Long nonlinear waves in an unbounded rotating jet or rotating two-fluid flow

Abstract

The objective of this paper is to study weakly nonlinear waves in an infinitely long rotating jet and a rotating two-fluid flow bounded by an infinitely long rigid cylinder with surface tension at the interface. The critical values for Rossby number, a nondimensional wave speed, are found. When the Rossby number is near one of the critical values, nonlinear theory is developed under long-wave approximation and the well-known Korteweg-de Vries (KdV) equations for the free surface and free interface are obtained. Then the solitary wave solutions are given as the first-order approximations of the solutions of the equations governing the motion of the flows. The analogy between the rotating fluid hows and a two-dimensional flow with density stratification is discussed.