DAMPING OF TRANSIENT ENERGY GROWTH OF 3-DIMENSIONAL PERTURBATIONS IN HYDROMAGNETIC PIPE-FLOW

The stability of infinitesimal three-dimensional perturbations in hydr omagnetic pipe flow where the applied magnetic field is in the streamw ise direction is considered. The study is limited to the case of small magnetic Reynolds numbers and the main objective of the paper is to s tudy the transient evolution of the kinetic energy. A general effect o f the magnetic field is to increase the damping of the eigenvalues of the individual perturbation modes. For the case of infinitely long per turbations, which in the non-magnetic case has been found to have the largest transient growth, the magnetic field perturbations are decoupl ed from the flow and there is no effect on the stability properties of the flow. For shorter waves, and for moderate values of the interacti on parameter (I = R(m)A(2) approximate to 1-3) the hydromagnetic dampi ng effect on the transient energy growth is, however, substantial, esp ecially for small azimuthal mode numbers n. (Here R(m) is the magnetic Reynolds number and A is the Alfven number.) This parameter range has been found in experiments to give significantly higher transitional R eynolds numbers (Fraim and Heiser, 1968). Since the hydromagnetic damp ing effect is weak for long waves and large for shorter waves, the imp lications of the results to ordinary pipe flow is that the energy grow th found for short waves may be more crucial as a mechanism for transi tion than the corresponding growth for longer waves.