A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability

Abstract

The frequency and amplification rates for a disturbance growing with respect to time are compared with those of a spatially-growing wave having the same wave-number. For small rates of amplification it is shown that the frequencies are equal to a high order of approximation, and that the spatial growth is related to the time growth by the group velocity.