Spectra of Internal Waves and Turbulence in Stratified Fluids: 2. Experiments on the Breaking of Internal Waves in a Two-Fluid System

Radio Science ◽  
1969 ◽  
Vol 4 (12) ◽  
pp. 1321-1325 ◽  
Author(s):  
J. Michael Hall ◽  
Yih-Ho Pao
Keyword(s):  
Internal Waves ◽  
Stratified Fluids ◽  
Fluid System ◽  
Two Fluid

Fully nonlinear higher-order model equations for long internal waves in a two-fluid system

2010 ◽  
Vol 654 ◽  
pp. 281-303 ◽  
Author(s):  
SUMA DEBSARMA ◽  
K. P. DAS ◽  
JAMES T. KIRBY
Keyword(s):  
Internal Waves ◽  
Solitary Waves ◽  
Lower Layer ◽  
Numerical Approach ◽  
Single Equation ◽  
Fluid System ◽  
Fully Nonlinear ◽  
Coupled Equations ◽  
Model Equations ◽  
Two Fluid

Fully nonlinear model equations, including dispersive effects at one-order higher approximation than in the model of Choi & Camassa (J. Fluid Mech., vol. 396, 1999, pp. 1–36), are derived for long internal waves propagating in two spatial horizontal dimensions in a two-fluid system, where the lower layer is of infinite depth. The model equations consist of two coupled equations for the displacement of the interface and the horizontal velocity of the upper layer at an arbitrary elevation, and they are correct to O(μ2) terms, where μ is the ratio of thickness of the upper-layer fluid to a typical wavelength. For solitary waves propagating in one horizontal direction, the two coupled equations reduce to a single equation for the elevation of the interface. Solitary wave profiles obtained numerically from this equation for different wave speeds are in good agreement with computational results based on Euler's equations. A numerical approach for the propagation of solitary waves is provided in the weakly nonlinear case.

scholarly journals DECOUPLED AND UNIDIRECTIONAL ASYMPTOTIC MODELS FOR THE PROPAGATION OF INTERNAL WAVES

2013 ◽  
Vol 24 (01) ◽  
pp. 1-65 ◽  
Author(s):  
VINCENT DUCHÊNE
Keyword(s):  
Initial Data ◽  
Internal Waves ◽  
Evolution Equations ◽  
Approximate Solutions ◽  
Type Model ◽  
Fluid System ◽  
Asymptotic Models ◽  
Counterpropagating Waves ◽  
Scalar Equations ◽  
Two Fluid

We study the relevance of various scalar equations, such as inviscid Burgers', Korteweg–de Vries (KdV), extended KdV, and higher order equations, as asymptotic models for the propagation of internal waves in a two-fluid system. These scalar evolution equations may be justified in two ways. The first method consists in approximating the flow by two uncoupled, counterpropagating waves, each one satisfying such an equation. One also recovers these equations when focusing on a given direction of propagation, and seeking unidirectional approximate solutions. This second justification is more restrictive as for the admissible initial data, but yields greater accuracy. Additionally, we present several new coupled asymptotic models: a Green–Naghdi type model, its simplified version in the so-called Camassa–Holm regime, and a weakly decoupled model. All of the models are rigorously justified in the sense of consistency.

On the shape of progressive internal waves

1968 ◽  
Vol 263 (1145) ◽  
pp. 563-614 ◽  
Keyword(s):  
Experimental Evidence ◽  
Internal Waves ◽  
Gravity Waves ◽  
Boussinesq Approximation ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Fluid System ◽  
Expansion Technique ◽  
Theoretical Predictions ◽  
Two Fluid

An expansion technique, analogous to that of Stokes in the study of surface waves, is used to investigate the effects of finite amplitude on a progressive train of internal gravity waves. The paper is divided into two main parts, a study of interfacial waves in a two-fluid system and an examination of internal waves in a continuously stratified fluid. Experimental evidence is presented which confirms some of the theoretical predictions. The validity of the Boussinesq approximation is examined and particular examples are taken to illustrate the general results.

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