NUMERICAL STUDY OF VISCOUS-FLOW IN A ROTATING RECTANGULAR CHANNEL

A numerical study of the incompressible viscous flow in rotating channel with rectangular cross-section is presented in this paper. The incompressible parabolized Navier-Stokes equations are solved by a finite difference technique for various Reynolds and Rossby numbers in the laminar regime. At weak rotating rate, a pair of stable vortex secondary flow appears in the transverse planes of the channel and the flow can be developed fully in the channel. In the regime of the middle rotating rate, there are several unstable vortexes in the secondary flow and the fully developed flow in the channel can not be obtained. At a more rapid rotating rate, the stable secondary flow and fully developed flow appear again. At lower Reynolds numbers, a pair of stable vortex secondary flow and fully developed flow appear in the channel even if the rotating rate is rapid. To determine the critical condition of the stability of the flow ir. the rotating channel, the eigenvalues of the Jacobian matrix of the linearized Navier-Stokes equation are predicted.