scholarly journals The Close Relationship between Internal Wave and Ocean Free Surface Wave

2021 ◽  
Vol 9 (12) ◽  
pp. 1330
Author(s):  
Bang-Fuh Chen ◽  
Yi-Jei Huang
Keyword(s):  
Free Surface ◽  
Surface Wave ◽  
Internal Wave ◽  
Surface Waves ◽  
Wave Height ◽  
Water Surface ◽  
Simple Method ◽  
Wave Signal ◽  
Close Relationship ◽  
Free Surface Wave

A numerical model was used to simulate the propagation of internal waves (IW) along the surface layer. The results show that strong water exchange during IW propagation results in strong free surface flow and produces small but distinct free surface waves. We found a close relationship between the internal and ocean surface waves. Our intuitive reaction is that by training the relationship between the water surface wave height and the internal wave waveform, the internal wave waveform can be reversed from the water surface wave height value. This paper intends to validate our intuition. The artificial neural network (ANN) method was used to train the Fluent simulated results, and then the trained ANN model was used to predict the inner waves below by the free surface wave signal. In addition, two linear internal wave equations (I and II) were derived, one based on the Archimedes principle and the other based on the long wave and Boussinesq approximation. The prediction by equation (II) was superior to the prediction of equation (I), which is independent of depth. The predicted IW of the proposed ANN method was in good agreement with the simulated results, and the predicted quality was much better than the two linear wave formulas. The proposed simple method can help researchers infer the magnitude of IW from the free surface wave signal. In the future, the spatial distribution of IW below the sea surface might be obtained by the proposed method without costly field investigation.

scholarly journals Numerical Simulations of Linearly Stratified Flow Past Submerged Bodies

2018 ◽  
Vol 25 (s3) ◽  
pp. 68-77
Author(s):  
Weizhuang Ma ◽  
Yunbo Li ◽  
Yong Ding ◽  
Kaiye Hu ◽  
Linxin Lan
Keyword(s):  
Free Surface ◽  
Surface Wave ◽  
Density Gradient ◽  
Wave Height ◽  
Near Field ◽  
Turbulence Models ◽  
Stratified Flow ◽  
Stratified Flows ◽  
Detached Eddy Simulation ◽  
Free Surface Wave

Abstract In this study, a methodology was presented to predict density stratified flows in the near-field of submerged bodies. The energy equation in temperature form was solved coupled with momentum and mass conservation equations. Linear stratification was achieved by the definition of the density as a function of temperature. At first, verifications were performed for the stratified flows passing a submerged horizontal circular cylinder, showing excellent agreement with available experimental data. The ability of the method to cope with variable density was demonstrated. Different turbulence models were used for different Re numbers and flow states. Based on the numerical methods proposed in this paper, the stratified flow was studied for the real scale benchmark DAPRA Suboff submarine. The approach used the VOF method for tracing the free surface. Turbulence was implemented with a k − ω based Detached Eddy Simulation (DES) approach. The effects of submarine speed, depth and density gradient on the free surface wave pattern were quantitatively analyzed. It was shown that, with the increasing of the speed of the submarine, the wavelength and wave height of the free surface wave were gradually increasing. The wave height of the free surface wave was gradually reduced as the submarine’s depth increased. Relative to the speed and submarine depth, the changes of the gradient density gradient have negligible effects on the free surface wave field.

Large amplitude progressive interfacial waves

1979 ◽  
Vol 93 (3) ◽  
pp. 433-448 ◽  
Author(s):  
Judith Y. Holyer
Keyword(s):  
Free Surface ◽  
Surface Wave ◽  
Surface Waves ◽  
Large Amplitude ◽  
Phase Speed ◽  
Maximum Height ◽  
Interfacial Waves ◽  
Free Surface Waves ◽  
Lower Fluid ◽  
Over The Top

