scholarly journals Energy cascades in rapidly rotating and stratified turbulence within elongated domains

2021 ◽  
Vol 933 ◽  
Author(s):  
Adrian van Kan ◽  
Alexandros Alexakis
Keyword(s):  
Energy Cascade ◽  
Asymptotic Region ◽  
Rossby Number ◽  
Brute Force ◽  
Stratified Turbulence ◽  
Inverse Cascade ◽  
Energy Cascades ◽  
Forward Energy ◽  
Weak Stratification ◽  
Shed Light

We study forced, rapidly rotating and stably stratified turbulence in an elongated domain using an asymptotic expansion at simultaneously low Rossby number $\mathit {Ro}\ll 1$ and large domain height compared with the energy injection scale, $h=H/\ell _{in}\gg 1$ . The resulting equations depend on the parameter $\lambda =(h \mathit {Ro} )^{-1}$ and the Froude number $\mathit {Fr}$ . An extensive set of direct numerical simulations (DNS) is performed to explore the parameter space $(\lambda,\mathit {Fr})$ . We show that a forward energy cascade occurs in one region of this space, and a split energy cascade outside it. At weak stratification (large $\mathit {Fr}$ ), an inverse cascade is observed for sufficiently large $\lambda$ . At strong stratification (small $\mathit {Fr}$ ) the flow becomes approximately hydrostatic and an inverse cascade is always observed. For both weak and strong stratification, we present theoretical arguments supporting the observed energy cascade phenomenology. Our results shed light on an asymptotic region in the phase diagram of rotating and stratified turbulence, which is difficult to attain by brute-force DNS.

scholarly journals Spectral non-locality, absolute equilibria and Kraichnan–Leith–Batchelor phenomenology in two-dimensional turbulent energy cascades

2013 ◽  
Vol 725 ◽  
pp. 332-371 ◽  
Author(s):  
B. H. Burgess ◽  
T. G. Shepherd
Keyword(s):  
Energy Spectrum ◽  
Energy Flux ◽  
Turnover Time ◽  
Inertial Range ◽  
Energy Cascade ◽  
Two Dimensional ◽  
Inverse Cascade ◽  
Energy Cascades ◽  
Self Similar ◽  
Non Locality

AbstractWe study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in $\alpha $ turbulence, governed by $\partial \theta / \partial t+ J(\psi , \theta )= \nu {\nabla }^{2} \theta + f$, where $\theta = {(- \Delta )}^{\alpha / 2} \psi $ is generalized vorticity, and $\hat {\psi } (\boldsymbol{k})= {k}^{- \alpha } \hat {\theta } (\boldsymbol{k})$ in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow ($\alpha = 1$), regular two-dimensional flow ($\alpha = 2$) and rotating shallow flow ($\alpha = 3$), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general $\alpha $, and point out their limitations. Using an $\alpha $-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as $\alpha $ increases. More importantly, the energy cascade is downscale in the self-similar inertial range for $2. 5\lt \alpha \lt 10$. At $\alpha = 2. 5$ and $\alpha = 10$, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for $\alpha \lt 4$. However, downscale energy flux in the EDQNM self-similar inertial range for $\alpha \gt 2. 5$ leads us to predict that any inverse cascade for $\alpha \geq 2. 5$ will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for $\alpha \geq 2. 5$ is significantly steeper than the KLB prediction, while for $\alpha \lt 2. 5$ we obtain the KLB spectrum.

scholarly journals Eddy Phase Speeds in a Two-Layer Model of Quasigeostrophic Baroclinic Turbulence with Applications to Ocean Observations

2016 ◽  
Vol 46 (6) ◽  
pp. 1963-1985 ◽  
Author(s):  
Lei Wang ◽  
Malte Jansen ◽  
Ryan Abernathey
Keyword(s):  
Practical Importance ◽  
Phase Speed ◽  
Wave Theory ◽  
Inverse Cascade ◽  
Barotropic Mode ◽  
Eddy Fluxes ◽  
Circumpolar Current ◽  
The Antarctic ◽  
Ocean Observations ◽  
Shed Light

