scholarly journals Second-order random internal and surface waves in a two-fluid system

2006 ◽  
Vol 33 (6) ◽  
Author(s):  
Chi-Min Liu
Keyword(s):  
Surface Waves ◽  
Second Order ◽  
Fluid System ◽  
Two Fluid

Interfacial periodic waves of permanent form with free-surface boundary conditions

2001 ◽  
Vol 437 ◽  
pp. 325-336 ◽  
Author(s):  
EMILIAN PĂRĂU ◽  
FREDERIC DIAS
Keyword(s):  
Surface Waves ◽  
Phase Speed ◽  
Finite Amplitude ◽  
Surface Boundary ◽  
Periodic Waves ◽  
Internal Mode ◽  
Fluid System ◽  
External Mode ◽  
Two Fluid ◽  
Permanent Form

In a two-fluid system where the upper surface of the upper fluid is free, there are two independent modes of oscillation about the state of equilibrium, an ‘internal’ mode and an ‘external’ mode, which are described by two distinct dispersion curves. An efficient numerical scheme based on Fourier series expansions is used to calculate periodic waves of permanent form and of finite amplitude. Three kinds of waves are calculated: combination waves resulting from the interaction between an ‘internal’ mode and an ‘external’ mode with the same phase speed but wavelengths in a ratio of 2 (1:2 resonance), combination waves resulting from the interaction between a long ‘internal’ mode and a short ‘external’ mode with the same phase speed, and pure ‘external’ waves. It is shown that the 1:2 resonance, which is well-known for capillary – gravity surface waves and can profoundly affect wave field evolution, can affect pure gravity waves in a two-fluid system, but not in oceanic conditions. On the other hand, it is shown that the long/short wave resonance can occur in ocean-type conditions. Finally it is confirmed that pure external waves of finite amplitude behave like surface waves.

scholarly journals On the Study of Second-Order Wave Theory and Its Convergence for a Two-Fluid System

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Chi-Min Liu ◽  
Hwung-Hweng Hwung ◽  
Ray-Yeng Yang
Keyword(s):  
Transfer Functions ◽  
Perturbation Technique ◽  
Wave Theory ◽  
Order Theory ◽  
Second Order ◽  
Stokes Wave ◽  
Order Effects ◽  
Fluid System ◽  
Two Fluids ◽  
Two Fluid

Second-order solutions of internal and surface waves in a two-fluid system are theoretically analyzed in this study. Using the perturbation technique, the derivation of second-order solutions for internal waves is revisited, and the results are expressed in one-by-one forms instead of a matrix form. Second-order solutions arising from the interactions of two arbitrary linear waves of different frequencies contain the sum-frequency (superharmonic) and the difference-frequency (subharmonic) components, which are separately examined. Internal Stokes wave being a special case of present solutions is firstly investigated. Next, the convergence of second-order theory and the second-order effects on wave profiles are analyzed. For general cases, the effects of the thickness ratio of two fluids and the ratio of wavenumbers of two first-order waves on second-order wave characteristics, which include transfer functions and particle velocities, are also examined. Moreover, most existing theories for the one-fluid and two-fluid systems can be deduced from present solutions.

Subharmonic resonance of short internal standing waves by progressive surface waves

1996 ◽  
Vol 321 ◽  
pp. 217-233 ◽  
Author(s):  
D. F. Hill ◽  
M. A. Foda
Keyword(s):  
Surface Wave ◽  
Internal Wave ◽  
Surface Waves ◽  
Internal Waves ◽  
Growth Rates ◽  
Evolution Equations ◽  
Standing Waves ◽  
Second Order ◽  
Inviscid Limit ◽  
Initial Growth

Experimental evidence and a theoretical formulation describing the interaction between a progressive surface wave and a nearly standing subharmonic internal wave in a two-layer system are presented. Laboratory investigations into the dynamics of an interface between water and a fluidized sediment bed reveal that progressive surface waves can excite short standing waves at this interface. The corresponding theoretical analysis is second order and specifically considers the case where the internal wave, composed of two oppositely travelling harmonics, is much shorter than the surface wave. Furthermore, the analysis is limited to the case where the internal waves are small, so that only the initial growth is described. Approximate solution to the nonlinear boundary value problem is facilitated through a perturbation expansion in surface wave steepness. When certain resonance conditions are imposed, quadratic interactions between any two of the harmonics are in phase with the third, yielding a resonant triad. At the second order, evolution equations are derived for the internal wave amplitudes. Solution of these equations in the inviscid limit reveals that, at this order, the growth rates for the internal waves are purely imaginary. The introduction of viscosity into the analysis has the effect of modifying the evolution equations so that the growth rates are complex. As a result, the amplitudes of the internal waves are found to grow exponentially in time. Physically, the viscosity has the effect of adjusting the phase of the pressure so that there is net work done on the internal waves. The growth rates are, in addition, shown to be functions of the density ratio of the two fluids, the fluid layer depths, and the surface wave conditions.

scholarly journals Stability of a sloping interface in a rotating two-fluid system

Tellus ◽  
1970 ◽  
Vol 22 (5) ◽  
pp. 493-503 ◽  
Author(s):  
Desiraju B. Rao ◽  
T. J. Simons
Keyword(s):  
Fluid System ◽  
Two Fluid
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