A Theory of Baroclinic Turbulence

Understanding the physical mechanism maintaining fluid turbulence remains a fundamental theoretical problem. The two-layer model is an analytically and computationally simple system in which the dynamics of turbulence can be conveniently studied; in this work, a maximally simplified model of the sta...

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Bibliographic Details
Published in:Journal of the atmospheric sciences 2009-08, Vol.66 (8), p.2444-2454
Main Authors: FARRELL, Brian F, IOANNOU, Petros J
Format: Article
Language:English
Subjects:
Agreements
Atmospheric circulation
Atmospheric turbulence
Earth, ocean, space
Equilibrium
Exact sciences and technology
External geophysics
Fluid flow
Fluxes
General circulation
Heat
Hypotheses
Legislation
Meteorology
Midlatitude atmosphere
Modelling
Nonlinear systems
Nonlinearity
Perturbation
Physics
Physics of the high neutral atmosphere
Planetary atmospheres
Replenishment
Scaling
Simulation
Stochastic processes
Stochasticity
Structural stability
Theories
Theory
Turbulence
Turbulence models
Turbulent fluxes
Vortices
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Summary:Understanding the physical mechanism maintaining fluid turbulence remains a fundamental theoretical problem. The two-layer model is an analytically and computationally simple system in which the dynamics of turbulence can be conveniently studied; in this work, a maximally simplified model of the statistically steady turbulent state in this system is constructed to isolate and identify the essential mechanism of turbulence. In this minimally complex turbulence model the effects of nonlinearity are parameterized using an energetically consistent stochastic process that is white in both space and time, turbulent fluxes are obtained using a stochastic turbulence model (STM), and statistically steady turbulent states are identified using stochastic structural stability theory (SSST). These turbulent states are the fixed-point equilibria of the nonlinear SSST system. For parameter values typical of the midlatitude atmosphere, these equilibria predict the emergence of marginally stable eddy-driven baroclinic jets. The eddy variances and fluxes associated with these jets and the power-law scaling of eddy variances and fluxes are consistent with observations and simulations of baroclinic turbulence. This optimally simple model isolates the essential physics of baroclinic turbulence: maintenance of variance by transient perturbation growth, replenishment of the transiently growing subspace by nonlinear energetically conservative eddy–eddy scattering, and equilibration to a statistically steady state of marginal stability by a combination of nonlinear eddy-induced mean jet modification and eddy dissipation. These statistical equilibrium states provide a theory for the general circulation of baroclinically turbulent planetary atmospheres.
ISSN:0022-4928
1520-0469
DOI:10.1175/2009JAS2989.1