This paper contains a study of large amplitude, progressive interfacial waves moving between two infinite fluids of different densities. The highest wave has been calculated using the criterion that it has zero horizontal fluid velocity at the interface in a frame moving at the phase speed of the waves. For free surface waves this criterion is identical to the criterion due to Stokes, namely that there is a stagnation point at the crest of each wave. I t is found that as the density of the upper fluid increases relative to the density of the lower fluid the maximum height of the wave, for fixed wavelength, increases. The maximum height of a Boussinesq wave, which has the density almost the same above and below the interface, is 2·5 times the maximum height of a surface wave of the same wavelength. A wave with air over the top of it can be about 2% higher than the highest free surface wave. The point at which the limiting criterion is first satisfied moves from the crest for free surface waves to the point half-way between the crest and the trough for Boussinesq waves. The phase speed, momentum, energy and other wave properties are calculated for waves up to the highest using Padé approximants. For free surface waves and waves with air above the interface the maximum value of these properties occurs for waves which are lower than the highest. For Boussinesq waves and waves with the density of the upper fluid onetenth of the density of the lower fluid these properties each increase monotonically with the wave height.

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.

On the interaction of surface and internal waves

1972 ◽  
Vol 52 (1) ◽  
pp. 179-191 ◽  
Author(s):  
A. E. Gargettt ◽  
B. A. Hughes
Keyword(s):  
Surface Wave ◽  
Internal Wave ◽  
Surface Waves ◽  
Internal Waves ◽  
Wind Waves ◽  
Phase Speed ◽  
Surface Current ◽  
Propagation Direction ◽  
Wave Crest ◽  
Critical Position

The steady-state interaction between surface waves and long internal waves is investigated theoretically using the radiation stress concepts derived by Longuet-Higgins & Stewart (1964) (or Phillips 1966). It is shown that, over internal wave crests, those surface waves for which cg0cosϕ0 > ci experience a change in direction of propagation towards the line of propagation of the internal waves and their amplitudes are increased. Here cg0 is the surface-wave group speed at U = 0, ϕ0 is the angle between the propagation direction of the surface waves at U = 0 and the propagation direction of the internal waves, and ci is the phase speed of the internal waves. If cg0cos ϕ0 < ci the direction of the surface waves is turned away and their amplitudes are decreased. Over troughs the opposite effects occur.At positions where the local velocity of surface-wave energy transmission measured relative to the internal wave phase velocity is zero, i.e. cg + U − ci = 0, there is a singularity in the energy of the surface waves with resulting infinite amplitudes. It is shown that at these critical positions two wavenumbers which were real and distinct on one side coalesce and become complex on the other. The critical positions are thus shown to be barriers to the propagation of those wave-numbers. It is also shown that there is a critical position representing the coalescence of three wavenumbers. Surface-wave crest configurations are shown for three numerical examples. The frequency and direction of propagation of surface waves that exhibit critical positions somewhere in an internal wave field are shown as a function of the maximum horizontal surface current. This is compared with measurements of wind waves that have been reported elsewhere.

Exposure of internal waves on the sea surface

2009 ◽  
Vol 626 ◽  
pp. 1-20 ◽  
Author(s):  
HWUNG-HWENG HWUNG ◽  
RAY-YENG YANG ◽  
IGOR V. SHUGAN
Keyword(s):  
Surface Wave ◽  
Internal Wave ◽  
Surface Waves ◽  
Internal Waves ◽  
High Frequency ◽  
Numerical Solutions ◽  
Wave Excitation ◽  
Resonance Frequencies ◽  
The Impact ◽  
Current Zone

We theoretically analyse the impact of subsurface currents induced by internal waves on nonlinear Stokes surface waves. We present analytical and numerical solutions of the modulation equations under conditions that are close to group velocity resonance. Our results show that smoothing of the downcurrent surface waves is accompanied by a relatively high-frequency modulation, while the profile of the opposing current is reproduced by the surface wave's envelope. We confirm the possibility of generating an internal wave forerunner that is a modulated surface wave packet. Long surface waves can create such a wave modulation forerunner ahead of the internal wave, while other relatively short surface waves comprise the trace of the internal wave itself. Modulation of surface waves by a periodic internal wavetrain may exhibit a characteristic period that is less than the internal wave period. This period can be non-uniform while the wave crosses the current zone. Our results confirm that surface wave excitation by means of internal waves, as observed at their group resonance frequencies, is efficient only in the context of opposing currents.

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