Selective withdrawal and blocking wave in rotating fluids

Abstract

An analysis is made of the axially symmetric flow of a rotating inviscid incompressible fluid into a point sink a t sufficiently low values of the Rossby number. Based on the experimental observations, a theoretical flow model involving a surface of velocity discontinuity which separates the central flowing core from the surrounding stagnant region is proposed. A family of solutions is obtained after posing the problem as one involving a free streamline which is the line of velocity discontinuity in the axial plane. It is found that the flow possesses a minimum flow force as well as a minimum energy flux. Corresponding to such a state, a unique intrinsic Rossby number R′ based on the properties of the flowing core with a value of 1/[npar ]8 is determined. A discussion is made of the flow field development induced by a sudden start of a sink discharge. A theoretical model involving a blocking wave propagating upstream is proposed. The speeds of blocking waves are found to be higher than the maximum group velocity of the infinitesimal waves for R > 0.06. On the other hand, for R < 0.03, the waves are linear and dispersive in nature.