A multi-layer model for nonlinear internal wave propagation in shallow water

2012 ◽  
Vol 695 ◽  
pp. 341-365 ◽  
Author(s):  
Philip L.-F. Liu ◽  
Xiaoming Wang
Keyword(s):  
Wave Propagation ◽  
Internal Wave ◽  
Shallow Water ◽  
Internal Waves ◽  
Bottom Topography ◽  
Laboratory Data ◽  
Constant Density ◽  
Layer Model ◽  
Fluid System ◽  
Nonlinear Internal Wave

AbstractIn this paper, a multi-layer model is developed for the purpose of studying nonlinear internal wave propagation in shallow water. The methodology employed in constructing the multi-layer model is similar to that used in deriving Boussinesq-type equations for surface gravity waves. It can also be viewed as an extension of the two-layer model developed by Choi & Camassa. The multi-layer model approximates the continuous density stratification by an $N$-layer fluid system in which a constant density is assumed in each layer. This allows the model to investigate higher-mode internal waves. Furthermore, the model is capable of simulating large-amplitude internal waves up to the breaking point. However, the model is limited by the assumption that the total water depth is shallow in comparison with the wavelength of interest. Furthermore, the vertical vorticity must vanish, while the horizontal vorticity components are weak. Numerical examples for strongly nonlinear waves are compared with laboratory data and other numerical studies in a two-layer fluid system. Good agreement is observed. The generation and propagation of mode-1 and mode-2 internal waves and their interactions with bottom topography are also investigated.

Internal wave propagation in an inhomogeneous fluid of non-uniform depth

1969 ◽  
Vol 38 (2) ◽  
pp. 365-374 ◽  
Author(s):  
Joseph B. Keller ◽  
Van C. Mow
Keyword(s):  
Wave Propagation ◽  
Internal Wave ◽  
Experimental Result ◽  
Bottom Surface ◽  
Radius Of Curvature ◽  
Constant Density ◽  
Trapped Waves ◽  
Inhomogeneous Fluid ◽  
Sloping Beach ◽  
Scale Length

An asymptotic solution is obtained to the problem of internal wave propagation in a horizontally stratified inhomogeneous fluid of non-uniform depth. It also applies to fluids which are not stratified, but in which the constant density surfaces have small slopes. The solution is valid when the wavelength is small compared to all horizontal scale lengths, such as the radius of curvature of a wavefront, the scale length of the bottom surface variations and the scale length of the horizontal density variations. The theory underlying the solution involves rays, a phase function satisfying the eiconal equation, and amplitude functions satisfying transport equations. All these equations are solved in terms of the rays and of the solution of the internal wave problem for a horizontally stratified fluid of constant depth. The theory is thus very similar to geometrical optics and its extensions. It can be used to treat problems of propagation, reflexion from vertical cliffs or from shorelines, refraction, determination of the frequencies and wave patterns of trapped waves, etc. For fluid of constant density, it reduces to the theory of Keller (1958). The theory is applied to waves in a fluid with an exponential density distribution on a uniformly sloping beach. The predicted wavelength is shown to agree well with the experimental result of Wunsch (1969). It is also applied to determine edge waves near a shoreline and trapped waves in a channel.

Internal waves in a horizontally inhomogeneous flow

1984 ◽  
Vol 142 ◽  
pp. 233-249 ◽  
Author(s):  
A. Ya. Basovich ◽  
L. Sh. Tsimring
Keyword(s):  
Wave Propagation ◽  
Internal Wave ◽  
Internal Waves ◽  
Short Wave ◽  
Wave Transformation ◽  
Wave Trapping ◽  
Wave Amplification ◽  
Normal Surfaces ◽  
Inhomogeneous Flow ◽  
Horizontally Inhomogeneous

