collision Process between Hydroelastic Solitary Waves in the Presence of a Uniform Current

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 333 ◽  
Author(s):  
Muhammad Bhatti ◽  
Dong Lu
Keyword(s):  
Solitary Waves ◽  
Elastic Plate ◽  
Wave Speed ◽  
Nonlinear Partial Differential Equations ◽  
Thin Elastic Plate ◽  
Beam Model ◽  
Singular Perturbation Method ◽  
Highly Nonlinear ◽  
Uniform Current ◽  
Run Up

The present study discusses an analytical simulation of the head-on collision between a pair of hydroelastic solitary waves propagating in the opposite directions in the presence of a uniform current. An infinite thin elastic plate is floating on the surface of water. The mathematical modeling of the thin elastic plate is based on the Euler–Bernoulli beam model. The resulting kinematic and dynamic boundary conditions are highly nonlinear, which are solved analytically with the help of a singular perturbation method. The Poincaré–Lighthill–Kuo method is applied to obtain the solution of the nonlinear partial differential equations. The resulting solutions are presented separately for the left- and right-going waves. The behavior of all the emerging parameters are presented mathematically and discussed graphically for the phase shift, maximum run-up amplitude, distortion profile, wave speed, and solitary wave profile. It is found that the presence of a current strongly affects the wavelength and wave speed of both solitary waves. A graphical comparison with pure-gravity waves is also presented as a particular case of our study.

scholarly journals An application of Nwogu’s Boussinesq model to analyze the head-on collision process between hydroelastic solitary waves

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 177-191 ◽  
Author(s):  
Muhammad Mubashir Bhatti ◽  
Dong-Qiang Lu
Keyword(s):  
Phase Shift ◽  
Solitary Waves ◽  
Free Parameter ◽  
Wave Speed ◽  
Physical Parameters ◽  
Beam Model ◽  
Boussinesq Model ◽  
Highly Nonlinear ◽  
Run Up ◽  
The Impact

AbstractThis article deals with the nonlinear head-on collision between two hydroelastic solitary waves in plate–covered water with Nwogou’s Boussinesq model for the nonlinear fluid motion. This model contains a parameter α that is associated with horizontal velocities according to the chosen level of horizontal velocity variables. A thin elastic cover is considered as the Euler–Bernoulli beam model. To derive the series solution, we apply the Poincaré–Lighthill–Kuo (PLK) method to solve analytically the highly nonlinear coupled partial differential equations. The impact of all the physical parameters is discussed with the help of the asymptotic solutions and graphic representations. In particular, the authors address the behavior of plate deflection, maximum run-up during a collision, phase shift, distortion profile, and wave speed. It is found that the variation of the free parameter α and plate terms dramatically change the amplitude of a solitary wave. It is noticed that a very small tilting occurs due to the distortion in wave profile. The maximum run-up amplitude and the wave speed rise due to a greater influence of the free parameter. The phase shift tends to diminish due to an increment in the free parameter and plate terms. The novelty of the present methodology is compared with previously published results.

Hydroelastic solitary wave during the head-on collision process in a stratified fluid

2019 ◽  
Vol 233 (17) ◽  
pp. 6135-6148 ◽  
Author(s):  
MM Bhatti ◽  
DQ Lu
Keyword(s):  
Elastic Plate ◽  
Wave Speed ◽  
Lower Layer ◽  
Order Approximation ◽  
Asymptotic Series ◽  
Density Ratio ◽  
Thin Elastic Plate ◽  
Series Solutions ◽  
Interfacial Wave ◽  
Highly Nonlinear

In this study, head-on collision between hydroelastic solitary waves propagating in a two-layer fluid beneath a thin elastic plate is analytically investigated. The plate structure is modeled using the Euler–Bernoulli beam theory with the effect of compressive stress. We consider that the lower- and upper-layer fluids having different constant densities are incompressible, and the motion is irrotational. The asymptotic series solutions of the resulting highly nonlinear coupled differential equations are deduced with the combination of a method of strained coordinates and the Poincaré–Lighthill–Kuo method. The series solutions obtained are presented up to the third-order approximation. The inclusion of all the emerging parameters is discussed graphically and mathematically against interfacial waves, plate deflection, wave speed, phase shift, maximum run-up amplitude, and the velocity functions. The presence of the elastic plate reveals a decreasing impact on the wave profiles in the upper- and lower-layer fluid. However, the distortion profile shows converse behavior in the upper-layer fluid as compared with the lower-layer fluid. Interfacial wave speed also tends to diminish due to the elastic plate parameter and the density ratio as the wave amplitude is high.

