Double-diffusive convection with an imposed magnetic field

Abstract

The linear and finite amplitude two-dimensional double-diffusive magnetoconvection (thermohaline convection in the presence of a magnetic field) has been studied analytically with free horizontal boundaries held at fixed temperature and concentration. It is shown that the magnetic field acts as a third diffusing component and its effect is to suppress convection. In the case of linear theory the conditions for direct and oscillatory modes are obtained and the stability boundaries for salt-finger and double-diffusive convection are predicted in the Rayleigh number plane. If τ₂, the ratio of magnetic diffusivity to thermal diffusivity, is small and the solute Rayleigh number R_s and Chandrasekhar number Q are sufficiently large convection sets in as overstable oscillations and the onset of it is approximated by two straight lines in the Rayleigh number plane. It is found that the salt-finger and overstable modes may be simultaneously unstable over a wide range of conditions and the effect of the magnetic field is to suppress this region. In the case of nonlinear theory it is found that the finite amplitude magnetoconvection exists for subcritical values of the Rayleigh number R, for all Q and τ₁ (which is the ratio of solute diffusivity to the thermal diffusivity) when τ₂ = 0.1 and R_s = 10⁴. It is found that the heat transport increases with an increase in R and decrease in τ₂ but decreases with Q.