A Unified Model Spectrum for Anisotropic Stratified and Isotropic Turbulence in the Ocean and Atmosphere

2019 ◽  
Vol 49 (2) ◽  
pp. 385-407 ◽  
Author(s):  
Eric Kunze
Keyword(s):  
Internal Waves ◽  
Isotropic Turbulence ◽  
Internal Gravity Waves ◽  
Energy Cascade ◽  
Vertical Shear ◽  
Horizontal Shear ◽  
Aspect Ratios ◽  
Geophysical Turbulence ◽  
Forward Energy ◽  
New Interpretation

AbstractIn the decade or so below the Ozmidov wavenumber (N3/ε)1/2, that is, on scales between those attributed to internal gravity waves and isotropic turbulence, ocean and atmosphere measurements consistently find k1/3 horizontal wavenumber spectra for horizontal shear uh and horizontal temperature gradient Th and m−1 vertical wavenumber spectra for vertical shear uz and strain ξz. Dimensional scaling is used to construct model spectra below as well as above the Ozmidov wavenumber that reproduces observed spectral slopes and levels in these two bands in both vertical and horizontal wavenumber. Aspect ratios become increasingly anisotropic below the Ozmidov wavenumber until reaching ~O(f/N), where horizontal shear uh ~ f. The forward energy cascade below the Ozmidov wavenumber found in observations and numerical simulations suggests that anisotropic and isotropic turbulence are manifestations of the same nonlinear downscale energy cascade to dissipation, and that this turbulent cascade originates from anisotropic instability of finescale internal waves at horizontal wavenumbers far below the Ozmidov wavenumber. Isotropic turbulence emerges as the cascade proceeds through the Ozmidov wavenumber where shears become strong enough to overcome stratification. This contrasts with the present paradigm that geophysical isotropic turbulence arises directly from breaking internal waves. This new interpretation of the observations calls for new approaches to understand anisotropic generation of geophysical turbulence patches.

scholarly journals Destabilization of an Oceanic Meddy-Like Vortex: Energy Transfers and Significance of Numerical Settings

2018 ◽  
Vol 48 (5) ◽  
pp. 1151-1168 ◽  
Author(s):  
C. Ménesguen ◽  
S. Le Gentil ◽  
P. Marchesiello ◽  
N. Ducousso
Keyword(s):  
Energy Cascade ◽  
Coriolis Parameter ◽  
Primitive Equation ◽  
Oceanic Turbulence ◽  
Aspect Ratios ◽  
Interaction Processes ◽  
Energy Transfers ◽  
Forward Energy ◽  
Fifth Order ◽  
Very High

Abstract The increase of computational capabilities led recent studies to implement very high-resolution simulations that gave access to new scale interaction processes, particularly those associated with the transfer of energy from the oceanic mesoscales to smaller scales through an interior route to dissipation, which is still underexplored. In this context, we study spindown simulations of a mesoscale interior vortex, unstable to a mixed baroclinic–barotropic instability. Even though the global energy is almost conserved, some energy is transferred down to dissipation scales during the development of instabilities. However, in our parameter regime, there is no substantial forward energy cascade sustained by unbalanced dynamics. Rather than exploring the physical parameter range, we clarify numerical discretization issues that can be detrimental to the physical solutions and our interpretation of finescale dynamics. Special care is given to determining the effective resolution of the different simulations. We improve it by a factor of 2 in our primitive equation (PE) finite-difference Coastal and Regional Ocean Community (CROCO) model by implementing a fifth-order accurate horizontal advection scheme. We also explore a range of grid aspect ratios dx/dz and find that energy spectra converge for aspect ratios that are close to N/f, the ratio of the stratification N over the Coriolis parameter f. However, convergence is not reached in the PE model when using a fourth-order centered scheme for vertical tracer advection (standard in ROMS-family codes). The scheme produces dispersion errors that trigger baroclinic instabilities and generate spurious submesoscale horizontal features. This spurious instability shows great impact on submesoscale production and energy cascade, emphasizing the significance of numerical settings in oceanic turbulence studies.

