Surface waves on a rotating fluid

Small-amplitude waves on the free surface of a liquid rotating at constant angular velocity about a vertical axis are studied analytically and experimentally In the experiments, surface waves are produced by mounting a rotating cylinder partially filled with water on a vibration table and oscillating the entire assembly vertically Subharmonic waves are found to occur as in the nonrotating case, but in the presence of rotation a larger forcing amplitude is required to produce instability A synchronous response, i e , at the forcing frequency, not present in the nonrotating case is also predicted and observed Depending on whether the surface wave frequency is greater or less than twice the rotational speed, the governing field equation is either elliptic or hyperbolic The elliptic case is similar to the nonrotating case, and the disturbance decays rapidly with depth In the hyperbolic case there is no decay of the motion with depth The results may be of interest in connection with sloshing in missile fuel tanks