Gravitationally forced surface waves in a rotating cylinder

A thin layer of fluid, flowing axially along the inner surface of a horizontal rotating cylinder is subjected to a periodic forcing due to the gravitational acceleration. Since the frequency of the forcing lies within the critical range ($[0,\,2 \Omega]$) for which the inviscid problem is of a hyperbolic nature, the solution which in this case may be obtained on closed form displays a characteristic ``Mach wave''-like behavior.