scholarly journals The Stability of Short Symmetric Internal Waves on Sloping Fronts: Beyond the Traditional Approximation

2012 ◽  
Vol 42 (3) ◽  
pp. 459-475 ◽  
Author(s):  
Alain Colin de Verdière
Keyword(s):  
Kinetic Energy ◽  
Internal Waves ◽  
Relative Vorticity ◽  
Rotation Vector ◽  
Vertical Shear ◽  
Earth’S Rotation ◽  
Horizontal Shear ◽  
Mean Flow ◽  
Earth's Rotation ◽  
The Mean

Abstract The interaction of internal waves with geostrophic flows is found to be strongly dependent upon the background stratification. Under the traditional approximation of neglecting the horizontal component of the earth’s rotation vector, the well-known inertial and symmetric instabilities highlight the asymmetry between positive and negative vertical components of relative vorticity (horizontal shear) of the mean flow, the former being stable. This is a strong stratification limit but, if it becomes too low, the traditional approximation cannot be made and the Coriolis terms caused by the earth’s rotation vector must be kept in full. A new asymmetry then appears between positive and negative horizontal components of relative vorticity (vertical shear) of the mean flow, the latter becoming more unstable. Particularly conspicuous at low latitudes, this new asymmetry does not require vanishing stratification to occur as it operates readily for rotation/stratification ratios 2Ω/N as small as 0.25 (the stratification still dominates over rotation) for realistic vertical shears. Given that such ratios are easily found in ocean–atmosphere boundary layers or in the deep ocean, such ageostrophic instabilities may be important for the routes to dissipation of the energy of the large-scale motions. The energetics show that, depending on the orientation of the internal wave crests with respect to the mean isopycnal surfaces, the unstable motions can draw their energy either from the kinetic energy or from the available potential energy of the mean flow. The kinetic energy source is usually the leading contribution when the growth rates reach their maxima.

Interleaving intrusions produced by internal waves: a laboratory experiment

2008 ◽  
Vol 602 ◽  
pp. 219-239 ◽  
Author(s):  
ROSS W. GRIFFITHS ◽  
ALI A. BIDOKHTI
Keyword(s):  
Water Column ◽  
Internal Waves ◽  
Internal Gravity Waves ◽  
Horizontal Gradient ◽  
Sugar Solution ◽  
Passive Tracer ◽  
Horizontal Shear ◽  
Buoyant Plumes ◽  
Upward Moving ◽  
Double Diffusive

A statically stable stratified water column that also contains horizontal property contrasts (either of passive tracer alone or of two dynamically active solutes) is generated and continuously maintained for a long period by releasing two turbulent buoyant plumes of equal buoyancy fluxes into opposite ends of a long channel of water. The bottom outflows from the plumes also continuously excite internal gravity waves that produce a series of counter-flowing quasi-horizontal shear layers which are quasi-stationary relative to the box but whose phase propagates downward through the upward-moving water column. We report that the flow further involves an oscillation associated with the internal waves that gives rise to a sequence of interleaving intrusions across the horizontal gradient region. The wave-driven intrusions are advected upward with the ‘filling-box’ circulation and have the appearance of a spatially growing instability. The intrusions are examined in cases having no horizontal property differences other than a passive tracer. In further experiments where one plume is salt solution and the other is sugar solution, there is vigorous double-diffusive convection on the interleaving intrusions, including salt fingering and diffusive density interfaces, but this convection has only a weak influence on the intrusion thicknesses and velocities. We conclude that under all conditions attained in these experiments, the interleaving is driven by internal waves and not by the property gradients, and we infer that the wave-generated intrusions enhance double-diffusive buoyancy fluxes.

scholarly journals Stimulated Imbalance and the Enhancement of Eddy Kinetic Energy Dissipation by Internal Waves

