Reynolds stresses from hydrodynamic turbulence with shear and rotation^*

¹ Observatory, PO Box 14, 00014 University of Helsinki, Finland e-mail: jan.snellman@helsinki.fi
² NORDITA, Roslagstullsbacken 23, 10691 Stockholm, Sweden

Received: 8 June 2009
Accepted: 3 August 2009

Abstract

Aims. We study the Reynolds stresses which describe turbulent momentum transport from turbulence affected by large-scale shear and rotation.

Methods. Three-dimensional numerical simulations are used to study turbulent transport under the influences of large-scale shear and rotation in homogeneous, isotropically forced turbulence. We study three cases: one with only shear, and two others where in addition to shear, rotation is present. These cases differ by the angle (0 or 90°) the rotation vector makes with respect to the z-direction. Two subsets of runs are performed with both values of θ where either rotation or shear is kept constant. When only shear is present, the off-diagonal stress can be described by turbulent viscosity whereas if the system also rotates, nondiffusive contributions (Λ-effect) to the stress can arise. Comparison of the direct simulations are made with analytical results from a simple closure model.

Results. We find that the turbulent viscosity is of the order of the first order smoothing result in the parameter regime studied and that for sufficiently large Reynolds numbers the Strouhal number, describing the ratio of correlation to turnover times, is roughly 1.5. This is consistent with the closure model based on the minimal tau-approximation which produces a reasonable fit to the simulation data for similar Strouhal numbers. In the cases where rotation is present, separating the diffusive and nondiffusive components of the stress turns out to be challenging but taking the results at face value, we can obtain nondiffusive contributions of the order of 0.1 times the turbulent viscosity. We also find that the simple closure model is able to reproduce most of the qualitative features of the numerical results provided that the Strouhal number is of the order of unity.