Rotational instability of a horizontal shear flow in a stratified rotating fluid

The rotational instability of a thermally stratified, viscous, conducting, rotating fluid is investigated by means of linearized perturbation equations. It is assumed that the basic horizontal flow is vertically uniform and that the horizontal shear is confined in a thin layer. By solving a simplified boundary value problem as a model of rotational instability in the sea, we have shown that the vertical wave length of the neutral disturbance is of order 10 times as large as the laminar Ekman layer thickness, and that this scale is proportional to (L/N)^1/3, whereL is the width of the shear layer andN is the Brunt-Vaisala frequency.