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 velocityUin the directionOxand a uniform angular velocity Ω aboutOx. It is slightly disturbed, the resulting motion having velocity components (u+U,v, Ωr+w) relative to cylindrical polar axes (x,r, θ), centreOand in whichrmeasures distance fromOx, while θ is the azimuthal angle. Assuming thatu, v, ware sufficiently small for their squares and products to be neglected, and are independent of θ, the equations governing their behaviour reduce to