Exploiting self-organized criticality in strongly stratified turbulence

Abstract

A multiscale reduced description of turbulent free shear flows in the presence of strong stabilizing density stratification is derived via asymptotic analysis of the Boussinesq equations in the simultaneous limits of small Froude and large Reynolds numbers. The analysis explicitly recognizes the occurrence of dynamics on disparate spatiotemporal scales, yielding simplified partial differential equations governing the coupled evolution of slow large-scale hydrostatic flows and fast small-scale isotropic instabilities and internal waves. The dynamics captured by the coupled reduced equations is illustrated in the context of two-dimensional strongly stratified Kolmogorov flow. A noteworthy feature of the reduced model is that the fluctuations are constrained to satisfy quasilinear (QL) dynamics about the comparably slowly-varying large-scale fields. Crucially, this QL reduction is not invoked as an ad hoc closure approximation, but rather is derived in a physically relevant and mathematically consistent distinguished limit. Further analysis of the resulting slow-fast QL system shows how the amplitude of the fast stratified-shear instabilities is slaved to the slowly-evolving mean fields to ensure the marginal stability of the latter. Physically, this marginal stability condition appears to be compatible with recent evidence of self-organized criticality in both observations and simulations of stratified turbulence. lgorithmically, the slaving of the fluctuation fields enables numerical simulations to be time-evolved strictly on the slow time scale of the hydrostatic flow. The reduced equations thus provide a solid mathematical foundation for future studies of three-dimensional strongly stratified turbulence in extreme parameter regimes of geophysical relevance and suggest avenues for new sub-grid-scale parameterizations.

References in corpus (7)

• Direct Statistical Simulation of Out-of-Equilibrium Jets
• Astrophysical Fluid Dynamics via Direct Statistical Simulation
• Asymptotic dynamics of high dynamic range stratified turbulence
• Reduced description of exact coherent states in parallel shear flows
• A statistical state dynamics approach to wall-turbulence
• Irreversible mixing by unstable periodic orbits in buoyancy dominated stratified turbulence
• Multiple scales analysis of slow--fast quasilinear systems

Cited by in corpus (5)

• Recent Developments in Theories of Inhomogeneous and Anisotropic Turbulence
• On large-scale dynamos with stable stratification and the application to stellar radiative zones
• Critical Balance and Scaling of Strongly Stratified Turbulence at Low Prandtl Number
• Numerical validation of scaling laws for stratified turbulence
• Spontaneous generation of helical flows by salt fingers