scholarly journals Internal wave drag in stratified flow over mountains on a beta plane

2008 ◽  
Vol 134 (630) ◽  
pp. 11-19 ◽  
Author(s):  
M. A. C. Teixeira ◽  
Branko Grisogono
Keyword(s):  
Internal Wave ◽  
Stratified Flow ◽  
Wave Drag ◽  
Beta Plane

Lee waves in a stratified flow Part 1. Thin barrier

1968 ◽  
Vol 32 (3) ◽  
pp. 549-567 ◽  
Author(s):  
John W. Miles
Keyword(s):  
Integral Equation ◽  
Half Space ◽  
Dynamic Pressure ◽  
Separation Of Variables ◽  
Stratified Flow ◽  
Wave Drag ◽  
Variational Approximations ◽  
Lee Waves ◽  
Lee Wave ◽  
Thin Barrier

The lee-wave amplitudes and wave drag for a thin barrier in a two-dimensional stratified flow in which the upstream dynamic pressure and density gradient are constant (Long's model) are determined as functions of barrier height and Froude number for a channel of finite height and for a half-space. Variational approximations to these quantities are obtained and validated by comparison with the earlier results of Drazin & Moore (1967) for the channel and with the results of an exact solution for the half-space, as obtained through separation of variables. An approximate solution of the integral equation for the channel also is obtained through a reduction to a singular integral equation of potential theory. The wave drag tends to increase with decreasing wind speed, but it seems likely that the flow is unstable in the region of high drag. The maximum attainable drag coefficient consistent with stable lee-wave formation appears to be roughly two and almost certainly less than three.

Lee waves in a stratified flow. Part 4. Perturbation approximations

1969 ◽  
Vol 35 (3) ◽  
pp. 497-525 ◽  
Author(s):  
John W. Miles ◽  
Herbert E. Huppert
Keyword(s):  
Integral Equation ◽  
Rayleigh Scattering ◽  
Dynamic Pressure ◽  
Slenderness Ratio ◽  
Stratified Flow ◽  
Approximate Solutions ◽  
Wave Drag ◽  
Wave Formation ◽  
Lee Wave ◽  
Dipole Form

A two-dimensional stratified flow over an obstacle in a half space is considered on the assumptions that the upstream dynamic pressure and density gradient are constant (Long's model). A general solution of the resulting boundary-value problem is established in terms of an assumed distribution of dipole sources. Asymptotic solutions for prescribed bodies are established for limiting values of the slenderness ratio ε (height/breadth) of the obstacle and the reduced frequency k (inverse Froude number based on the obstacle breadth) as follows: (i) ε → 0 withkfixed; (ii)k→ 0 with ε fixed; (iii)k→ ∞ withkεfixed. The approximation (i) is deveoped to both first (linearized theory) and second order in ε in terms of Fourier integrals. The approximation (ii), which constitutes a modification of Rayleigh-scattering theory, is obtained by the method of matched asymptotic expansions and depends essentially on thedipole form(which is proportional to the sum of the displaced and virtual masses) of the obstacle with respect to a uniform flow. A simple approximation to this dipole form is proposed and validated by a series of examples in an appendix. The approximation (iii) is obtained through the reduction of the original integral equation to a singular integral equation of Hilbert's type that is solved by the techniques of function theory. A composite approximation to the lee-wave field that is valid in each of the limits (i)-(iii) also is obtained. The approximation (iii) yields an estimate of the maximum value ofkεfor which completely stable lee-wave formation behind a slender obstacle is possible. The differential and total scattering cross-sections and the wave drag on the obstacle are related to the power spectrum of the dipole density. It is shown that the drag is invariant under a reversal of the flow in the limits (i) and (ii), but only for a symmetric obstacle in the limit (iii). The results are applied to a semi-ellipse, an asymmetric generalization thereof, the Witch of Agnesi (Queney's mountain), and a rectangle. The approximate results for the semi-ellipse are compared with the more accurate results obtain by Huppert & Miles (1969). It appears from this comparison that the approximate solutions should be adequate for any slender obstacle within the range ofkεfor which completely stable lee-wave formation is possible. The extension to obstacles in a channel of finite height is considered in an appendix.

scholarly journals Impact of Parameterized Internal Wave Drag on the Semidiurnal Energy Balance in a Global Ocean Circulation Model

