A note on forward wakes in rotating fluids

The two studies by Professor Miles (1970a, b) on the motion of a rotating fluid past a body raise the important question of the determinancy of such flows, by theoretical arguments, which it seems worth while making more precise. Suppose we have a fluid which when undisturbed has a uniform velocity U in the direction Ox and a uniform angular velocity Ω about Ox. It is slightly disturbed, the resulting motion having velocity components (u + U, v, Ωr + w) relative to cylindrical polar axes (x, r, θ), centre O and in which r measures distance from Ox, while θ is the azimuthal angle. Assuming that u, v, w are sufficiently small for their squares and products to be neglected, and are independent of θ, the equations governing their behaviour reduce to