Forcing of oceanic mean flows by dissipating internal tides

2012 ◽  
Vol 708 ◽  
pp. 250-278 ◽  
Author(s):  
Nicolas Grisouard ◽  
Oliver Bühler
Keyword(s):  
Numerical Study ◽  
Three Dimensional ◽  
Wave Drag ◽  
Perturbation Series ◽  
Internal Tides ◽  
Time Averaging ◽  
Mean Flow ◽  
Wave Source ◽  
Lee Waves ◽  
Lee Wave

AbstractWe present a theoretical and numerical study of the effective mean force exerted on an oceanic mean flow due to the presence of small-amplitude internal waves that are forced by the oscillatory flow of a barotropic tide over undulating topography and are also subject to dissipation. This extends the classic lee-wave drag problem of atmospheric wave–mean interaction theory to a more complicated oceanographic setting, because now the steady lee waves are replaced by oscillatory internal tides and, most importantly, because now the three-dimensional oceanic mean flow is defined by time averaging over the fast tidal cycles rather than by the zonal averaging familiar from atmospheric theory. Although the details of our computation are quite different, we recover the main action-at-a-distance result from the atmospheric setting, namely that the effective mean force that is felt by the mean flow is located in regions of wave dissipation, and not necessarily near the topographic wave source. Specifically, we derive an explicit expression for the effective mean force at leading order using a perturbation series in small wave amplitude within the framework of generalized Lagrangian-mean theory, discuss in detail the range of situations in which a strong, secularly growing mean-flow response can be expected, and then compute the effective mean force numerically in a number of idealized examples with simple topographies.

A closure for lee wave drag on the large-scale ocean circulation

2021 ◽  
Author(s):  
Carsten Eden ◽  
Dirk Olbers ◽  
Thomas Eriksen
Keyword(s):  
Large Scale ◽  
Surface Wind ◽  
Wave Drag ◽  
Ocean Model ◽  
Mean Flow ◽  
Model Simulations ◽  
Energy Transfers ◽  
Lee Waves ◽  
Lee Wave ◽  
The Mean

AbstractA new, energetically and dynamically consistent closure for the lee wave drag on the large scale circulation is developed and tested in idealized and realistic ocean model simulations. The closure is based on the radiative transfer equation for internal gravity waves, integrated over wavenumber space, and consists of two lee wave energy compartments for up-and downward propagating waves, which can be co-integrated in an ocean model. Mean parameters for vertical propagation, mean-ow interaction, and the vertical wave momentum flux are calculated assuming that the lee waves stay close to the spectral shape given by linear theory of their generation.Idealized model simulations demonstrate how lee waves are generated and interact with the mean flow and contribute to mixing, and document parameter sensitivities. A realistic eddy-permitting global model at 1/10° resolution coupled to the new closure yields a globally integrated energy flux of 0.27 TW into the lee wave field. The bottom lee wave stress on the mean flow can be locally as large as the surface wind stress and can reach into the surface layer. The interior energy transfers by the stress are directed from the mean flow to the waves, but this often reverses, for example in the Southern Ocean in case of shear reversal close to the bottom. The global integral of the interior energy transfers from mean ow to waves is 0.14 TW, while 0.04 TW is driving the mean ow, but this share depends on parameter choices for non-linear effects.

Dissipating and reflecting internal waves

2021 ◽  
Author(s):  
Callum J. Shakespeare ◽  
Brian K. Arbic ◽  
Andrew McC. Hogg
Keyword(s):  
Numerical Simulations ◽  
Linear Theory ◽  
Internal Waves ◽  
Energy Flux ◽  
Internal Tide ◽  
Internal Tides ◽  
Linear Wave ◽  
Lee Waves ◽  
Lee Wave ◽  
Upper Boundary

AbstractInternal waves generated at the seafloor propagate through the interior of the ocean, driving mixing where they break and dissipate. However, existing theories only describe these waves in two limiting cases. In one limit, the presence of an upper boundary permits bottom-generated waves to reflect from the ocean surface back to the seafloor, and all the energy flux is at discrete wavenumbers corresponding to resonant modes. In the other limit, waves are strongly dissipated such that they do not interact with the upper boundary and the energy flux is continuous over wavenumber. Here, a novel linear theory is developed for internal tides and lee waves that spans the parameter space in between these two limits. The linear theory is compared with a set of numerical simulations of internal tide and lee wave generation at realistic abyssal hill topography. The linear theory is able to replicate the spatially-averaged kinetic energy and dissipation of even highly non-linear wave fields in the numerical simulations via an appropriate choice of the linear dissipation operator, which represents turbulent wave breaking processes.

