Linking dissipation, anisotropy, and intermittency in rotating stratified turbulence at the threshold of linear shear instabilities

2019 ◽  
Vol 31 (10) ◽  
pp. 105116 ◽  
Author(s):  
A. Pouquet ◽  
D. Rosenberg ◽  
R. Marino
Keyword(s):  
Stratified Turbulence ◽  
Linear Shear ◽  
Shear Instabilities

scholarly journals A wave interaction approach to studying non-modal homogeneous and stratified shear instabilities

2014 ◽  
Vol 755 ◽  
pp. 336-364 ◽  
Author(s):  
Anirban Guha ◽  
Gregory A. Lawrence
Keyword(s):  
Steady State ◽  
Normal Mode ◽  
Interaction Model ◽  
Wave Interaction ◽  
Interfacial Waves ◽  
Modal Gain ◽  
Mode Theory ◽  
Linear Shear ◽  
Normal Mode Theory ◽  
Shear Instabilities

AbstractHomboe (Geophys. Publ., vol. 24, 1962, pp. 67–112) postulated that resonant interaction between two or more progressive, linear interfacial waves produces exponentially growing instabilities in idealized (broken-line profiles), homogeneous or density-stratified, inviscid shear layers. Here we have generalized Holmboe’s mechanistic picture of linear shear instabilities by (i) not initially specifying the wave type, and (ii) providing the option for non-normal growth. We have demonstrated the mechanism behind linear shear instabilities by proposing a purely kinematic model consisting of two linear, Doppler-shifted, progressive interfacial waves moving in opposite directions. Moreover, we have found a necessary and sufficient (N&S) condition for the existence of exponentially growing instabilities in idealized shear flows. The two interfacial waves, starting from arbitrary initial conditions, eventually phase-lock and resonate (grow exponentially), provided the N&S condition is satisfied. The theoretical underpinning of our wave interaction model is analogous to that of synchronization between two coupled harmonic oscillators. We have re-framed our model into a nonlinear autonomous dynamical system, the steady-state configuration of which corresponds to the resonant configuration of the wave interaction model. When interpreted in terms of the canonical normal-mode theory, the steady-state/resonant configuration corresponds to the growing normal mode of the discrete spectrum. The instability mechanism occurring prior to reaching steady state is non-modal, favouring rapid transient growth. Depending on the wavenumber and initial phase-shift, non-modal gain can exceed the corresponding modal gain by many orders of magnitude. Instability is also observed in the parameter space which is deemed stable by the normal-mode theory. Using our model we have derived the discrete spectrum non-modal stability equations for three classical examples of shear instabilities: Rayleigh/Kelvin–Helmholtz, Holmboe and Taylor–Caulfield. We have shown that the N&S condition provides a range of unstable wavenumbers for each instability type, and this range matches the predictions of the normal-mode theory.

Shear instability in spilling breakers

1994 ◽  
Vol 446 (1927) ◽  
pp. 399-409 ◽  
Keyword(s):  
High Speed ◽  
Capillary Waves ◽  
Shear Instability ◽  
Wave Crest ◽  
Initial Surface ◽  
Linear Shear ◽  
Shear Instabilities ◽  
Spilling Breakers

High-speed photographs of a gently breaking water wave have shown the particular instability of the wave crest predicted by Longuet-Higgins et al . ( J . Fluid Mech . 259, 333 –344 (1994)) and Longuet-Higgins & Cleaver ( J . Fluid Mech . 258, 115 –129 (1994)), with a ‘bulge’ on the forward face of the wave and the generation of parasitic capillaries ahead of the instability, emanating from the ‘toe’ of the bulge. The photographs also show the unexpected occurence of longer (type 2) capillary waves above the toe of the bulge. In this paper it is shown that the type 2 capillaries are probably shear-flow instabilities arising from the vorticity shed by type 1 (parasitic) capillaries. At large amplitudes the initially linear shear instabilities must break up into discrete vortices. By formulating a simple model of the shear instabilities as vortex waves it is shown that the wavelength of the type 2 capillaries should be about 4 times the wavelength of the type 1 capillaries, a result in agreement with observation. When the flow separates at the toe of the bulge, the use of Prandtl’s rule to estimate the strength of the vortices confirms the above relation. At larger length-scales when surface tension is negligible, the argument leads to a simple rule for predicting the wavelength of the initial surface roughness of a spilling breaker.

