A Dynamical System Approach to Spatial Statistics of Rotating Turbulence

Abstract: The Navier-Stokes equation, a partial differential equation (PDE), incorporating the Coriolis force term, mathematically describes rotating turbulence, a ubiquitous phenomenon observed in natural turbulent systems such as geophysical flows. In this talk, I shall present an alternative low-dimensional, dynamical system approach to rotating turbulence and the results from numerical simulations.

We found an explicit relation between the (anomalous) scaling exponents of equal-time structure functions in the inertial range and the generalized dimensions associated with the energy dissipation rate by using the multifractal description of the energy dissipation rate. This theoretical prediction is validated by detailed simulations of a helical shell model. We performed direct numerical simulations of the Navier-Stokes equation, with the Coriolis force incorporated, to confirm the conclusions drawn from our multifractal and shell model studies. A good agreement is observed between solutions of the Navier-Stokes equation in a rotating frame with those obtained from low-dimensional dynamical systems such as the shell model.