Surface and Internal Waves in Heavy Ideal Fluid

2010 ◽  
Keyword(s):  
Internal Waves ◽  
Ideal Fluid

Dynamics of ideal fluid flows over an uneven bottom

1987 ◽  
Vol 185 ◽  
pp. 551-568 ◽  
Author(s):  
Eugene S. Benilov
Keyword(s):  
Internal Waves ◽  
Ideal Fluid ◽  
Multiple Scales ◽  
Fluid Flows ◽  
Internal Gravity Waves ◽  
Negative Energy ◽  
Basic Flow ◽  
Hamiltonian Approach ◽  
Uneven Bottom ◽  
The Stability

Two problems of the stability of ideal fluid flows over an uneven bottom are considered. The first is the study of stratified flow with a ‘rigid lid’. We use the method of multiple scales to derive an equation describing the evolution of internal waves corresponding to different modes and wave vectors. For the case of sinusoidal bottom irregularities we have constructed a solution describing the increase in time of the internal wave field - this proves the instability of the basic flow. The phenomenon is interpreted as a result of interaction (mutual generation) of internal waves with energies of opposite signs. Our consideration is based on the Hamiltonian approach which enables us to prove in the most simple way the existence of waves carrying negative energy. The case of random (not sinusoidal) bottom irregularities is also studied. Using the kinetic equation for the amplitudes of internal waves derived in the paper, we have established that the basic flow remains unstable as well. In the second part of the paper we consider the homogeneous flows with a free upper boundary. It is shown that this problem can be reduced to the previous one, with the only difference being that the role of unstable perturbations is now played by the surface (not internal) gravity waves. The Hamiltonian approach is consistently applied and allows us to take into account the nonlinearity of waves.

Numerical Simulation of a Weakly Nonlinear Model for Internal Waves

2012 ◽  
Vol 12 (5) ◽  
pp. 1461-1481
Author(s):  
Robyn Canning Gregory ◽  
David P. Nicholls
Keyword(s):  
Numerical Simulation ◽  
Wave Packet ◽  
Internal Waves ◽  
Nonlinear Model ◽  
Ideal Fluid ◽  
Weakly Nonlinear ◽  
Fluid Layers ◽  
Infinite Extent ◽  
Spectral Algorithm ◽  
Weakly Nonlinear Model

Abstract Internal waves arise in a wide array of oceanographic problems of both theoretical and engineering interest. In this contribution we present a new model, valid in the weakly nonlinear regime, for the propagation of disturbances along the interface between two ideal fluid layers of infinite extent and different densities. Additionally, we present a novel high-order/spectral algorithm for its accurate and stable simulation. Numerical validation results and simulations of wave-packet evolution are provided.

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

An analogy between electromagnetic and internal waves

2019 ◽  
Vol 485 (4) ◽  
pp. 428-433
Author(s):  
V. G. Baydulov ◽  
P. A. Lesovskiy
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Internal Wave ◽  
Special Relativity ◽  
Internal Waves ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Lagrange Function ◽  
Lorentz Transformations ◽  
Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

On the energy spectra of a random field of internal waves

Tellus ◽  
1972 ◽  
Vol 24 (2) ◽  
pp. 161-163 ◽  
Author(s):  
Jacques C. J. Nihoul
Keyword(s):  
Random Field ◽  
Internal Waves ◽  
Energy Spectra

Convection and Internal Waves in a Stably Stratified Shear Flow,

1994 ◽  
Author(s):  
Patrick C. Gallacher ◽  
Hemantha W. Wijesekera
Keyword(s):  
Shear Flow ◽  
Internal Waves ◽  
Stratified Shear Flow ◽  
Stably Stratified Shear Flow
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