Three-Dimensional Scattering of Internal Waves Off a Uniformly Sloping Bottom

2001 ◽  
Author(s):  
Rudolf C. Kloosterziel
Keyword(s):  
Internal Waves ◽  
Three Dimensional ◽  
Sloping Bottom

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.

The Generation of Nonlinear Internal Waves in the South China Sea: A Three‐Dimensional, Nonhydrostatic Numerical Study

2019 ◽  
Vol 124 (12) ◽  
pp. 8949-8968 ◽  
Author(s):  
Zhigang Lai ◽  
Guangzhen Jin ◽  
Yongmao Huang ◽  
Haiyun Chen ◽  
Xiaodong Shang ◽  
...  
Keyword(s):  
South China Sea ◽  
Internal Waves ◽  
South China ◽  
Numerical Study ◽  
Three Dimensional ◽  
The South China Sea ◽  
The South ◽  
Nonlinear Internal Waves ◽  
China Sea

scholarly journals Derivation of Three-Dimensional Radiation Stress Based on Lagrangian Solutions of Progressive Waves

2017 ◽  
Vol 47 (11) ◽  
pp. 2829-2842 ◽  
Author(s):  
Chao Ji ◽  
Qinghe Zhang ◽  
Yongsheng Wu
Keyword(s):  
Coordinate Transformation ◽  
Atmospheric Pressure ◽  
Three Dimensional ◽  
Sea Surface ◽  
Lagrangian Description ◽  
Radiation Stress ◽  
New Approach ◽  
Progressive Waves ◽  
Analytical Expressions ◽  
Sloping Bottom

AbstractA new approach has been proposed to derive the expressions for three-dimensional radiation stress using solutions of the pressure and velocity distributions and the coordinate transformation function that are derived from a Lagrangian description wherein the pressure is zero (relative to the atmospheric pressure) at the sea surface. Using this approach, analytical expressions of horizontal and vertical depth-dependent radiation stress are derived at a uniform depth and for a sloping bottom, respectively. The results of the depth integration of the expressions agree well with the theory of Longuet-Higgins and Stewart. In the case involving a sloping bottom, the radiation stress expressions from this study provide a better balance of the net momentum compared to those from previous studies.

On the three-dimensional internal waves excited by topography in the flow of a stratified fluid

1994 ◽  
Vol 263 ◽  
pp. 293-318 ◽  
Author(s):  
Hideshi Hanazaki
Keyword(s):  
Internal Waves ◽  
Numerical Study ◽  
Mach Reflection ◽  
Three Dimensional ◽  
Stratified Fluid ◽  
Linear Wave ◽  
Kp Equation ◽  
Subcritical Flow ◽  
Boussinesq Fluid ◽  
Upstream Waves

A numerical study of the three-dimensional internal waves excited by topography in the flow of a stratified fluid is described. In the resonant flow of a nearly two-layer fluid, it is found that the time-development of the nonlinearly excited waves agrees qualitatively with the solution of the forced KP equation or the forced extended KP equation. In this case, the upstream-advancing solitary waves become asymptotically straight crested because of abnormal reflection at the sidewall similar to Mach reflection. The same phenomenon also occurs in the subcritical flow of a nearly two-layer fluid. However, in the subcritical flow of a linearly stratified Boussinesq fluid, the two-dimensionalization of the upstream waves can be interpreted as the separation of the lateral modes due to the differences in the group velocity of the linear wave, although this does not mean in general that the generation of upstream waves is describable by the linearized equation.

scholarly journals Three-Dimensional Evolution of Large-Amplitude Internal Waves in the Strait of Gibraltar

2009 ◽  
Vol 39 (9) ◽  
pp. 2230-2246 ◽  
Author(s):  
Vasiliy Vlasenko ◽  
Jose C. Sanchez Garrido ◽  
Nataliya Stashchuk ◽  
Jesus Garcia Lafuente ◽  
Miguel Losada
Keyword(s):  
Internal Waves ◽  
Large Amplitude ◽  
Wave Train ◽  
Three Dimensional ◽  
Regular Structure ◽  
Strait Of Gibraltar ◽  
Multiple Reflections ◽  
In Situ Data ◽  
Scattered Energy

Abstract The modeling of large-amplitude internal waves (LAIWs) propagating in the Strait of Gibraltar is carried out using a fully nonlinear nonhydrostatic numerical model. The focus of the modeling efforts was on three-dimensional peculiarities of LAIW evolution, namely, cross-strait variability, interaction with lateral boundaries (including wave breaking and water mixing), radiation of secondary waves from orographic features, and interaction of secondary scattered internal waves. The along-channel propagation of packets of LAIWs reveals remarkable three-dimensional behavior. Due to the Coriolis force and multiple reflections from the lateral boundaries, the largest leading LAIW loses its energy much faster than that in the packet tail, which captures the scattered energy from the leading wave as it propagates and grows in amplitude. As a result of the energy transfer, the initially rank-ordered wave packet loses its regular structure to evolve into a non-rank-ordered wave train. In situ data collected in the eastern part of the Strait of Gibraltar confirm the idea that the non-rank-ordered structure is a common feature of internal wave packets emerging from the strait into the Alboran Sea.

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