We use the machinery usually employed for studying the onset of Rayleigh-Bénard convection in hydro-and magnetohydrodynamic settings to address the onset of convection induced by the magnetothermal instability and the heat-flux-buoyancy-driveninstability in the weakly-collisional magnetized plasma permeating the intracluster medium. Since most of the related numerical simulations consider the plasma being bounded between two 'plates' on which boundary conditions are specified, our strategy provides a framework that could enable a more direct connection between analytical and numerical studies. We derive the conditions for the onset of these instabilities considering the effects of induced magnetic tension resulting from a finite plasma beta. We provide expressions for the Rayleigh number in terms of the wave vector associated with a given mode, which allow us to characterize the modes that are first to become unstable. For both the heat-flux-buoyancy-driven-instability and the magnetothermal instability, oscillatory marginal stable states are possible.PACS numbers 98.65. Hb, 44.25.+f

We investigate the connection between the inertial range and the dissipation range statistics of rotating turbulence through detailed simulations of a helical shell model and a multifractal analysis. In particular, by using the latter, we find an explicit relation between the (anomalous) scaling exponents of equal-time structure functions in the inertial range in terms of the generalized dimensions associated with the energy dissipation rate. This theoretical prediction is validated by detailed simulations of a helical shell model for various strengths of rotation from where the statistics of the dissipation rate and, thus, the generalized dimensions, as well as the inertial range, in particular, the anomalous scaling exponents, are extracted. Our work also underlines a surprisingly good agreement—such as that in the spatial structure of the energy dissipation rates and the decrease in inertial range intermittency with increasing strengths of rotation—between solutions of the Navier–Stokes equation in a rotating frame with those obtained from low-dimensional, dynamical systems such as the shell model, which are not explicitly anisotropic. Finally, we perform direct numerical simulations of the Navier–Stokes equation, with the Coriolis force incorporated, to confirm the robustness of the conclusions drawn from our multifractal and shell model studies.

No abstract

We investigate the predictability aspects of rotating turbulent flows through extensive numerical simulations of a shell model of rotating turbulence. In particular, we measure the large-scale predictability time and find that it increases with rotation rate to satisfy a power law in Rossby number with a scaling exponent of −2/3. Intriguingly, we find that before entering the algebraic growth stage, the error dynamics freezes for a time period determined by the finite Rossby number. We further analyse the scale dependence of the predictability time and observe that it tends to become scale independent in the Zeman range as the Rossby number decreases. Finally, we compute the finite size Lyapunov exponent and validate the dimensional prediction of its scaling ∼ δ −1 for large δ of the order of velocities in the Zeman range for small Rossby numbers.