On the Bifurcation of Laminar Flows through a Curved Rectangular Tube

Bifurcating solutions are obtained for a flow through a slightly curved tube of rectangular cross-section. An aspect ratio of cross-section, γ, is changed over 1≦γ≦5 with the Dean number fixed to be 100. If γ<3.02, there is only a two-vortex solution. If γ≧3.02, there are dual solutions one of which is a two-vortex solution, the other is a four-vortex solution. Numerical solution of the unsteady Navier-Stokes equation at γ=4.9 shows that a two-vortex solution changes toward a four-vortex solution when it is disturbed by asymmetric disturbances.