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.

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

Numerical study of internal wave–wave interactions in a stratified fluid

2000 ◽  
Vol 415 ◽  
pp. 65-87 ◽  
Author(s):  
A. JAVAM ◽  
J. IMBERGER ◽  
S. W. ARMFIELD
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Numerical Study ◽  
Experimental Studies ◽  
Interaction Mechanism ◽  
Stratified Fluid ◽  
Interaction Region ◽  
Staggered Grid ◽  
Open Boundary ◽  
Wave Interactions

A finite volume method is used to study the generation, propagation and interaction of internal waves in a linearly stratified fluid. The internal waves were generated using single and multiple momentum sources. The full unsteady equations of motion were solved using a SIMPLE scheme on a non-staggered grid. An open boundary, based on the Sommerfield radiation condition, allowed waves to propagate through the computational boundaries with minimum reflection and distortion. For the case of a single momentum source, the effects of viscosity and nonlinearity on the generation and propagation of internal waves were investigated.Internal wave–wave interactions between two wave rays were studied using two momentum sources. The rays generated travelled out from the sources and intersected in interaction regions where nonlinear interactions caused the waves to break. When two rays had identical properties but opposite horizontal phase velocities (symmetric interaction), the interactions were not described by a triad interaction mechanism. Instead, energy was transferred to smaller wavelengths and, a few periods later, to standing evanescent modes in multiples of the primary frequency (greater than the ambient buoyancy frequencies) in the interaction region. The accumulation of the energy caused by these trapped modes within the interaction region resulted in the overturning of the density field. When the two rays had different properties (apart from the multiples of the forcing frequencies) the divisions of the forcing frequencies as well as the combination of the different frequencies were observed within the interaction region.The model was validated by comparing the results with those from experimental studies. Further, the energy balance was conserved and the dissipation of energy was shown to be related to the degree of nonlinear interaction.

scholarly journals Three-dimensional stability of a horizontally sheared flow in a stably stratified fluid

2007 ◽  
Vol 570 ◽  
pp. 297-305 ◽  
Author(s):  
AXEL DELONCLE ◽  
JEAN-MARC CHOMAZ ◽  
PAUL BILLANT
Keyword(s):  
Froude Number ◽  
Dimensional Stability ◽  
Numerical Study ◽  
Three Dimensional ◽  
Stratified Fluid ◽  
Two Dimensional ◽  
Horizontal Shear ◽  
Homogeneous Fluid ◽  
Sheared Flow ◽  
Vertical Scales

This paper investigates the three-dimensional stability of a horizontal flow sheared horizontally, the hyperbolic tangent velocity profile, in a stably stratified fluid. In an homogeneous fluid, the Squire theorem states that the most unstable perturbation is two-dimensional. When the flow is stably stratified, this theorem does not apply and we have performed a numerical study to investigate the three-dimensional stability characteristics of the flow. When the Froude number, Fh, is varied from ∞ to 0.05, the most unstable mode remains two-dimensional. However, the range of unstable vertical wavenumbers widens proportionally to the inverse of the Froude number for Fh ≪ 1. This means that the stronger the stratification, the smaller the vertical scales that can be destabilized. This loss of selectivity of the two-dimensional mode in horizontal shear flows stratified vertically may explain the layering observed numerically and experimentally.

Numerical Study of Three Dimensional Effects of Wave Impact on an Oscillating Wave Surge Converter

2015 ◽  
Author(s):  
Yanji Wei ◽  
Frederic Dias
Keyword(s):  
Numerical Study ◽  
Computational Cost ◽  
Three Dimensional ◽  
Wave Interaction ◽  
Diffraction Reflection ◽  
Linear Wave ◽  
Computational Domain ◽  
Wave Impact ◽  
Relaxation Zone ◽  
3D Effects

A CFD model to study the three-dimensional (3D) effects of wave impact on an Oscillating Wave Surge Converter (OWSC) has been demonstrated. Considering the excessive computational cost of CFD models, a relative small computational domain is used here. The velocity at the outside boundary is prescribed based on the classical non-linear wave theory. A relaxation zone is applied to absorb the diffraction/reflection waves by the device to avoid the re-reflection from the outer boundary. This zone is implemented by adding momentum source terms in the N–S equations to blend the near field flow into the far-field wave environment. The simulation of wave interaction with a fixed flap is performed to demonstrate the validity of the relaxation zone. Simulations of wave interaction with an OWSC by various wave conditions (different wave heights and incident angles) are then carried out to understand the 3D effects of the wave impact. The water elevation in the simulation is in agreement with the observations in the experiment. The variation of the pressure distribution indicates that the wave impact is enhanced at the centre of the flap, due to the water re-entry from the sides of the flap into the centre in 3D tests.

scholarly journals Schlieren visualisation and measurement of axisymmetric disturbances

2003 ◽  
Vol 10 (3) ◽  
pp. 303-309 ◽  
Author(s):  
B. R. Sutherland ◽  
M. R. Flynn ◽  
K. Onu
Keyword(s):  
Wave Field ◽  
Internal Waves ◽  
Three Dimensional ◽  
Ccd Camera ◽  
Stratified Fluid ◽  
Apparent Displacement ◽  
A New Technique ◽  
Axisymmetric Disturbances ◽  
Pixel Scale ◽  
Special Case

Abstract. Synthetic schlieren is a new technique that allows one easily and inexpensively to visualise density variations, such as those caused by internal waves propagating in a density stratified fluid. In the special case of two-dimensional internal waves (for example, those created by an oscillating cylinder), synthetic schlieren allows one to measure non-intrusively the wave amplitudes everywhere in space and time. The technique works by measuring the apparent displacement of points in a digitised image (such as a grid of horizontal lines), which is observed by a CCD camera through the experimental test section. Synthetic schlieren is sufficiently sensitive that it can measure sub-pixel-scale disturbances. In this work, we report on the first step toward measuring fully three-dimensional disturbances. We perform laboratory experiments in which internal waves are generated in a uniformly salt-stratified fluid by a vertically oscillating sphere. Theory predicts that the resulting wave-field is in the form of two cones emanating above and below the sphere. Using inverse tomographic techniques, we exploit the axisymmetry of the wave-field to relate the apparent displacement of pixels in an image to the wave amplitudes.

Sign in / Sign up

Export Citation Format

Share Document