Tides in Rotating Fluids

We _consider t~e _tidal disturbance_ fo~c~d ~n a differentially rotating fluid by a rigidly rotating external potential. The flmd ~s assumed to be mviscid, msl:llated, and self-gravitating, and to have laminar unperturbed and pe~tu~bed velocity fields. The external potential may exert a steady torque on the fluid which is of second order m Its str~ngth. ~owever, to this. order, we prove that there are no secular changes in the angular momenta of flmd particles,_ except possibly at corotation where the angular velocity, Q(r, (J), is equal to the pattern speed of the potential, Ql'. A corollary of our theorem is that, except at corotation, all of the angular moment~m _transferre~ to the flmd by the external potential must be transported away by internal stresses. In the apphcatwns of which we are aware, these stresses are associated with waves. Subject headings: hydrodynamics rotation