Structure and decay of rotating homogeneous turbulence

Abstract

Navier-Stokes turbulence subject to solid-body rotation is studied by high-resolution direct numerical simulations (DNS) of freely decaying and stationary flows. Setups characterized by different Rossby numbers are considered. In agreement with experimental results strong rotation is found to lead to anisotropy of the direct nonlinear energy flux, which is attenuated primarily in the direction of the rotation axis. In decaying turbulence the evolution of kinetic energy follows an approximate power law with a distinct dependence of the decay exponent on the rotation frequency. A simple phenomenological relation between exponent and rotation rate reproduces this observation. Stationary turbulence driven by large-scale forcing exhibits $k_\perp^{-2}$-scaling in the rotation-dominated inertial range of the one-dimensional energy spectrum taken perpendicularly to the rotation axis. The self-similar scaling is shown to be the cumulative result of individual spectral contributions which, for low rotation rate, display $k_\perp^{-3}$-scaling near the $k_\parallel=0$ plane. A phenomenology which incorporates the modification of the energy cascade by rotation is proposed. In the observed regime the nonlinear turbulent interactions are strongly influenced by rotation but not suppressed. {Longitudinal two-point velocity structure functions taken perpendicularly to the axis of rotation indicate weak intermittency of the $k_\parallel=0$ (2D) component of the flow while the intermittent scaling of $k_\parallel\neq 0$ (3D) fluctuations is well captured by a modified She-Lévêque intermittency model which yields the expression $ζ_p=p/6 + 2(1-(2/3)^{p/2})$ for the structure function scaling exponents.