AbstractThe phase speed spectrum of ocean mesoscale eddies is fundamental to understanding turbulent baroclinic flows. Since eddy phase propagation has been shown to modulate eddy fluxes, an understanding of eddy phase speeds is also of practical importance for the development of improved eddy parameterizations for coarse resolution ocean models. However, it is not totally clear whether and how linear Rossby wave theory can be used to explain the phase speed spectra in various weakly turbulent flow regimes. Using linear analysis, theoretical constraints are identified that control the eddy phase speed in a two-layer quasigeostrophic (QG) model. These constraints are then verified in a series of nonlinear two-layer QG simulations, spanning a range of parameters with potential relevance to the ocean. In the two-layer QG model, the strength of the inverse cascade exerts an important control on the eddy phase speed. If the inverse cascade is weak, the phase speed spectrum is reasonably well approximated by the phase speed of the linearly most unstable mode. A significant inverse cascade instead leads to barotropization, which in turn leads to mean phase speeds closer to those of barotropic-mode Rossby waves. The two-layer QG results are qualitatively consistent with the observed eddy phase speed spectra in the Antarctic Circumpolar Current and may also shed light on the interpretation of phase speed spectra observed in other regions.

scholarly journals Waves and vortices in the inverse cascade regime of stratified turbulence with or without rotation

2016 ◽  
Vol 806 ◽  
pp. 165-204 ◽  
Author(s):  
Corentin Herbert ◽  
Raffaele Marino ◽  
Duane Rosenberg ◽  
Annick Pouquet
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Vertical Shear ◽  
Energy Spectra ◽  
Stratified Turbulence ◽  
Viscous Effects ◽  
Inverse Cascade ◽  
Main Effects ◽  
The Waves

We study the partition of energy between waves and vortices in stratified turbulence, with or without rotation, for a variety of parameters, focusing on the behaviour of the waves and vortices in the inverse cascade of energy towards the large scales. To this end, we use direct numerical simulations in a cubic box at a Reynolds number $Re\approx 1000$, with the ratio between the Brunt–Väisälä frequency $N$ and the inertial frequency $f$ varying from $1/4$ to 20, together with a purely stratified run. The Froude number, measuring the strength of the stratification, varies within the range $0.02\leqslant Fr\leqslant 0.32$. We find that the inverse cascade is dominated by the slow quasi-geostrophic modes. Their energy spectra and fluxes exhibit characteristics of an inverse cascade, even though their energy is not conserved. Surprisingly, the slow vortices still dominate when the ratio $N/f$ increases, also in the stratified case, although less and less so. However, when $N/f$ increases, the inverse cascade of the slow modes becomes weaker and weaker, and it vanishes in the purely stratified case. We discuss how the disappearance of the inverse cascade of energy with increasing $N/f$ can be interpreted in terms of the waves and vortices, and identify the main effects that can explain this transition based on both inviscid invariants arguments and viscous effects due to vertical shear.

Dissipation of Synoptic-Scale Flow by Small-Scale Turbulence

2008 ◽  
Vol 65 (3) ◽  
pp. 766-791 ◽  
Author(s):  
K. Ngan ◽  
P. Bartello ◽  
D. N. Straub
Keyword(s):  
Normal Modes ◽  
Base Flow ◽  
Small Scale ◽  
Stratified Turbulence ◽  
Synoptic Scale ◽  
Boussinesq Model ◽  
Weak Stratification ◽  
Balanced Flow ◽  
Scale Turbulence ◽  
Scale Motion

Abstract Although it is now accepted that imbalance in the atmosphere and ocean is generic, the feedback of the unbalanced motion on the balanced flow has not received much attention. In this work the parameterization problem is examined in the context of rotating stratified turbulence, that is, with a nonhydrostatic Boussinesq model. Using the normal modes as a first approximation to the balanced and unbalanced flow, the growth of ageostrophic perturbations to the quasigeostrophic flow and the associated feedback are studied. For weak stratification, there are analogies with the three-dimensionalization of decaying 2D turbulence: the growth rate of the ageostrophic perturbation follows a linear estimate, geostrophic energy is extracted from the base flow, and the associated damping on the geostrophic base flow (the “eddy viscosity”) is peaked at large horizontal scales. For strong stratification, the transfer spectra and eddy viscosities maintain this structure if there is synoptic-scale motion and the buoyancy scale is adequately resolved. This has been confirmed for global Rossby and Froude numbers of O(0.1). Implications for atmospheric and oceanic modeling are discussed.

