The flow helicity in quasi-ordered cellular convection

Getling Alexander V., a.getling@mail.ru, Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, 119991, Russia


Abstract
An important role in producing the alpha effect, which controls the dynamo action of a turbulent medium, is attributed to the helicity of the velocity field. In mean-field electrodynamics, the estimated helicity depends strongly on the assumptions concerning the properties of turbulence. Thus, the estimates of the coefficient alpha for the conditions of the solar convection zone vary by four orders of magnitude, which obviously means a very high degree of arbitrariness in passing from the calculation results for dynamo models to the actual solar conditions. There is, however, a certain stretch in representing the velocity field in the solar convection zone as an ensemble of chaotic pulsations. The convective flows of the solar plasma exhibit a considerable degree of ordering, and numerical simulations of “deterministic” cellular convection could be used to determine its efficiency as a generator of magnetic fields. In this study, finite-difference numerical simulations are carried out to investigate the behaviour of the helicity of cellular convective flows in a horizontal layer of a compressible fluid (gas) heated from below and rotating about a vertical axis. The medium is assumed to be polytropically stratified. A thermal perturbation that produces a system of Benard-type hexagonal convection cells is introduced at the initial time. The cells are further deformed by the action of the Coriolis force; however, at some stage of evolution, the flow is nearly steady (at later times, the cells break down). Given the Rayleigh and Prandtl numbers, the velocity-field helicity for this stage, averaged over the layer, increases with the decrease of the polytrope index (i.e., with the increase of the curvature of the static entropy profile) and has a maximum at a certain rotational velocity of the layer. The aspect ratios of the computational domain are varied, and convection regimes differing in the degree of order of the cellular pattern are investigated. Numerical simulations of such quasi-ordered convective flows should substantially reduce uncertainties in the estimates of helicity needed to describe the solar dynamo in the language of mean-field electrodynamics compared to the estimates inferred from analyses of chaotic fields.