2017 ◽  
Vol 47 (1) ◽  
pp. 181-198 ◽  
Author(s):  
Roy Barkan ◽  
Kraig B. Winters ◽  
James C. McWilliams
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Internal Waves ◽  
High Frequency ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Energy Cascade ◽  
Scale Analysis ◽  
Direct Extraction ◽  
Forward Energy

AbstractThe effects of internal waves (IWs), externally forced by high-frequency wind, on energy pathways are studied in submesoscale-resolving numerical simulations of an idealized wind-driven channel flow. Two processes are examined: the direct extraction of mesoscale energy by externally forced IWs followed by an IW forward energy cascade to dissipation and stimulated imbalance, a mechanism through which externally forced IWs trigger a forward mesoscale to submesoscale energy cascade to dissipation. This study finds that the frequency and wavenumber spectral slopes are shallower in solutions with high-frequency forcing compared to solutions without and that the volume-averaged interior kinetic energy dissipation rate increases tenfold. The ratio between the enhanced dissipation rate and the added high-frequency wind work is 1.3, demonstrating the significance of the IW-mediated forward cascades. Temporal-scale analysis of energy exchanges among low- (mesoscale), intermediate- (submesoscale), and high-frequency (IW) bands shows a corresponding increase in kinetic energy Ek and available potential energy APE transfers from mesoscales to submesoscales (stimulated imbalance) and mesoscales to IWs (direct extraction). Two direct extraction routes are identified: a mesoscale to IW Ek transfer and a mesoscale to IW APE transfer followed by an IW APE to IW Ek conversion. Spatial-scale analysis of eddy–IW interaction in solutions with high-frequency forcing shows an equivalent increase in forward Ek and APE transfers inside both anticyclones and cyclones.

Small-scale energy cascade in homogeneous isotropic turbulence

2019 ◽  
Vol 4 (10) ◽  
Author(s):  
Mohamad Ibrahim Cheikh ◽  
James Chen ◽  
Mingjun Wei
Keyword(s):  
Isotropic Turbulence ◽  
Energy Cascade ◽  
Small Scale ◽  
Homogeneous Isotropic Turbulence

A conservation law for internal gravity waves

1976 ◽  
Vol 78 (2) ◽  
pp. 209-216 ◽  
Author(s):  
Michael Milder
Keyword(s):  
Internal Wave ◽  
Group Velocity ◽  
Internal Waves ◽  
Gravity Waves ◽  
Conservation Law ◽  
Short Wavelength ◽  
Internal Gravity Waves ◽  
Volume Integral ◽  
Weak Density ◽  
Progressive Waves

The scaled vorticity Ω/N and strain ∇ ζ associated with internal waves in a weak density gradient of arbitrary depth dependence together comprise a quantity that is conserved in the usual linearized approximation. This quantity I is the volume integral of the dimensionless density DI = ½[Ω2/N2 + (∇ ζ)2]. For progressive waves the ‘kinetic’ and ‘potential’ parts are equal, and in the short-wavelength limit the density DI and flux FI are related by the ordinary group velocity: FI = DIcg. The properties of DI suggest that it may be a useful measure of local internal-wave saturation.

DETERMINATION OF WIND SHEAR AND TURBULENCE INTENSITY ACCORDING TO YAK42-D “ROSHYDROMET” RESEARCH AIRCRAFT DATA

2021 ◽  
pp. 117-129
Author(s):  
V. V. VOLKOV ◽  
◽  
M. A. STRUNIN ◽  
A. M. STRUNIN ◽  
◽  
...  
Keyword(s):  
Boundary Layer ◽  
Wind Speed ◽  
Wind Shear ◽  
Vertical Shear ◽  
Horizontal Shear ◽  
S 100 ◽  
Research Aircraft ◽  
The Difference ◽  
Wind Shears ◽  
Aircraft Data

