Solitary waves in Poiseuille flow of a rotating fluid

Abstract

Solutions are obtained for various modes of solitary waves in a strongly rotating fluid in Poiseuille flow. The nonlinear Bragg-Hawthorne equation is the basis of the theory, and the method of solution can be carried to any order of approximation. There are two sequences of modes, each infinite in number. One consists of modes travelling with the flow, called P modes, and the other consists of modes travelling against it, called N modes. Generally, the displacements of streamlines from their asymptotic positions are in opposite directions for two corresponding modes of the two sequences. In particular, the streamlines of the first mode travelling with the flow are displaced radially outward from their asymptotic positions, and those of the first mode travelling against the flow are displaced radially inward. In other words, the first P mode is a bulging wave, whereas the first N mode is a pinching or necking one.