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 $k_{\parallel }\ne 0$ (3D) fluctuations is well captured by a modified She-Lévêque intermittency model which yields the expression ${\zeta }_p=p/6+2(1-(2/3{)}^{p/2})$ for the structure function scaling exponents.

accepted for publication in Journal of Fluid Mechanics, 2 figure in reduced quality (data reduction)

References in corpus (3)

• Scale interactions and scaling laws in rotating flows at moderate Rossby numbers and large Reynolds numbers
• Scaling and energy transfer in rotating turbulence
• On the decrease of intermittency in decaying rotating turbulence

Cited by in corpus (20)

• Cascades and transitions in turbulent flows
• Critical balance in magnetohydrodynamic, rotating and stratified turbulence: towards a universal scaling conjecture
• Coherent structures and extreme events in rotating multiphase turbulent flows
• Direct and inverse energy cascades in a forced rotating turbulence experiment
• On the 2D behavior of 3D MHD with a strong guiding field
• On the energy spectrum of rapidly rotating forced turbulence
• Condensates in rotating turbulent flows
• Statistical features of rapidly rotating decaying turbulence: enstrophy and energy spectra, and coherent structures
• Rotating Taylor-Green Flow
• Critical transition in fast-rotating turbulence within highly elongated domains
• Onset of three-dimensionality in rapidly rotating turbulent flows
• Bridging Inertial and Dissipation Range Statistics in Rotating Turbulence
• Turbulent 2.5 dimensional dynamos
• The decay of Batchelor and Saffman rotating turbulence
• Large scale effects on the decay of rotating helical and non-helical turbulence
• Multi-particle Lagrangian statistics in homogeneous rotating turbulence
• Dynamic Scaling in Rotating Turbulence: A Shell Model Study
• Geophysical flows over topography, a playground for laboratory experiments
• Did lunar tides sustain the early Earth's dynamo?
• Decay of isotropic flow and anisotropic flow with rotation or magnetic field or both in a weakly nonlinear regime