seminar

Zonal flows are mean flows in the east--west direction, which are ubiquitous on planets,  and can be formed through ‘zonostrophic instability’: within turbulence or random waves, a weak large-scale zonal flow can grow exponentially to become prominent. In this paper, we study the statistical behaviour of the zonostrophic instability and the effect of magnetic fields. We use a stochastic white noise forcing to drive random waves, and study the growth of a mean flow in this random system. The dispersion relation for the growth rate of the expectation of the mean flow is derived, with simple expressions in limits of strong and weak magnetic diffusivity. Numerical simulation of the stochastic flow is performed to confirm the theory. Results indicate that the magnetic field can significantly increase the randomness of the zonal flow.