A numerical study of three-dimensional vortex ring instabilities: viscous corrections and early nonlinear stage

1994 ◽  
Vol 279 ◽  
pp. 351-375 ◽  
Author(s):  
Karim Shariff ◽  
Roberto Verzicco ◽  
Paolo Orlandi
Keyword(s):  
Growth Rates ◽  
Numerical Study ◽  
Initial Perturbation ◽  
Three Dimensional ◽  
Instability Wave ◽  
Mean Flow ◽  
Hairpin Vortices ◽  
Single Wave ◽  
Second Mode ◽  
Radial Structure

Finite-difference calculations with random and single-mode perturbations are used to study the three-dimensional instability of vortex rings. The basis of current understanding of the subject consists of a heuristic inviscid model (Widnall, Bliss & Tsai 1974) and a rigorous theory which predicts growth rates for thin-core uniform vorticity rings (Widnall & Tsai 1977). At sufficiently high Reynolds numbers the results correspond qualitatively to those predicted by the heuristic model: multiple bands of wavenumbers are amplified, each band having a distinct radial structure. However, a viscous correction factor to the peak inviscid growth rate is found. It is well described by the first term, 1 – α1(β)/Res, for a large range of Res. Here Res is the Reynolds number defined by Saffman (1978), which involves the curvature-induced strain rate. It is found to be the appropriate choice since then α1(β) varies weakly with core thickness β. The three most nonlinearly amplified modes are a mean azimuthal velocity in the form of opposing streams, an n = 1 mode (n is the azimuthal wavenumber) which arises from the interaction of two second-mode bending waves and the harmonic of the primary second mode. When a single wave is excited, higher harmonics begin to grow successively later with nonlinear growth rates proportional to n. The modified mean flow has a doubly peaked azimuthal vorticity. Since the curvature-induced strain is not exactly stagnation-point flow there is a preference for elongation towards the rear of the ring: the outer structure of the instability wave forms a long wake consisting of n hairpin vortices whose waviness is phase shifted π/n relative to the waviness in the core. Whereas the most amplified linear mode has three radial layers of structure, higher radial modes having more layers of radial structure (hairpins piled upon hairpins) are excited when the initial perturbation is large, reminiscent of visualization experiments on the formation of a turbulent ring at the generator.

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.

scholarly journals Orographic Drag Associated with Lee Waves Trapped at an Inversion

2013 ◽  
Vol 70 (9) ◽  
pp. 2930-2947 ◽  
Author(s):  
Miguel A. C. Teixeira ◽  
José Luis Argaín ◽  
Pedro M. A. Miranda
Keyword(s):  
Numerical Simulations ◽  
Mixed Boundary ◽  
Single Layer ◽  
Temperature Inversion ◽  
Static Stability ◽  
Wave Drag ◽  
Low Level ◽  
Flow Parameters ◽  
Lee Waves ◽  
Lee Wave

Abstract The drag produced by 2D orographic gravity waves trapped at a temperature inversion and waves propagating in the stably stratified layer existing above are explicitly calculated using linear theory, for a two-layer atmosphere with neutral static stability near the surface, mimicking a well-mixed boundary layer. For realistic values of the flow parameters, trapped-lee-wave drag, which is given by a closed analytical expression, is comparable to propagating-wave drag, especially in moderately to strongly nonhydrostatic conditions. In resonant flow, both drag components substantially exceed the single-layer hydrostatic drag estimate used in most parameterization schemes. Both drag components are optimally amplified for a relatively low-level inversion and Froude numbers Fr ≈ 1. While propagating-wave drag is maximized for approximately hydrostatic flow, trapped-lee-wave drag is maximized for l2a = O(1) (where l2 is the Scorer parameter in the stable layer and a is the mountain width). This roughly happens when the horizontal scale of trapped lee waves matches that of the mountain slope. The drag behavior as a function of Fr for l2H = 0.5 (where H is the inversion height) and different values of l2a shows good agreement with numerical simulations. Regions of parameter space with high trapped-lee-wave drag correlate reasonably well with those where lee-wave rotors were found to occur in previous nonlinear numerical simulations including frictional effects. This suggests that trapped-lee-wave drag, besides giving a relevant contribution to low-level drag exerted on the atmosphere, may also be useful to diagnose lee-rotor formation.

