Tides in rotating fluids

Abstract

We consider the tidal disturbance forced in a differentially rotating fluid by a rigidly rotating external potential. The fluid is assumed to be inviscid, insulated, and self-gravitating, and to have laminar unperturbed and perturbed velocity fields. The external potential may exert a steady torque on the fluid which is of second order in Its strength. However, to this order, we prove that there are no secular changes in the angular momenta of fluid particles, except possibly at corotation where the angular velocity, Ω(r,θ), is equal to the pattern speed of the potential, Ω_p. A corollary of our theorem is that, except at corotation, all of the angular momentum transferred to the fluid by the external potential must be transported away by internal stresses. In the applications of which we are aware, these stresses are associated with waves.