The effect of horizontally inhomogeneous flows on internal wave propagation in a stratified ocean with a constant Brunt-Väisälä frequency is analysed. Dispersion characteristics of internal waves in a moving fluid and kinematics of wave packets in smoothly inhomogeneous flows are considered using wave-normal surfaces. It is shown that internal-wave blocking and short-wave transformation may occur in longitudinally inhomogeneous flows. For parallel flows internal-wave trapping is possible in the vicinity of the limiting layer where the wave frequency in the locally comoving frame of reference coincides with the Brunt-Väisälä frequency. Internal-wave trapping also takes place in jet-type flows in the vicinity of the flow-velocity maximum. WKB solutions of the equation describing internal-wave propagation in a parallel horizontally inhomogeneous flow in the linear approximation are obtained. Singular points of this equation and the related effect of internal-wave amplification (overreflection) under the action of the flow are investigated. The spectrum and the growth rate of internal-wave localized modes in a jet-type flow are obtained.

ACOUSTIC TRAVEL-TIME PERTURBATIONS DUE TO SHALLOW-WATER INTERNAL WAVES IN THE YELLOW SEA

2014 ◽  
Vol 22 (01) ◽  
pp. 1440003
Author(s):  
FAN LI ◽  
XINYI GUO ◽  
TAO HU ◽  
LI MA
Keyword(s):  
Internal Wave ◽  
Shallow Water ◽  
Travel Time ◽  
Internal Waves ◽  
Yellow Sea ◽  
High Frequency ◽  
Simple Relation ◽  
Ocean Dynamics ◽  
The Yellow Sea ◽  
Acoustic Travel Time

Internal waves in shallow-water cause variations in sound speed profiles and lead to acoustic travel-time perturbations. In summer 2007, a combined acoustics/physical oceanography experiment was performed to study both the acoustical properties and the ocean dynamics of the Yellow Sea. The internal waves were recorded by the thermistor arrays. The receiving hydrophone array is enabled to monitor the acoustic travel-time fluctuations over the internal wave activities. It is shown that the activity of high frequency internal waves (having 3–6 min period) dominated the travel time perturbation. In this paper, we compare the data of high frequency internal wave with acoustic travel-time perturbation data and analyze the correlation between them. A simple relation between the modal travel-time perturbation and the displacement of the thermocline is developed which might be useful for monitoring purposes.

Nonlinear internal wave generation over the Yermak Plateau 

2021 ◽  
Author(s):  
Gabin Urbancic ◽  
Kevin Lamb ◽  
Ilker Fer ◽  
Laurie Padman
Keyword(s):  
Internal Wave ◽  
Arctic Ocean ◽  
Internal Waves ◽  
Wave Generation ◽  
The Arctic ◽  
Nonlinear Internal Wave ◽  
Nonlinear Internal Waves ◽  
The Arctic Ocean ◽  
Yermak Plateau ◽  
Internal Wave Generation

<p>North of the critical latitude (78.4), internal waves of the M<sub>2</sub> tidal frequency can no longer freely propagate, and the energy conversion from the barotropic to the internal tides vanishes. Near the continental slopes around the Arctic Ocean, internal wave energy is enhanced and comparable to values at mid-latitudes (Rippeth et al. 2015, Levine et al. 1985). Observations on the northern flank of the Yermak Plateau (YP) has characterized the region as one of enhanced internal wave activity and nonlinear internal waves have been observed (Czipott et al. 1991, Padman and Dillon 1991).</p><p>The YP is a bathymetry feature stretching out into the Fram Strait north-west of Svalbard. The YP plays a prominent role in the Arctic’s heat balance due to its interaction with the West-Spitsbergen current which is a main contributor to the heat transport into the Arctic Ocean. Nonlinear waves generated over the YP are a significant energy source for mixing and can therefore modulate and force exchange processes.</p><p>To study the nonlinear internal wave generation mechanisms over the YP, we used a high resolution, nonlinear, non-hydrostatic model. We found that nonlinear internal waves are forced not by the M<sub>2</sub> but the K<sub>1</sub> tide which has been observed to have significant variability over the YP (Padman et al. 1992). Barotropic, diurnal shelf waves generated on the eastern side of the YP propagates counter-clockwise, amplifying the cross-slope currents. This amplification is the necessary condition for nonlinear internal wave generation over the YP.</p>

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