A buoyant flow structure in a magnetic field: Quasi-steady states and linear–nonlinear transitions

Abstract

The confined evolution of a buoyant blob of fluid subject to a vertical magnetic field is investigated in the limit of low magnetic Reynolds number. When the applied magnetic field is strong, the rise velocity of the blob is small. As the vorticity diffuses along the magnetic field lines, a quasi-steady state characterised by a balance between the work done by buoyancy and Ohmic dissipation is eventually reached at time t q s ∼ ( L 2 / δ 2 ) τ , where L is the axial dimension of the fluid domain, δ is the radius of the buoyant blob and τ is the magnetic damping time. However, when the applied magnetic field is weak or the axial length is sufficiently large compared to the blob size, the growth of axial velocity eventually makes the advection of vorticity significant. The typical time for the attainment of this nonlinear phase is t n l ∼ N 0 2 / 3 τ , where N 0 is the magnetic interaction parameter at time t = τ . The order-of-magnitude estimates for the timescales t q s and t n l are verified by computational experiments that capture both the linear and nonlinear phases.