The lee-wave régime for a slender body in a rotating flow

The uniform motion of a closed, axisymmetric body along the axis of an unbounded, rotating, inviscid, incompressible fluid is considered on Long's hypotheses that: the flow is steady; the flow is uniform far upstream of the body; the inertial waves excited by the body cannot propagate upstream. The appropriate similarity parameters arek, an inverse Rossby number based on the body length, and δ, the slenderness ratio of the body. It is conjectured that an upper bound to the parametric régime in which the solution implied by Long's hypotheses remains valid, saykδ≡k