scholarly journals RIP CURRENTS ON A BARRED BEACH

2012 ◽  
Vol 1 (33) ◽  
pp. 38
Author(s):  
Andrea Ruju ◽  
Pablo Higuera ◽  
Javier L. Lara ◽  
Inigo J. Losada ◽  
Giovanni Coco
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Wave Generation ◽  
Dimensional Structure ◽  
Navier Stokes ◽  
Rip Currents ◽  
Mean Flow ◽  
Forcing Mechanisms

This work presents the numerical study of rip current circulation on a barred beach. The numerical simulations have been carried out with the IH-FOAM model which is based on the three dimensional Reynolds Averaged Navier-Stokes equations. The new boundary conditions implemented in IH-FOAM have been used, including three dimensional wave generation as well as active wave absorption at the boundary. Applying the specific wave generation boundary conditions, the model is validated to simulate rip circulation on a barred beach. Moreover, this study addresses the identification of the forcing mechanisms and the three dimensional structure of the mean flow.

Onset of three-dimensionality, equilibria, and early transition in flow over a backward-facing step

1991 ◽  
Vol 231 ◽  
pp. 501-528 ◽  
Author(s):  
Lambros Kaiktsis ◽  
George Em Karniadakis ◽  
Steven A. Orszag
Keyword(s):  
Numerical Study ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Shear Layers ◽  
Secondary Instability ◽  
Transition To Turbulence ◽  
Single Frequency ◽  
Mean Flow ◽  
Backward Facing Step ◽  
Numerical Predictions

A numerical study of three-dimensional equilibria and transition to turbulence in flow over a backward-facing step is performed using direct numerical solution of the incompressible Navier-Stokes equations. The numerical method is a high-order-accurate mixed spectral/spectral-element method with efficient viscous outflow boundary conditions. The appearance of three-dimensionality in nominally two-dimensional geometries is investigated at representative Reynolds numbers ranging from the onset of three-dimensional bifurcation to later transitional stages. Strongly three-dimensional regions are identified through standard correlation coefficients and new three-dimensionality indices, as well as through instantaneous and time-average streamline patterns and vorticity contours. Our results indicate that onset of three-dimensionality occurs at the boundaries between the primary and secondary recirculating zones with the main channel flow, the latter being the most stable flow component. There is. therefore, strong secondary instability in the shear layers, mainly due to the one emanating from the step corner.The flow further downstream is excited through the action of the upstream shear layers acquiring a wavy form closely resembling Tollmien–Schlichting waves both spatially and temporally with a characteristic frequency f1; upstream, at the shear layer another incommensurate frequency, f2, is present. The two-frequency flow locks-in to a single frequency if external excitations are imposed at the inflow at a frequency close to f1 or f2; the smaller amplitude excitations, however, may cause a strong quasi-periodic response. Such excitations may significantly increase or decrease (by more than 20%) the length of the primary separation zone XR at lock-in or quasi-periodic states. The equilibrium states resulting from the secondary instability at supercritical Reynolds numbers produce a flow modulated in the spanwise direction, with corresponding variations in the reattachment location XR. While three-dimensionality explains partially the discrepancy between numerical predictions and experimental results on XR at higher Reynolds number Re, the main source of discrepancy is attributed to the inflow conditions, and in particular to external disturbances superimposed on the mean flow, the latter being the main reason also for the somewhat earlier transition found in laboratory experiments.

Stratified rotating flow over and around isolated three-dimensional topography

1987 ◽  
Vol 322 (1564) ◽  
pp. 213-241 ◽  
Keyword(s):  
Numerical Model ◽  
Three Dimensional ◽  
Wave Pattern ◽  
The Body ◽  
Lee Waves ◽  
Lee Wave ◽  
Long Time ◽  
Dynamical Parameters ◽  
The Right ◽  
Eddy Shedding

Laboratory and numerical experiments have been conducted on the flow of a linearly stratified rotating fluid past isolated obstacles of revolution (conical and cosinesquared profiles). Laboratory experiments are considered for a range of Rossby, Ekman and Burger numbers, the pertinent dynamical parameters of the system. In these experiments, inertial, Coriolis, pressure, viscous and buoyancy forces all play a significant role. Emphasis is given to examining the nature of the time development of the flow fields as well as its long-time behaviour, including eddy shedding. It is shown, for example, that increased stratification tends to diminish the steering effect of the obstacle, other parameters being fixed, at elevation levels above the topography. At levels below the top of the obstacle, increased stratification tends to force the fluid around rather than over the body and this, in turn, tends to develop vortex shedding at smaller Reynolds numbers than would occur in corresponding lower stratification cases. Data for the cone reveal that the Strouhal number for the eddy-shedding regime is relatively insensitive to the values of Ro , Ek and S for the range of parameters investigated. Stratification tends to induce lee waves in the topography wake, and the nature of this lee-wave pattern is modified by the presence of rotation. For example, it is demonstrated that for vertically upward rotation, the lee waves on the right, facing downstream, have a larger amplitude than their counterparts at the same location on the left. The steering effects, as predicted by a three-level quasigeostrophic numerical model, are shown to be in good agreement with the laboratory results for a narrow range of parameter space. The numerical model is used to examine the effects of rotation, friction and stratification in modifying the flow. The quasigeostrophic numerical simulations do not produce eddy shedding, and it is concluded that a full, primitive equation numerical model would be needed to explore this phenomenon.

