Some Predictions from the Mean Field Equations of Magnetoconvection

Abstract

Nonlinear magnetic convection is investigated by the mean field approximation. The boundary layer method is used assuming large Rayleigh number R for different ranges of the Chandrasekhar number Q. The heat flux F is determined for wavenumbers CXn which optimize F. It is shown that there are a finite number of modes in the ranges Q ~ R2/3 and R2/3 ~ Q ~ R, and that the number of modes increases with increasing Q in the former range and decreases with increasing Q in the latter range. For Q = 0(R2/3) there are infinitely many modes, and F is proportional to Rl/3 While the optimal F is independent of Q for Q ~ Rl/2, it is found to decrease with increasing Q in the range Rl/2 ~ Q ~ R and eventually to become of 0(1) as Q -> OCR), and the layer becomes stable.