2016 ◽  
Vol 46 (5) ◽  
pp. 1399-1419 ◽  
Author(s):  
Maarten C. Buijsman ◽  
Joseph K. Ansong ◽  
Brian K. Arbic ◽  
James G. Richman ◽  
Jay F. Shriver ◽  
...  
Keyword(s):  
Internal Wave ◽  
Ocean Circulation ◽  
Deep Water ◽  
Mode Conversion ◽  
Circulation Model ◽  
Wave Drag ◽  
Ocean Model ◽  
Internal Tides ◽  
Global Ocean ◽  
Numerical Dissipation

AbstractThe effects of a parameterized linear internal wave drag on the semidiurnal barotropic and baroclinic energetics of a realistically forced, three-dimensional global ocean model are analyzed. Although the main purpose of the parameterization is to improve the surface tides, it also influences the internal tides. The relatively coarse resolution of the model of ~8 km only permits the generation and propagation of the first three vertical modes. Hence, this wave drag parameterization represents the energy conversion to and the subsequent breaking of the unresolved high modes. The total tidal energy input and the spatial distribution of the barotropic energy loss agree with the Ocean Topography Experiment (TOPEX)/Poseidon (TPXO) tidal inversion model. The wave drag overestimates the high-mode conversion at ocean ridges as measured against regional high-resolution models. The wave drag also damps the low-mode internal tides as they propagate away from their generation sites. Hence, it can be considered a scattering parameterization, causing more than 50% of the deep-water dissipation of the internal tides. In the near field, most of the baroclinic dissipation is attributed to viscous and numerical dissipation. The far-field decay of the simulated internal tides is in agreement with satellite altimetry and falls within the broad range of Argo-inferred dissipation rates. In the simulation, about 12% of the semidiurnal internal tide energy generated in deep water reaches the continental margins.

scholarly journals The Effect of Wind Shear and Curvature on the Gravity Wave Drag Produced by a Ridge

2004 ◽  
Vol 61 (21) ◽  
pp. 2638-2643 ◽  
Author(s):  
Miguel A. C. Teixeira ◽  
Pedro M. A. Miranda
Keyword(s):  
Gravity Wave ◽  
Analytical Model ◽  
Wind Shear ◽  
Stratified Flow ◽  
Wave Drag ◽  
Mountain Ridge ◽  
Vertical Variation ◽  
Hydrostatic Approximation

Abstract The analytical model proposed by Teixeira, Miranda, and Valente is modified to calculate the gravity wave drag exerted by a stratified flow over a 2D mountain ridge. The drag is found to be more strongly affected by the vertical variation of the background velocity than for an axisymmetric mountain. In the hydrostatic approximation, the corrections to the drag due to this effect do not depend on the detailed shape of the ridge as long as this is exactly 2D. Besides the drag, all the perturbed quantities of the flow at the surface, including the pressure, may be calculated analytically.

scholarly journals A Closure for Internal Wave–Mean Flow Interaction. Part II: Wave Drag

2017 ◽  
Vol 47 (6) ◽  
pp. 1403-1412 ◽  
Author(s):  
Carsten Eden ◽  
Dirk Olbers
Keyword(s):  
Wave Propagation ◽  
Internal Wave ◽  
Ocean Circulation ◽  
Wave Drag ◽  
Ocean Model ◽  
Vertical Shear ◽  
Mean Flow ◽  
Flow Interaction ◽  
Two Dimensional Flow ◽  
Novel Concept

AbstractA novel concept for parameterizing internal wave–mean flow interaction in ocean circulation models is extended to an arbitrary two-dimensional flow with vertical shear. The concept is based on the description of the entire wave field by the wave-energy density in physical and wavenumber space and its prognostic computation by the radiative transfer equation integrated in wavenumber space. Energy compartments result for the horizontal direction of wave propagation as additional prognostic model variables, of which only four are taken here for simplicity. The mean flow is interpreted as residual velocities with respect to the wave activity. The effect of wave drag and energy exchange due to the vertical shear of the residual mean flow is then given simply by a vertical flux of momentum. This flux is related to the asymmetries in upward, downward, alongflow, and counterflow wave propagation described by the energy compartments. A numerical implementation in a realistic eddying ocean model shows that the wave drag effect is a significant sink of kinetic energy in the interior ocean.

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.

scholarly journals Resonant gravity-wave drag enhancement in linear stratified flow over mountains

2005 ◽  
Vol 131 (609) ◽  
pp. 1795-1814 ◽  
Author(s):  
M. A. C. Teixeira ◽  
P. M. A. Miranda ◽  
J. L. Argain ◽  
M. A. Valente
Keyword(s):  
Gravity Wave ◽  
Stratified Flow ◽  
Wave Drag
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