scholarly journals The cauchy-poisson waves in an inviscid rotating stratified liquid

1990 ◽  
Vol 3 (1) ◽  
pp. 57-64
Author(s):  
Lokenath Debnath ◽  
Uma B. Guha ◽  
Manjusri Basu
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Large Time ◽  
Boussinesq Approximation ◽  
Free Surface Flows ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Initial Value ◽  
Surface Disturbance ◽  
Stratified Liquid

Based upon the Boussinesq approximation, an initial value investigation is made of the axisymmetric free surface flows generated in an inviscid rotating stratified liquid of infinite depth by the prescribed free surface disturbance. The asymptotic analysis of the integral solution is carried out by the stationary phase method to describe the solution for large time and large distance from the source of the disturbance. The asymptotic solution is found to consist of the classical free surface gravity waves and the internal-inertial waves.

scholarly journals Transient development of gravity waves for two layered fluids

1992 ◽  
Vol 15 (2) ◽  
pp. 333-338 ◽  
Author(s):  
A. H. Essawy ◽  
M. S. Faltas
Keyword(s):  
Free Surface ◽  
Asymptotic Analysis ◽  
Gravity Waves ◽  
Initial Value Problem ◽  
Large Time ◽  
Generalized Functions ◽  
Incompressible Fluids ◽  
Initial Value ◽  
Wave Maker

The transient gravity waves generated by a harmonically oscillating wave maker immersed in two incompressible fluids, the upper fluid having a free surface, is considered. The resulting linearized initial value problem is solved using the method of generalized functions, and asymptotic analysis for large time and distance are given for the elevation.

scholarly journals Dispersive Estimates for Full Dispersion KP Equations

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Didier Pilod ◽  
Jean-Claude Saut ◽  
Sigmund Selberg ◽  
Achenef Tesfahun
Keyword(s):  
Stationary Phase ◽  
Initial Value Problem ◽  
Bessel Functions ◽  
Linear Part ◽  
Independent Interest ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Initial Value ◽  
Kp Equations ◽  
Well Posed

AbstractWe prove several dispersive estimates for the linear part of the Full Dispersion Kadomtsev–Petviashvili introduced by David Lannes to overcome some shortcomings of the classical Kadomtsev–Petviashvili equations. The proof of these estimates combines the stationary phase method with sharp asymptotics on asymmetric Bessel functions, which may be of independent interest. As a consequence, we prove that the initial value problem associated to the Full Dispersion Kadomtsev–Petviashvili is locally well-posed in $$H^s(\mathbb R^2)$$ H s ( R 2 ) , for $$s>\frac{7}{4}$$ s > 7 4 , in the capillary-gravity setting.

scholarly journals Surface water waves due to an oscillatory wavemaker in the presence of surface tension

1992 ◽  
Vol 15 (2) ◽  
pp. 399-404
Author(s):  
B. N. Mandal ◽  
S. Banerjea
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Surface Water ◽  
Water Waves ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Transient Component ◽  
Surface Water Waves ◽  
Qualitative Nature ◽  
Surface Depression

The initial value problem of generation of surface water waves by a harmonically oscillating plane vertical wavemaker in an infinite incompressible fluid under the action of gravity and surface tension is investigated. In the asymptotic evaluation of the free surface depression for large time and distance, the contribution to the integral by stationary phase method gives rise to transient component of the free surface depression while the contribution from the poles give rise to steady state component. It is observed that the presence of surface tension sometimes changes the qualitative nature of the transient component of free surface depression.

scholarly journals Solitary gravity waves and free surface flows past a point vortex

2017 ◽  
Vol 82 (4) ◽  
pp. 821-835 ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Point Vortex ◽  
Free Surface Flows ◽  
Surface Flows

scholarly journals Numerical simulation of fluid structure interaction in free-surface flows: the WEC case

2021 ◽  
Vol 2116 (1) ◽  
pp. 012122
Author(s):  
Eugenio Schillaci ◽  
Federico Favre ◽  
Peter Troch ◽  
Assensi Oliva
Keyword(s):  
Free Surface ◽  
Single Point ◽  
Fluid Structure Interaction ◽  
Free Surface Flows ◽  
Immersed Boundary ◽  
Phase Method ◽  
Surface Flows ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Linear Waves

Abstract In this work we present a numerical framework to carry-out numerical simulations of fluid-structure interaction phenomena in free-surface flows. The framework employs a single-phase method to solve momentum equations and interface advection without solving the gas phase, an immersed boundary method (IBM) to represent the moving solid within the fluid matrix and a fluid structure interaction (FSI) algorithm to couple liquid and solid phases. The method is employed to study the case of a single point wave energy converter (WEC) device, studying its free decay and its response to progressive linear waves.

scholarly journals Generation of Surface Waves Due to Initial Axisymmetric Surface Disturbance in Water with a Porous Bottom

2019 ◽  
Vol 24 (3) ◽  
pp. 625-644 ◽  
Author(s):  
P. Kundu ◽  
B.N. Mandal
Keyword(s):  
Free Surface ◽  
Asymptotic Form ◽  
Velocity Potential ◽  
Hankel Transform ◽  
Initial Surface ◽  
Initial Value ◽  
Poisson Problem ◽  
Different Types ◽  
Surface Disturbance ◽  
Infinite Integral

Abstract A two-dimensional Cauchy Poisson problem for water with a porous bottom generated by an axisymmetric initial surface disturbance is investigated here. The problem is formulated as an initial value problem for the velocity potential describing the motion in the fluid. The Laplace and Hankel transform techniques have been used in the mathematical analysis to obtain the form of the free surface in terms of a multiple infinite integral. This integral is then evaluated asymptotically by the method of stationary phase. The asymptotic form of the free surface is depicted graphically in a number of figures for different values of the porosity parameter and for different types of initial disturbances.

scholarly journals Transient development of capillary-gravity waves in a running stream

1973 ◽  
Vol 9 (3) ◽  
pp. 417-432 ◽  
Author(s):  
Kalyan Kumar Bagchi ◽  
Lokenath Debnath
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Gravity Waves ◽  
Critical Speed ◽  
Shallow Depth ◽  
Stream Velocity ◽  
Inviscid Fluid ◽  
Generalized Fourier Transform ◽  
Free Surface Elevation ◽  
Initial Value

An initial value investigation is made of the propagation of capillary-gravity waves generated by an oscillating pressure distribution acting at the free surface of a running stream of finite, infinite, and shallow depth. The solution for the free surface elevation is obtained explicitly by using the generalized Fourier transform and its asymptotic expansion. It is found that the solution consists of both the steady state and the transient components. The latter decays asymptotically as t → ∞ and the ultimate steady state is attained. It is shown that the steady state consists of two or four progressive capillary-gravity waves travelling both upstream and downstream according as the basic stream velocity is less or greater than the critical speed. Special attention is given to the existence of the critical values associated with the running stream of finite, infinite, and shallow depth. A comparison is made between the unsteady wave motions in an inviscid fluid with or without surface tension.

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