scholarly journals Energy Sinks for Lee Waves in Shear Flow

2019 ◽  
Vol 49 (11) ◽  
pp. 2851-2865 ◽  
Author(s):  
Eric Kunze ◽  
Ren-Chieh Lien
Keyword(s):  
Wave Generation ◽  
Flow Speed ◽  
Wave Action ◽  
Wave Radiation ◽  
Bottom Current ◽  
Mean Flow ◽  
Turbulent Dissipation ◽  
Lee Waves ◽  
Lee Wave ◽  
The Mean

AbstractMicrostructure measurements in Drake Passage and on the flanks of Kerguelen Plateau find turbulent dissipation rates ε on average factors of 2–3 smaller than linear lee-wave generation predictions, as well as a factor of 3 smaller than the predictions of a well-established parameterization based on finescale shear and strain. Here, the possibility that these discrepancies are a result of conservation of wave action E/ωL = E/|kU| is explored. Conservation of wave action will transfer a fraction of the lee-wave radiation back to the mean flow if the waves encounter weakening currents U, where the intrinsic or Lagrangian frequency ωL = |kU| ↓ |f| and k the along-stream horizontal wavenumber, where kU ≡ k ⋅ V. The dissipative fraction of power that is lost to turbulence depends on the Doppler shift of the intrinsic frequency between generation and breaking, hence on the topographic height spectrum and bandwidth N/f. The partition between dissipation and loss to the mean flow is quantified for typical topographic height spectral shapes and N/f ratios found in the abyssal ocean under the assumption that blocking is local in wavenumber. Although some fraction of lee-wave generation is always dissipated in a rotating fluid, lee waves are not as large a sink for balanced energy or as large a source for turbulence as previously suggested. The dissipative fraction is 0.44–0.56 for topographic spectral slopes and buoyancy frequencies typical of the deep Southern Ocean, insensitive to flow speed U and topographic splitting. Lee waves are also an important mechanism for redistributing balanced energy within their generating bottom current.

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.

scholarly journals Energy Loss from Transient Eddies due to Lee Wave Generation in the Southern Ocean

2018 ◽  
Vol 48 (12) ◽  
pp. 2867-2885 ◽  
Author(s):  
Luwei Yang ◽  
Maxim Nikurashin ◽  
Andrew M. Hogg ◽  
Bernadette M. Sloyan
Keyword(s):  
Southern Ocean ◽  
Energy Loss ◽  
Wave Generation ◽  
Global Ocean ◽  
Small Scale ◽  
Transient Eddy ◽  
Mean Flow ◽  
Lee Waves ◽  
Lee Wave ◽  
Eddy Flow

ABSTRACTObservations suggest that enhanced turbulent dissipation and mixing over rough topography are modulated by the transient eddy field through the generation and breaking of lee waves in the Southern Ocean. Idealized simulations also suggest that lee waves are important in the energy pathway from eddies to turbulence. However, the energy loss from eddies due to lee wave generation remains poorly estimated. This study quantifies the relative energy loss from the time-mean and transient eddy flow in the Southern Ocean due to lee wave generation using an eddy-resolving global ocean model and three independent topographic datasets. The authors find that the energy loss from the transient eddy flow (0.12 TW; 1 TW = 1012 W) is larger than that from the time-mean flow (0.04 TW) due to lee wave generation; lee wave generation makes a larger contribution (0.12 TW) to the energy loss from the transient eddy flow than the dissipation in turbulent bottom boundary layer (0.05 TW). This study also shows that the energy loss from the time-mean flow is regulated by the transient eddy flow, and energy loss from the transient eddy flow is sensitive to the representation of anisotropy in small-scale topography. It is implied that lee waves should be parameterized in eddy-resolving global ocean models to improve the energetics of resolved flow.

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.

The Reflection of a Stationary Gravity Wave by a Viscous Boundary Layer

2007 ◽  
Vol 64 (9) ◽  
pp. 3363-3371 ◽  
Author(s):  
François Lott
Keyword(s):  
Boundary Layer ◽  
Gravity Wave ◽  
Richardson Number ◽  
Critical Level ◽  
Inviscid Limit ◽  
Mean Flow ◽  
Viscous Boundary Layer ◽  
Lee Waves ◽  
The Mean ◽  
Viscous Boundary