Balance dynamics in rotating stratified turbulence

2016 ◽  
Vol 795 ◽  
pp. 914-949 ◽  
Author(s):  
Hossein A. Kafiabad ◽  
Peter Bartello
Keyword(s):  
Energy Spectrum ◽  
Rossby Number ◽  
Stratified Turbulence ◽  
Nonlinear Normal Mode ◽  
Initial Flow ◽  
First Order ◽  
Initialization Scheme ◽  
Nonlinear Normal ◽  
Balance Dynamics ◽  
Normal Mode Initialization

If classical quasigeostrophic (QG) flow breaks down at smaller scales, it gives rise to questions of whether higher-order nonlinear balance can be maintained, to what scale and for how long. These are naturally followed by asking how this is affected by stratification and rotation. To address these questions, we perform non-hydrostatic Boussinesq simulations where the initial data is balanced using the Baer–Tribbia nonlinear normal mode initialization scheme (NNMI), which is accurate to second order in the Rossby number, as the next-order improvement to first-order QG theory. The NNMI procedure yields an ageostrophic contribution to the energy spectrum that has a very steep slope. However, as time passes, a shallow range emerges in the ageostrophic spectrum when the Rossby number is large enough for a given Reynolds number. It is argued that this shallow range is the unbalanced part of the motion that develops spontaneously in time and eventually dominates the energy at small scales. If the initial flow is not nonlinearly balanced, the shallow range emerges at even lower Rossby number and it appears at larger scales. Through numerous simulations at different rotation and stratification, this study gives a clear picture of how energy is cascaded in different initially balanced regimes of rotating stratified flow. We find that at low Rossby number the flow mainly consists of a geostrophic part and a balanced ageostrophic part with a steep spectrum. As the Rossby number increases, the unbalanced part of the ageostrophic energy increases at a rate faster than the balanced part. Hence, the total energy spectrum displays a shallow range above a transition wavenumber. This wavenumber evolves to smaller values as rotation weakens.

Barotropic and baroclinic inverse kinetic energy cascade in the Antarctic Circumpolar Current

2021 ◽  
Author(s):  
Hongjie Li ◽  
Yongsheng Xu
Keyword(s):  
Kinetic Energy ◽  
General Circulation ◽  
Antarctic Circumpolar Current ◽  
General Circulation Models ◽  
Energy Cascade ◽  
Turbulence Theory ◽  
Inverse Cascade ◽  
Spectral Flux ◽  
Circumpolar Current ◽  
The Antarctic

AbstractStratified geostrophic turbulence theory predicts an inverse energy cascade for the barotropic (BT) mode. Satellite altimetry has revealed a net inverse cascade in the baroclinic (BC) mode. Here the spatial variabilities of BT and BC kinetic energy fluxes in the Antarctic Circumpolar Current (ACC) were investigated using ECCO2 data, which synthesizes satellite data and in situ measurements with an eddy-permitting general circulation models containing realistic bathymetry and wind forcing. The BT and BC inverse kinetic energy cascades both reveal complex spatial variations that could not be explained fully by classical arguments. For example, the BC injection scales match better with most unstable scales than with the first-mode deformation scales, but the opposite is true for the BT mode. In addition, the BT and BC arrest scales do not follow the Rhines scale well in term of spatial variation, but show better consistency with their own energy-containing scales. The reverse cascade of the BT and BC modes was found related to their EKE, and better correlation was found between the BT inverse cascade and barotropization. Speculations of the findings were proposed. however, further observations and modeling experiments are needed to test these interpretations. Spectral flux anisotropy exhibits a feature associated with oceanic jets that is consistent with classical expectations. Specifically, the spectral flux along the along-stream direction remains negative at scales up to that of the studied domain (~2000km), while that in the perpendicular direction becomes positive close to the scale of the width of a typical jet.

