Generation of long subharmonic internal waves by surface waves

2016 ◽  
Vol 106 ◽  
pp. 12-26 ◽  
Author(s):  
Navid Tahvildari ◽  
James M. Kaihatu ◽  
William S. Saric
Keyword(s):  
Surface Waves ◽  
Internal Waves

Internal-inertia waves in a fluid of variable depth

1973 ◽  
Vol 73 (1) ◽  
pp. 205-213 ◽  
Author(s):  
W. D. McKee
Keyword(s):  
Exact Solutions ◽  
Surface Waves ◽  
Internal Waves ◽  
Vertical Velocity ◽  
General Problem ◽  
Three Dimensional ◽  
Variable Depth ◽  
Internal Inertia ◽  
Perturbation Pressure ◽  
Rotating Stratified Fluid

AbstractWaves in a rotating, stratified fluid of variable depth are considered. The perturbation pressure is used throughout as the dependent variable. This proves to have some advantages over the use of the vertical velocity. Some previous three-dimensional solutions for internal waves in a wedge are shown to be incorrect and the correct solutions presented. A WKB analysis is then performed for the general problem and the results compared with the exact solutions for a wedge. The WKB solution is also applied to long surface waves on a rotating ocean.

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.

Nonlinear internal resonance interaction between surface waves and internal waves in an inhomogeneous laminated liquid

2014 ◽  
Vol 59 (9) ◽  
pp. 1291-1299 ◽  
Author(s):  
S. O. Shiryaeva ◽  
N. A. Petrushov ◽  
A. I. Grigor’ev ◽  
M. S. Fedorov
Keyword(s):  
Surface Waves ◽  
Internal Waves ◽  
Internal Resonance ◽  
Resonance Interaction

Bottom pressure induced by the long nonlinear internal waves

2020 ◽  
Author(s):  
Tatiana Talipova ◽  
Efim Pelinovsky
Keyword(s):  
Internal Wave ◽  
Surface Waves ◽  
Internal Waves ◽  
Pressure Fluctuations ◽  
Pressure Sensors ◽  
Storm Surges ◽  
Andaman Sea ◽  
Bottom Pressure ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory

&lt;p&gt;The bottom pressure sensors are widely used for the purpose of registration of the sea surface movement. They are particularly efficient to measure long surface waves like tsunami and storm surges. The bottom pressure gauges can be also used to record internal waves in coastal waters. For instance, the perspective system of the internal wave warning in the Andaman Sea is based on the bottom pressure variation data. Here we investigate theoretically the relation between long internal waves and induced bottom pressure fluctuations. Firstly, the linear relations are derived for the multi-modal internal wave field. Then, the weakly nonlinear theory is developed. Structurally, the obtained formula for the bottom pressure induced by the long internal waves is similar to those known for the surface waves within the Green-Naghdi system framework, but the coefficients are determined through the integrals for the water density stratification and vertical mode wave functions. In particular, the bottom pressure variations are calculated for solitary waves in two- and three-layer flows described by the Gardner equation.&lt;br&gt;The research is supported by RFBR grants No. 19-55-15005 and 19-05-00161.&lt;/p&gt;

The focusing of surface waves by internal waves

1999 ◽  
Vol 384 ◽  
pp. 27-58 ◽  
Author(s):  
A. N. DONATO ◽  
D. H. PEREGRINE ◽  
J. R. STOCKER
Keyword(s):  
Surface Waves ◽  
Internal Waves ◽  
Gravity Waves ◽  
Initial Conditions ◽  
Surface Current ◽  
Analytic Solutions ◽  
Ray Theory ◽  
Linear Waves ◽  
Exact Analytic Solutions ◽  
The Waves

The surface current generated by internal waves in the ocean affects surface gravity waves. The propagation of short surface waves is studied using both simple ray theory for linear waves and a fully nonlinear numerical potential solver. Attention is directed to the case of short waves with initially uniform wavenumber, as may be generated by a strong gust of wind. In general, some of the waves are focused by the surface current and in these regions the waves steepen and may break. Comparisons are made between ray theory and the more accurate solutions. For ray theory, the occurrence of focusing is examined in some detail and exact analytic solutions are found for rays on currents with linear and quadratic spatial variation – only the latter giving focusing for our initial conditions. With regard to interpretation of remote sensing of the sea surface, we find that enhanced wave steepness is not necessarily associated with a particular phase of the internal wave, and simplistic interpretations may sometimes be misleading.

Sign in / Sign up

Export Citation Format

Share Document