Recirculation Eddies Generated by Solitary Waves in a Rotating Fluid

Abstract

Nonlinear waves in a rotating fluid passing through a long circular tube are studied numerically. The waves are resonantly excited by a local undulation of the tube wall. We consider a swirl of Burgers-vortex type which would be typical in the experiments and has often been used in a theoretical model of vortex breakdown. We show that the forced Korteweg–de Vries (fKdV) equation, which has been derived under the assumption of weak nonlinearity, describes well the time development of nonlinear waves even when the amplitude is large enough to form recirculation eddies on the tube axis. Each eddy is embedded in each crest of the solitary wave. This extends the previous results for steady flows that the sech 2 -type solution of the steady KdV equation can be applied to an inertial wave which sustains a recirculation eddy. It is found that, because of the form of modal eigenfunction for the Burgers vortex, the axial flow reversal first occurs almost inevitably on the tube axis. The recirculation eddy or axial flow reversal appears even when the amplitude of the wave governed by the fKdV equation is still small enough so that the assumption of weak nonlinearity is valid.