The results of the development and comparative analysis of methods for determining wind shear in the atmosphere (regression and difference ones) based on research aircraft data are presented. It is shown that shear calculation by the regression method gives the error of 0.002-0.006 (m/s)/km (depending on the length of the measurement sections) for horizontal shears and 0.04-0.12 (m/s)/100 m for vertical shears; the respective error of the difference method is 0.007 (m/s)/km and 0.07 (m/s)/100 m. Based on the Yak-42D “Roshydromet” research aircraft data, the values of shears of two horizontal components of wind speed in three directions (two horizontal and vertical) were calculated. According to the data of two research aircraft flights, the maximum values of the horizontal shear of wind speed components were reached above the boundary layer and were equal to 0.2 (m/s)/km, and the vertical shear was 1.2 (m/s)/100 m. The energy profiles of horizontal and vertical turbulent pulsations are constructed, it is shown that intense turbulence smooths wind shears in the convective atmospheric boundary layer.

scholarly journals High resolution parameter study of the vertical shear instability

2020 ◽  
Vol 499 (2) ◽  
pp. 1841-1853
Author(s):  
Natascha Manger ◽  
Hubert Klahr ◽  
Wilhelm Kley ◽  
Mario Flock
Keyword(s):  
Aspect Ratio ◽  
Large Scale ◽  
Dead Zone ◽  
Pressure Ratio ◽  
Theoretical Models ◽  
Shear Instability ◽  
Vertical Shear ◽  
Parameter Study ◽  
Aspect Ratios ◽  
Strong Scaling

ABSTRACT Theoretical models of protoplanetary discs have shown the vertical shear instability (VSI) to be a prime candidate to explain turbulence in the dead zone of the disc. However, simulations of the VSI have yet to show consistent levels of key disc turbulence parameters like the stress-to-pressure ratio α. We aim to reconcile these different values by performing a parameter study on the VSI with focus on the disc density gradient p and aspect ratio h = H/R. We use full 2π 3D simulations of the disc for chosen set of both parameters. All simulations are evolved for 1000 reference orbits, at a resolution of 18 cells per h. We find that the saturated stress-to-pressure ratio in our simulations is dependent on the disc aspect ratio with a strong scaling of α∝h2.6, in contrast to the traditional α model, where viscosity scales as ν∝αh2 with a constant α. We also observe consistent formation of large scale vortices across all investigated parameters. The vortices show uniformly aspect ratios of χ ≈ 10 and radial widths of approximately 1.5H. With our findings we can reconcile the different values reported for the stress-to-pressure ratio from both isothermal and full radiation hydrodynamics models, and show long-term evolution effects of the VSI that could aide in the formation of planetesimals.

scholarly journals Gravity Wave Emission by Shear Instability

2019 ◽  
Vol 49 (9) ◽  
pp. 2393-2406 ◽  
Author(s):  
Carsten Eden ◽  
Manita Chouksey ◽  
Dirk Olbers
Keyword(s):  
Gravity Wave ◽  
Single Layer ◽  
Internal Gravity Waves ◽  
Shear Instability ◽  
Vertical Shear ◽  
Wave Signal ◽  
Wave Emission ◽  
Balanced Flow ◽  
Single Layer Model

AbstractGravity wave emission by geostrophically balanced flow is diagnosed in numerical simulations of lateral and vertical shear instabilities. The diagnostic method in use allows for a separation of balanced flow and residual wave signal up to fourth order in the Rossby number (Ro). While evidence is found for a small but finite gravity wave emission from balanced flow in a single-layer model with large lateral shear and large Ro, a vertically resolved model with moderate velocity amplitudes appropriate to the interior ocean hardly shows any wave emission. Only when static instabilities generated by the shear instability of the balanced flow are allowed can a gravity wave signal similar to the ones reported in earlier studies be detected in the vertically resolved case. This result suggests a relatively small role of spontaneous wave emission in the classical sense of Lighthill radiation, and emphasizes the role of convective or symmetric instabilities during frontogenesis for the generation of internal gravity waves in the ocean and atmosphere.

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