Lee-Wave Resonances over Double Bell-Shaped Obstacles

2009 ◽  
Vol 66 (5) ◽  
pp. 1205-1228 ◽  
Author(s):  
Vanda Grubišić ◽  
Ivana Stiperski
Keyword(s):  
Sierra Nevada ◽  
Lower Boundary ◽  
Vertical Wind Shear ◽  
Separation Distance ◽  
Wave Drag ◽  
Owens Valley ◽  
Lower Boundary Condition ◽  
Atmospheric Structure ◽  
Lee Waves ◽  
Lee Wave

Abstract Lee-wave resonance over double bell-shaped obstacles is investigated through a series of idealized high-resolution numerical simulations with the nonhydrostatic Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) model using a free-slip lower boundary condition. The profiles of wind speed and stability as well as terrain derive from observations of lee-wave events over the Sierra Nevada and Inyo Mountains from the recently completed Terrain-Induced Rotor Experiment (T-REX). Numerical experiments show that double bell-shaped obstacles promote trapped lee waves that are in general shorter than those excited by an isolated ridge. While the permissible trapped lee-wave modes are determined by the upstream atmospheric structure, primarily vertical wind shear, the selected lee-wave wavelengths for two obstacles that are close or equal in height are dictated by the discrete terrain spectrum and correspond to higher harmonics of the primary orographic wavelength, which is equal to the ridge separation distance. The exception is the smallest ridge separation distance examined, one that corresponds to the Owens Valley width and is closest to the wavelength determined by the given upstream atmospheric structure, for which the primary lee-wave and orographic wavelengths were found to nearly coincide. The influence two mountains exert on the overall lee-wave field is found to persist at very large ridge separation distances. For the nonlinear nonhydrostatic waves examined, the ridge separation distance is found to exert a much stronger control over the lee-wave wavelengths than the mountain half-width. Positive and negative interferences of lee waves, which can be detected through their imprint on wave drag and wave amplitudes, were found to produce appreciable differences in the flow structure mainly over the downstream peak, with negative interference characterized by a highly symmetric flow pattern leading to a low drag state.

scholarly journals Improving Nonlinear and Nonhydrostatic Ocean Lee Wave Drag Parameterizations

2020 ◽  
Vol 50 (9) ◽  
pp. 2417-2435
Author(s):  
Frederick T. Mayer ◽  
Oliver B. Fringer
Keyword(s):  
Steady State ◽  
Characteristic Time ◽  
Wave Theory ◽  
Wave Drag ◽  
Characteristic Time Scale ◽  
Time Varying ◽  
Global Circulation ◽  
Global Circulation Models ◽  
Lee Waves ◽  
Lee Wave

AbstractOcean lee waves occur on length scales that are smaller than the grid scale of global circulation models (GCMs). Therefore, such models must parameterize the drag associated with launching lee waves. This paper compares the lee wave drag predicted by existing parameterizations with the drag measured in high-resolution nonhydrostatic numerical simulations of a lee wave over periodic sinusoidal bathymetry. The simulations afford a time-varying glimpse at the nonlinear and nonhydrostatic oceanic lee wave spinup process and identify a characteristic time scale to reach steady state. The maximum instantaneous lee wave drag observed during the spinup period is found to be well predicted by linear lee wave theory for all hill heights. In steady state, the simulations demonstrate the applicability of parameterizing the drag based on applying linear theory to the lowest overtopping streamline of the flow (LOTS), as is currently employed in GCMs. However, because existing parameterizations are based only on the height of the LOTS, they implicitly assume hydrostatic flow. For hills tall enough to trap water in their valleys, the simulations identify a set of nonhydrostatic processes that can result in a reduction of the lee wave drag from that given by hydrostatic parameterizations. The simulations suggest implementing a time-dependent nonhydrostatic version of the LOTS-based parameterization of lee wave drag and demonstrate the remarkable applicability of linear lee wave theory to oceanic lee waves.

Sign in / Sign up

Export Citation Format

Share Document