Asymptotic model for conical breakdown of inertial waves

Abstract

A theoretical asymptotic model for large amplitude stationary axisymmetric inertial waves in an axially symmetric swirling flow of an ideal fluid in a circular infinite tube with variable cross-section is described. Calculations are presented for the special, but important case when the upstream flow is uniform and always supercritical. It is found that the breakdown of inertial waves in divergent tubes is extremely sensitive to the variations of the cross-section. The breakdown bubble is generally asymmetric and it may turn into the diverging tail, especially in a convergent part of the tube. Possible relevance of the calculated structures to the experimentally observed types of the breakdown is discussed.