Numerical simulations of large-amplitude internal solitary waves

1998 ◽  
Vol 362 ◽  
pp. 53-82 ◽  
Author(s):  
DMITRY E. TEREZ ◽  
OMAR M. KNIO
Keyword(s):  
Phase Shift ◽  
Solitary Waves ◽  
Numerical Experiments ◽  
Wave Speed ◽  
Wave Amplitude ◽  
Stokes Equations ◽  
Fluid Model ◽  
Internal Solitary Waves ◽  
Highly Nonlinear ◽  
The Waves

A numerical model based on the incompressible two-dimensional Navier–Stokes equations in the Boussinesq approximation is used to study mode-2 internal solitary waves propagating on a pycnocline between two deep layers of different densities. Numerical experiments on the collapse of an initially mixed region reveal a train of solitary waves with the largest leading wave enclosing an intrusional ‘bulge’. The waves gradually decay as they propagate along the horizontal direction, with a corresponding reduction in the size of the bulge. When the normalized wave amplitude, a, falls below the critical value ac=1.18, the wave is no longer able to transport mixed fluid as it propagates away from the mixed region, and a sharp-nosed intrusion is left behind. The wave structure is studied using a Lagrangian particle tracking scheme which shows that for small amplitudes the bulges have a well-defined elliptic shape. At larger amplitudes, the bulge entrains and mixes fluid from the outside while instabilities develop in the rear part of the bulge. Results are obtained for different wave amplitudes ranging from small-amplitude ‘regular’ waves with a=0.7 to highly nonlinear unstable waves with a=3.8. The dependence of the wave speed and wavelength on amplitude is measured and compared with available experimental data and theoretical predictions. Consistent with experiments, the wave speed increases almost linearly with amplitude at small values of a. As a becomes large, the wave speed increases with amplitude at a smaller rate, which gradually approaches the asymptotic limit for a two-fluid model. Results show that in the parameter range considered the wave amplitude decreases linearly with time at a rate inversely proportional to the Reynolds number. Numerical experiments are also conducted on the head-on collision of solitary waves. The simulations indicate that the waves experience a negative phase shift during the collision, in accordance with experimental observations. Computations are used to determine the dependence of the phase shift on the wave amplitude.

scholarly journals Head-on collision between capillary–gravity solitary waves

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Marin Marin ◽  
M. M. Bhatti
Keyword(s):  
Surface Tension ◽  
Solitary Waves ◽  
Water Waves ◽  
Free Parameter ◽  
Order Approximation ◽  
Third Order ◽  
Boussinesq Model ◽  
Run Up ◽  
Physical Features ◽  
Third Order Approximation

AbstractThe present study deals with the head-on collision process between capillary–gravity solitary waves in a finite channel. The present mathematical modeling is based on Nwogu’s Boussinesq model. This model is suitable for both shallow and deep water waves. We have considered the surface tension effects. To examine the asymptotic behavior, we employed the Poincaré–Lighthill–Kuo method. The resulting series solutions are given up to third-order approximation. The physical features are discussed for wave speed, head-on collision profile, maximum run-up, distortion profile, the velocity at the bottom, and phase shift profile, etc. A comparison is also given as a particular case in our study. According to the results, it is noticed that the free parameter and the surface tension tend to decline the solitary-wave profile significantly. However, the maximum run-up amplitude was affected in great measure due to the surface tension and the free parameter.

scholarly journals Run-Up Simulation of Impulse-Generated Solitary Waves

2018 ◽  
Vol 144 (2) ◽  
pp. 04017170
Author(s):  
Viljami Laurmaa ◽  
Marco Picasso ◽  
Gilles Steiner ◽  
Frederic M. Evers ◽  
Willi H. Hager
Keyword(s):  
Solitary Waves ◽  
Run Up

scholarly journals On the numerical simulation of the nonbreaking solitary waves run up on sloping beaches

2015 ◽  
Vol 70 (9) ◽  
pp. 2270-2281 ◽  
Author(s):  
Asghar Farhadi ◽  
Homayoun Emdad ◽  
Ebrahim Goshtasbi Rad
Keyword(s):  
Numerical Simulation ◽  
Solitary Waves ◽  
Run Up
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