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 Numerical Study for Experiment on Wave Pattern of Internal Wave and Surface Wave in Stratified Fluid

2019 ◽  
Vol 33 (3) ◽  
pp. 236-244
Author(s):  
Ju-Han Lee ◽  
Kwan-Woo Kim ◽  
Kwang-Jun Paik ◽  
Won-Cheol Koo ◽  
Yeong-Gyu Kim
Keyword(s):  
Surface Wave ◽  
Internal Wave ◽  
Numerical Study ◽  
Wave Pattern ◽  
Stratified Fluid

scholarly journals Resurrecting dead-water phenomenon

2011 ◽  
Vol 18 (2) ◽  
pp. 193-208 ◽  
Author(s):  
M. J. Mercier ◽  
R. Vasseur ◽  
T. Dauxois
Keyword(s):  
Internal Waves ◽  
Large Amplitude ◽  
Experimental Studies ◽  
Nonlinear Effects ◽  
Stratified Fluid ◽  
Nonlinear Internal Waves ◽  
Induced Drag ◽  
Wave Induced ◽  
Dead Water ◽  
Peculiar Phenomenon

Abstract. We revisit experimental studies performed by Ekman on dead-water (Ekman, 1904) using modern techniques in order to present new insights on this peculiar phenomenon. We extend its description to more general situations such as a three-layer fluid or a linearly stratified fluid in presence of a pycnocline, showing the robustness of dead-water phenomenon. We observe large amplitude nonlinear internal waves which are coupled to the boat dynamics, and we emphasize that the modeling of the wave-induced drag requires more analysis, taking into account nonlinear effects. Dedicated to Fridtjöf Nansen born 150 yr ago (10 October 1861).

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.

Numerical study on the interaction between the internal and surface waves by a 2D hydrofoil moving in two-layer stratified fluid

2020 ◽  
pp. 147509022097416
Author(s):  
Kwan-Woo Kim ◽  
Ju-Han Lee ◽  
Kwang-Jun Paik ◽  
Weoncheol Koo ◽  
Young-Gyu Kim
Keyword(s):  
Internal Wave ◽  
Water Temperature ◽  
Mixture Model ◽  
Numerical Study ◽  
Stratified Flow ◽  
Stratified Fluid ◽  
Flow Volume ◽  
Cfd Model ◽  
Vof Model ◽  
Submergence Depth

The water temperature in the ocean varies according to its depth and generates a thermocline layer. An internal wave can be excited by an object moving near the thermocline layer because the density changes owing to the water temperature. The internal wave propagates and interacts with the surface wave. This study aims to investigate the internal wave propagation in a two-layer stratified flow, generated by 2D hydrofoil (NACA0012) using a RANS based CFD model. Eulerian multiphase methods were used for the modeling of the two-layer stratified flow; Volume of Fluid (VOF) model and mixture model. A two-layer stratified fluid consisting of air(ρair)-water1(ρw1)-water2(ρw2) is considered instead of the thermocline layer to simplify the numerical simulations. The generation and propagation of the internal wave were investigated, with different configurations of the speed and submergence depth of the hydrofoil. The result suggested that the VOF model shows better agreement with the experimental data compared to the mixture model.

Numerical study of internal wave–caustic and internal wave–shear interactions in a stratified fluid

2000 ◽  
Vol 415 ◽  
pp. 89-116 ◽  
Author(s):  
A. JAVAM ◽  
J. IMBERGER ◽  
S. W. ARMFIELD
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Turning Point ◽  
Critical Level ◽  
Numerical Study ◽  
Shear Instability ◽  
Level Energy ◽  
Mean Flow ◽  
Reflected Waves ◽  
The Mean

The behaviour of internal waves at a caustic level, turning point and critical layer have been investigated numerically. At a caustic reflection, a triad interaction was formed within the reflection region and the internal wave energy was transferred to lower frequencies (subharmonics). This resulted in a local subharmonic instability. One of the excited internal waves penetrated the caustic level and propagated downwards. This downward propagating wave then produced a second caustic where further reflection could take place. At a turning point, nonlinear interaction between the incident and reflected waves transferred energy to higher frequencies (evanescent trapped waves) which resulted in a superharmonic instability. At the critical level, energy was transferred to the mean flow. As the degree of nonlinearity increased, more energy was found to be transferred and overturning resulted due to a shear instability.

scholarly journals Observed Eddy–Internal Wave Interactions in the Southern Ocean

2020 ◽  
Vol 50 (10) ◽  
pp. 3043-3062
Author(s):  
Jesse M. Cusack ◽  
J. Alexander Brearley ◽  
Alberto C. Naveira Garabato ◽  
David A. Smeed ◽  
Kurt L. Polzin ◽  
...  
Keyword(s):  
Energy Transfer ◽  
Southern Ocean ◽  
Internal Wave ◽  
Wave Field ◽  
Internal Waves ◽  
Temporal Variability ◽  
Mesoscale Eddy ◽  
Linear Wave ◽  
Wave Interactions ◽  
Internal Wave Field

AbstractThe physical mechanisms that remove energy from the Southern Ocean’s vigorous mesoscale eddy field are not well understood. One proposed mechanism is direct energy transfer to the internal wave field in the ocean interior, via eddy-induced straining and shearing of preexisting internal waves. The magnitude, vertical structure, and temporal variability of the rate of energy transfer between eddies and internal waves is quantified from a 14-month deployment of a mooring cluster in the Scotia Sea. Velocity and buoyancy observations are decomposed into wave and eddy components, and the energy transfer is estimated using the Reynolds-averaged energy equation. We find that eddies gain energy from the internal wave field at a rate of −2.2 ± 0.6 mW m−2, integrated from the bottom to 566 m below the surface. This result can be decomposed into a positive (eddy to wave) component, equal to 0.2 ± 0.1 mW m−2, driven by horizontal straining of internal waves, and a negative (wave to eddy) component, equal to −2.5 ± 0.6 mW m−2, driven by vertical shearing of the wave spectrum. Temporal variability of the transfer rate is much greater than the mean value. Close to topography, large energy transfers are associated with low-frequency buoyancy fluxes, the underpinning physics of which do not conform to linear wave dynamics and are thereby in need of further research. Our work suggests that eddy–internal wave interactions may play a significant role in the energy balance of the Southern Ocean mesoscale eddy and internal wave fields.

An analogy between electromagnetic and internal waves

2019 ◽  
Vol 485 (4) ◽  
pp. 428-433
Author(s):  
V. G. Baydulov ◽  
P. A. Lesovskiy
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Internal Wave ◽  
Special Relativity ◽  
Internal Waves ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Lagrange Function ◽  
Lorentz Transformations ◽  
Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

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