Amplification of small perturbations in a Hartmann layer

We investigate in this paper the stability of the laminar Hartmann layer to small perturbations. Previous works have shown that the critical Reynolds number for linear stability is R(c)approximate to50 000. It is much higher than the experimental threshold values for laminarization of magnetohydrodynamic flows (150<250), highlighting a possible subcritical bifurcation. In the following, we discuss the validity of R-c as a good indicator of stability to small disturbances. We show that, far below R-c, there exist some very small perturbations which do not support the linear approximation. The main reason is the phenomenon of transient growth, due to the non-normality of the governing linear operator. Through numerical computations we determine the optimal amplification of three-dimensional small perturbations, in the absence of nonlinear effects. Then, we examine how nonlinear mechanisms modify the fluid velocity. In this way, we show that some very small perturbations evolve very differently from their linear approximation, and that, in such cases, the critical number R-c loses its physical meaning. (C) 2002 American Institute of Physics.