Geophysical Turbulence

Geophysical turbulence is observed to self-organize into large-scale flows such as zonal jets and coherent vortices. Previous studies of barotropic $\unicode[STIX]{x1D6FD}$-plane turbulence have shown that coherent flows emerge from a background of homogeneous turbulence as a bifurcation when the turbulence intensity increases. The emergence of large-scale flows has been attributed to a new type of collective, symmetry-breaking instability of the statistical state dynamics of the turbulent flow. In this work, we extend the analysis to stratified flows and investigate turbulent self-organization in a two-layer fluid without any imposed mean north–south thermal gradient and with turbulence supported by an external random stirring. We use a second-order closure of the statistical state dynamics, that is termed S3T, with an appropriate averaging ansatz that allows the identification of statistical turbulent equilibria and their structural stability. The bifurcation of the statistically homogeneous equilibrium state to inhomogeneous equilibrium states comprising zonal jets and/or large-scale waves when the energy input rate of the excitation passes a critical threshold is analytically studied. Our theory predicts that there is a large bias towards the emergence of barotropic flows. If the scale of excitation is of the order of (or larger than) the deformation radius, the large-scale structures are barotropic. Mixed barotropic–baroclinic states with jets and/or waves arise when the excitation is at scales shorter than the deformation radius with the baroclinic component of the flow being subdominant for low energy input rates and insignificant for higher energy input rates. The predictions of the S3T theory are compared with nonlinear simulations. The theory is found to accurately predict both the critical transition parameters and the scales of the emergent structures but underestimates their amplitude.

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Random Changes of Flow Topology in Two-Dimensional and Geophysical Turbulence

Physical Review Letters ◽

10.1103/physrevlett.102.094504 ◽

2009 ◽

Vol 102 (9) ◽

Cited By ~ 85

Author(s):

Freddy Bouchet ◽

Eric Simonnet

Keyword(s):

Two Dimensional ◽

Flow Topology ◽

Geophysical Turbulence

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Stratified Turbulence: A Possible Interpretation of Some Geophysical Turbulence Measurements

Journal of the Atmospheric Sciences ◽

10.1175/2007jas2455.1 ◽

2008 ◽

Vol 65 (7) ◽

pp. 2416-2424 ◽

Cited By ~ 96

Author(s):

James J. Riley ◽

Erik Lindborg

Keyword(s):

Inertial Range ◽

Geophysical Flows ◽

Stratified Flows ◽

Stratified Turbulence ◽

Length Scales ◽

Turbulence Measurements ◽

Atmospheric Data ◽

Geophysical Turbulence ◽

Similar Dynamic

Abstract Several existing sets of smaller-scale ocean and atmospheric data appear to display Kolmogorov–Obukov–Corrsin inertial ranges in horizontal spectra for length scales up to at least a few hundred meters. It is argued here that these data are inconsistent with the assumptions for these inertial range theories. Instead, it is hypothesized that the dynamics of stratified turbulence explain these data. If valid, these dynamics may also explain the behavior of strongly stratified flows in similar dynamic ranges of other geophysical flows.

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Geophysical turbulence dominated by inertia–gravity waves

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.465 ◽

2019 ◽

Vol 875 ◽

pp. 71-100 ◽

Cited By ~ 4

Author(s):

Jim Thomas ◽

Ray Yamada

Keyword(s):

Gravity Waves ◽

Boussinesq Equations ◽

Tidal Energy ◽

Ocean Model ◽

Small Scale ◽

Baroclinic Mode ◽

Transfer Energy ◽

Geophysical Turbulence ◽

Balanced Flow ◽

Inertia Gravity Waves

Recent evidence from both oceanic observations and global-scale ocean model simulations indicate the existence of regions where low-mode internal tidal energy dominates over that of the geostrophic balanced flow. Inspired by these findings, we examine the effect of the first vertical mode inertia–gravity waves on the dynamics of balanced flow using an idealized model obtained by truncating the hydrostatic Boussinesq equations on to the barotropic and the first baroclinic mode. On investigating the wave–balance turbulence phenomenology using freely evolving numerical simulations, we find that the waves continuously transfer energy to the balanced flow in regimes where the balanced-to-wave energy ratio is small, thereby generating small-scale features in the balanced fields. We examine the detailed energy transfer pathways in wave-dominated flows and thereby develop a generalized small Rossby number geophysical turbulence phenomenology, with the two-mode (barotropic and one baroclinic mode) quasi-geostrophic turbulence phenomenology being a subset of it. The present work therefore shows that inertia–gravity waves would form an integral part of the geophysical turbulence phenomenology in regions where balanced flow is weaker than gravity waves.

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