TY - JOUR

T1 - Two phenomenological constants explain similarity laws in stably stratified turbulence

AU - Katul, Gabriel G.

AU - Porporato, Amilcare

AU - Shah, Stimit

AU - Bou-Zeid, Elie

PY - 2014/2/12

Y1 - 2014/2/12

N2 - In stably stratified turbulent flows, the mixing efficiency associated with eddy diffusivity for heat, or equivalently the turbulent Prandtl number (Prt), is fraught with complex dynamics originating from the scalewise interplay between shear generation of turbulence and its dissipation by density gradients. A large corpus of data and numerical simulations agree on a near-universal relation between Prt and the Richardson number (Ri), which encodes the relative importance of buoyancy dissipation to mechanical production of turbulent kinetic energy. The Prt-Ri relation is shown to be derivable solely from the cospectral budgets for momentum and heat fluxes if a Rotta-like return to isotropy closure for the pressure-strain effects and Kolmogorov's theory for turbulent cascade are invoked. The ratio of the Kolmogorov to the Kolmogorov-Obukhov-Corrsin phenomenological constants, and a constant associated with isotropization of the production whose value (=3/5) has been predicted from Rapid Distortion Theory, explain all the macroscopic nonlinearities.

AB - In stably stratified turbulent flows, the mixing efficiency associated with eddy diffusivity for heat, or equivalently the turbulent Prandtl number (Prt), is fraught with complex dynamics originating from the scalewise interplay between shear generation of turbulence and its dissipation by density gradients. A large corpus of data and numerical simulations agree on a near-universal relation between Prt and the Richardson number (Ri), which encodes the relative importance of buoyancy dissipation to mechanical production of turbulent kinetic energy. The Prt-Ri relation is shown to be derivable solely from the cospectral budgets for momentum and heat fluxes if a Rotta-like return to isotropy closure for the pressure-strain effects and Kolmogorov's theory for turbulent cascade are invoked. The ratio of the Kolmogorov to the Kolmogorov-Obukhov-Corrsin phenomenological constants, and a constant associated with isotropization of the production whose value (=3/5) has been predicted from Rapid Distortion Theory, explain all the macroscopic nonlinearities.

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U2 - 10.1103/PhysRevE.89.023007

DO - 10.1103/PhysRevE.89.023007

M3 - Article

C2 - 25353571

AN - SCOPUS:84896936947

SN - 1539-3755

VL - 89

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 2

M1 - 023007

ER -