Instabilities of Jets and Fronts and their Nonlinear Evolution

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Nonlinear Evolution ◽  
Baroclinic Instability ◽  
Trapped Modes ◽  
Nonlinear Saturation ◽  
Parallel Flows ◽  
Inertial Instability ◽  
Shear Instabilities ◽  
Linear And Nonlinear ◽  
Flow Configurations ◽  
Characteristic Features

Notions of linear and nonlinear hydrodynamic (in)stability are explained and criteria of instability of plane-parallel flows are presented. Instabilities of jets are investigated by direct pseudospectral collocation method in various flow configurations, starting from the classical barotropic and baroclinic instabilities. Characteristic features of instabilities are displayed, as well as typical patterns of their nonlinear saturation. It is shown that in the Phillips model of Chapter 5, new ageostrophic Rossby–Kelvin and shear instabilities appear at finite Rossby numbers. These instabilities are interpreted in terms of resonances among waves counter-propagating in the flow. It is demonstrated that the classical inertial instability is a specific case of ageostrophic baroclinic instability. At the equator it appears also in the barotropic configuration, and is related to resonances of Yanai waves. The nature of the inertial instability in terms of trapped modes is established. A variety of instabilities of density fronts is displayed.

Flow structures and kinetic-potential exchange in forced rotating stratified turbulence

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Tianyi Li ◽  
Minping Wan ◽  
Jianchun Wang ◽  
Shiyi Chen
Keyword(s):  
Flow Structures ◽  
Stratified Turbulence

scholarly journals Invariant manifolds in stratified turbulence

2019 ◽  
Vol 4 (5) ◽  
Author(s):  
N. E. Sujovolsky ◽  
G. B. Mindlin ◽  
P. D. Mininni
Keyword(s):  
Invariant Manifolds ◽  
Stratified Turbulence

scholarly journals Turbulent thermal diffusion in strongly stratified turbulence: Theory and experiments

2017 ◽  
Vol 2 (6) ◽  
Author(s):  
G. Amir ◽  
N. Bar ◽  
A. Eidelman ◽  
T. Elperin ◽  
N. Kleeorin ◽  
...  
Keyword(s):  
Thermal Diffusion ◽  
Turbulence Theory ◽  
Stratified Turbulence ◽  
Theory And Experiments

scholarly journals Correlation between Buoyancy Flux, Dissipation and Potential Vorticity in Rotating Stratified Turbulence

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 157
Author(s):  
Duane Rosenberg ◽  
Annick Pouquet ◽  
Raffaele Marino
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Potential Vorticity ◽  
Isotropic Turbulence ◽  
Joint Probability ◽  
Buoyancy Flux ◽  
Turbulent Regime ◽  
Stratified Turbulence ◽  
Low Dissipation ◽  
Linear And Nonlinear

We study in this paper the correlation between the buoyancy flux, the efficiency of energy dissipation and the linear and nonlinear components of potential vorticity, PV, a point-wise invariant of the Boussinesq equations, contrasting the three identified regimes of rotating stratified turbulence, namely wave-dominated, wave–eddy interactions and eddy-dominated. After recalling some of the main novel features of these flows compared to homogeneous isotropic turbulence, we specifically analyze three direct numerical simulations in the absence of forcing and performed on grids of 10243 points, one in each of these physical regimes. We focus in particular on the link between the point-wise buoyancy flux and the amount of kinetic energy dissipation and of linear and nonlinear PV. For flows dominated by waves, we find that the highest joint probability is for minimal kinetic energy dissipation (compared to the buoyancy flux), low dissipation efficiency and low nonlinear PV, whereas for flows dominated by nonlinear eddies, the highest correlation between dissipation and buoyancy flux occurs for weak flux and high localized nonlinear PV. We also show that the nonlinear potential vorticity is strongly correlated with high dissipation efficiency in the turbulent regime, corresponding to intermittent events, as observed in the atmosphere and oceans.

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