Baroclinic Instability and Loss of Balance

2005 ◽  
Vol 35 (9) ◽  
pp. 1505-1517 ◽  
Author(s):  
M. Jeroen Molemaker ◽  
James C. McWilliams ◽  
Irad Yavneh
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Baroclinic Instability ◽  
Boussinesq Equations ◽  
Approximate Model ◽  
Slow Manifold ◽  
Energy Cascades ◽  
Centrifugal Instability ◽  
Forward Energy ◽  
Balanced Dynamics

Abstract Under the influences of stable density stratification and the earth’s rotation, large-scale flows in the ocean and atmosphere have a mainly balanced dynamics—sometimes called the slow manifold—in the sense that there are diagnostic hydrostatic and gradient-wind momentum balances that constrain the fluid acceleration. The nonlinear balance equations are a widely successful, approximate model for this regime, and mathematically explicit limits of their time integrability have been identified. It is hypothesized that these limits are indicative, at least approximately, of the transition from the larger-scale regime of inverse energy cascades by anisotropic flows to the smaller-scale regime of forward energy cascade to dissipation by more nearly isotropic flows and intermittently breaking inertia–gravity waves. This paper analyzes the particular example of an unbalanced instability of a balanced, horizontally uniform, vertically sheared current, as it occurs within the Boussinesq equations. This ageostrophic, anticyclonic, baroclinic instability is investigated with an emphasis on how it relates to the breakdown of balance in the neighborhood of loss of balanced integrability and on how its properties compare with other examples of ageostrophic anticyclonic instability of rotating, stratified, horizontally sheared currents. It is also compared with the more familiar types of instability for a vertically sheared current: balanced (geostrophic) baroclinic instability, centrifugal instability, and Kelvin–Helmholtz instability.

scholarly journals Spontaneous mirror-symmetry breaking induces inverse energy cascade in 3D active fluids

2017 ◽  
Vol 114 (9) ◽  
pp. 2119-2124 ◽  
Author(s):  
Jonasz Słomka ◽  
Jörn Dunkel
Keyword(s):  
Symmetry Breaking ◽  
Mirror Symmetry ◽  
Energy Transport ◽  
Fluid Model ◽  
Energy Cascade ◽  
Turbulence Theory ◽  
Scale Selection ◽  
Inverse Cascade ◽  
Inverse Energy Cascade ◽  
Self Organized

Classical turbulence theory assumes that energy transport in a 3D turbulent flow proceeds through a Richardson cascade whereby larger vortices successively decay into smaller ones. By contrast, an additional inverse cascade characterized by vortex growth exists in 2D fluids and gases, with profound implications for meteorological flows and fluid mixing. The possibility of a helicity-driven inverse cascade in 3D fluids had been rejected in the 1970s based on equilibrium-thermodynamic arguments. Recently, however, it was proposed that certain symmetry-breaking processes could potentially trigger a 3D inverse cascade, but no physical system exhibiting this phenomenon has been identified to date. Here, we present analytical and numerical evidence for the existence of an inverse energy cascade in an experimentally validated 3D active fluid model, describing microbial suspension flows that spontaneously break mirror symmetry. We show analytically that self-organized scale selection, a generic feature of many biological and engineered nonequilibrium fluids, can generate parity-violating Beltrami flows. Our simulations further demonstrate how active scale selection controls mirror-symmetry breaking and the emergence of a 3D inverse cascade.

Computer Simulation of Displacement Damage in Silicon Carbide

2004 ◽  
Vol 851 ◽  
Author(s):  
R. Devanathan ◽  
F. Gao ◽  
W. J. Weber
Keyword(s):  
Silicon Carbide ◽  
Radiation Effects ◽  
Threshold Energy ◽  
High Energy ◽  
Dynamics Simulation ◽  
Displacement Damage ◽  
Energy Cascades ◽  
Displacement Threshold ◽  
Atom Energy ◽  
Shed Light

ABSTRACTWe have performed molecular dynamics simulation of displacement events on silicon and carbon sublattices in silicon carbide for displacement doses ranging from 0.005 to 0.5 displacements per atom. Our results indicate that the displacement threshold energy is about 21 eV for C and 35 eV for Si, and amorphization can occur by accumulation of displacement damage regardless of whether Si or C is displaced. In addition, we have simulated defect production in high-energy cascades as a function of the primary knock-on atom energy and observed features that are different from the case of damage accumulation in Si. These systematic studies shed light on the phenomenon of non-ionizing energy loss that is relevant to understanding space radiation effects in semiconductor devices.

Sign in / Sign up

Export Citation Format

Share Document