Abstract The backward reflection of a stationary gravity wave (GW) propagating toward the ground is examined in the linear viscous case and for large Reynolds numbers (Re). In this case, the stationary GW presents a critical level at the ground because the mean wind is null there. When the mean flow Richardson number at the surface (J) is below 0.25, the GW reflection by the viscous boundary layer is total in the inviscid limit Re → ∞. The GW is a little absorbed when Re is finite, and the reflection decreases when both the dissipation and J increase. When J > 0.25, the GW is absorbed for all values of the Reynolds number, with a general tendency for the GW reflection to decrease when J increases. As a large ground reflection favors the downstream development of a trapped lee wave, the fact that it decreases when J increases explains why the more unstable boundary layers favor the onset of mountain lee waves. It is also shown that the GW reflection when J > 0.25 is substantially larger than that predicted by the conventional inviscid critical level theory and larger than that predicted when the dissipations are represented by Rayleigh friction and Newtonian cooling. The fact that the GW reflection depends strongly on the Richardson number indicates that there is some correspondence between the dynamics of trapped lee waves and the dynamics of Kelvin–Helmholtz instabilities. Accordingly, and in one classical example, it is shown that some among the neutral modes for Kelvin–Helmholtz instabilities that exist in an unbounded flow when J < 0.25 can also be stationary trapped-wave solutions when there is a ground and in the inviscid limit Re → ∞. When Re is finite, these solutions are affected by the dissipation in the boundary layer and decay in the downstream direction. Interestingly, their decay rate increases when both the dissipation and J increase, as does the GW absorption by the viscous boundary layer.

ABSOLUTE INSTABILITY OR CHAOS? — A TRIBUTE TO DR. DAVID G. CRIGHTON

2002 ◽  
Vol 10 (04) ◽  
pp. 407-419
Author(s):  
SEAN F. WU
Keyword(s):  
Elastic Plate ◽  
Equilibrium Position ◽  
Flexural Vibration ◽  
Critical Value ◽  
Flow Speed ◽  
Multiple Equilibrium ◽  
Absolute Instability ◽  
Mean Flow ◽  
Structural Nonlinearities ◽  
The Mean

The stabilities of an elastic plate clamped on an infinite, rigid baffle subject to any time dependent force excitation in the presence of mean flow are examined. The mechanisms that can cause plate flexural vibrations to be absolute unstable when the mean flow speed exceeds a critical value are revealed. Results show that the instabilities of an elastic plate are mainly caused by an added stiffness due to acoustic radiation in mean flow, but controlled by the structural nonlinearities. This added stiffness is shown to be negative and increase quadratically with the mean flow speed. Hence, as the mean flow speed approaches a critical value, the added stiffness may null the overall stiffness of the plate, leading to an unstable condition. Note that without the inclusion of the structural nonlinearities, the plate has only one equilibrium position, namely, its undeformed flat position. Under this condition, the amplitude of plate flexural vibration would grow exponentially in time everywhere, known as absolute instability. With the inclusion of structural nonlinearities, the plate may possess multiple equilibrium positions. When the mean flow speed exceeds the critical values, the plate may be unstable and jump from one equilibrium position to another. Since this jumping is random, the plate flexural vibration may seem chaotic.

scholarly journals Marginal Instability?

2009 ◽  
Vol 39 (9) ◽  
pp. 2373-2381 ◽  
Author(s):  
S. A. Thorpe ◽  
Zhiyu Liu
Keyword(s):  
Richardson Number ◽  
Maximum Growth ◽  
Flow Speed ◽  
Maximum Growth Rate ◽  
Buoyancy Frequency ◽  
Mean Flow ◽  
Boundary Layer Flows ◽  
Naturally Occurring ◽  
Marginal State ◽  
The Mean

Abstract Some naturally occurring, continually forced, turbulent, stably stratified, mean shear flows are in a state close to that in which their stability changes, usually from being dynamically unstable to being stable: the time-averaged flows that are observed are in a state of marginal instability. By “marginal instability” the authors mean that a small fractional increase in the gradient Richardson number Ri of the mean flow produced by reducing the velocity and, hence, shear is sufficient to stabilize the flow: the increase makes Rimin, the minimum Ri in the flow, equal to Ric, the critical value of this minimum Richardson number. The value of Ric is determined by solving the Taylor–Goldstein equation using the observed buoyancy frequency and the modified velocity. Stability is quantified in terms of a factor, Φ, such that multiplying the flow speed by (1 + Φ) is just sufficient to stabilize it, or that Ric = Rimin/(1 + Φ)2. The hypothesis that stably stratified boundary layer flows are in a marginal state with Φ < 0 and with |Φ| small compared to unity is examined. Some dense water cascades are marginally unstable with small and negative Φ and with Ric substantially less than ¼. The mean flow in a mixed layer driven by wind stress on the water surface is, however, found to be relatively unstable, providing a counterexample that refutes the hypothesis. In several naturally occurring flows, the time for exponential growth of disturbances (the inverse of the maximum growth rate) is approximately equal to the average buoyancy period observed in the turbulent region.

