Dynamic bifurcation and instability of Dean problem

Abstract

The main objective of this paper is to address the instability and dynamical bifurcation of the Dean problem. A nonlinear theory is obtained for the Dean problem, leading in particular to rigorous justifications of the linear theory used by physicists, and the vortex structure. The main technical tools are the dynamic bifurcation theory [15] developed recently by Ma and Wang.

16 pages,1figure