An experimental investigation of pulsating turbulent water flow in a tube

1971 ◽  
Vol 46 (1) ◽  
pp. 43-64 ◽  
Author(s):  
J. H. Gerrard
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Water Flow ◽  
Cylindrical Tube ◽  
Flow Speed ◽  
Mean Flow ◽  
Mean Velocity ◽  
Central Plateau ◽  
Transition Range ◽  
The Mean

Experiments were made on a pulsating water flow at a mean flow Reynolds number of 3770 in a cylindrical tube of diameter 3·81 cm. Pulsations were produced by a piston oscillating in simple harmonic motion with a period of 12 s. Turbulence was made visible by means of a sheet of dye produced by electrolysis from a fine wire stretched across a diameter. The sheet of dye is contorted by the turbulent eddies, and ciné-photography was used to find the velocity of convection which was shown to be the flow speed except in certain circumstances which are discussed. By subtracting the mean flow velocity profile the profile of the component of the motion oscillating at the imposed frequency was determined.The Reynolds number of these experiments lies in the turbulent transition range, so that large effects of laminarization are observed. In the turbulent phase, the velocity profile was found to possess a central plateau as does the laminar oscillating profile. The level and radial extent of this were little different from the laminar ones. Near to the wall, the turbulent oscillating profile is well represented by the mean velocity power law relationship, u/U ∝ (y/a)1/n. In the laminarized phase, the turbulent intensity is considerably reduced at this Reynolds number. The velocity profile for the whole flow (mean plus oscillating) relaxes towards the laminar profile. Laminarization contributes appreciably to the oscillating component.Extrapolation of the results to higher Reynolds numbers and different frequencies of oscillation is suggested.

EFFECT OF TURBULENCE ON SOUND RADIATION BY VORTEX–BODY INTERACTION

2009 ◽  
Vol 17 (01) ◽  
pp. 71-81
Author(s):  
TING-HUI ZHENG ◽  
GEORGIOS H. VATISTAS ◽  
S. K. TANG
Keyword(s):  
Flow Speed ◽  
Nonuniform Flow ◽  
Sound Waves ◽  
Mean Flow ◽  
Single Vortex ◽  
Body Interaction ◽  
Fundamental Properties ◽  
The Mean ◽  
Radiated Sound ◽  
Solid Bodies

This study examines the sound generated by the interaction between turbulent vortices and solid bodies, and its propagation in a nonuniform flow. Single vortex encounters with a flat plate and a nonrotating cylinder are considered. The solutions show that as the turbulence intensity increases, the sound radiated by the vortex–body interaction is strengthened while the effect of the mean flow speed on the sound waves weakens. The sound profile and sound directivity do not change with the Reynolds number. Neglecting turbulence in vortices will not affect the prediction of the fundamental properties of the radiated sound waves; however, it will underestimate the magnitude of the produced sound.

Hydraulic control of homogeneous shear flows

2003 ◽  
Vol 475 ◽  
pp. 163-172 ◽  
Author(s):  
CHRIS GARRETT ◽  
FRANK GERDES
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Water Waves ◽  
Flow Speed ◽  
Hydraulic Control ◽  
Mean Flow ◽  
Shallow Water Waves ◽  
Homogeneous Fluid ◽  
Apparent Paradox ◽  
The Mean

If a shear flow of a homogeneous fluid preserves the shape of its velocity profile, a standard formula for the condition for hydraulic control suggests that this is achieved when the depth-averaged flow speed is less than (gh)1/2. On the other hand, shallow-water waves have a speed relative to the mean flow of more than (gh)1/2, suggesting that information could propagate upstream. This apparent paradox is resolved by showing that the internal stress required to maintain a constant velocity profile depends on flow derivatives along the channel, thus altering the wave speed without introducing damping. By contrast, an inviscid shear flow does not maintain the same profile shape, but it can be shown that long waves are stationary at a position of hydraulic control.

Wave propagation and transport in the middle atmosphere

1980 ◽  
Vol 296 (1418) ◽  
pp. 73-85 ◽  
Keyword(s):  
Wave Propagation ◽  
Middle Atmosphere ◽  
Transport Processes ◽  
Planetary Waves ◽  
Wave Radiation ◽  
Mean Flow ◽  
Flow Interaction ◽  
Wave Transport ◽  
Equatorial Wave ◽  
The Mean

The dynamics of wave propagation and wave transport are reviewed for vertically propagating, forced, planetary scale waves in the middle atmosphere. Such waves can be divided into two major classes: extratropical planetary waves and equatorial waves. The most important waves of the former class are quasi-stationary Rossby modes of zonal wave numbers 1 and 2 (1 or 2 waves around a latitude circle), which propagate vertically only during the w inter season when the m ean winds are westerly. These modes transport heat and ozone towards the poles, thus maintaining the mean temperature above its radiative equilibrium value in high latitudes and producing the high latitude ozone maximum . It is shown that these wave transport processes depend on wave transience and wave dam ping. The precise form of this dependency is illustrated for transport of a strongly stratified tracer by small amplitude planetary waves. The observed equatorial wave modes are of two types: an eastward propagating Kelvin m ode and a westward propagating mixed Rossby—gravity mode. These modes are therm ally damped in the stratosphere where they interact with the mean flow to produce eastward and westward accelerations, respectively. It is shown tha t in the absence of mechanical dissipation this wave—mean flow interaction is caused by the vertical divergence of a wave ‘radiation stress’. This wave—mean flow interaction process is responsible for producing the well known equatorial quasi-biennial oscillation.

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