Pattern competition in the sequential bifurcation approach to turbulence in homogeneously heated inclined fluid and solid layers

Non-linear solutions and their stability are presented for homogeneously heated channel flows with a simple geometry under the influence of a constant pressure gradient or when the vanishing of the mass flux across any lateral cross-section of the channel is imposed. The critical Grashof number is determined by linear stability analysis for various values of the Prandtl number. In our numerical study the angle of inclination of the channel is taken into account. We found that in each case studied, with the exception of a horizontal layer of fluid and when the applied constant pressure gradient is zero, the basic flow looses stability through a Hopf bifurcation. Following the linear stability analysis our numerical studies are focused on the emerging secondary flows and their stability, in order to identify possible bifurcation points for tertiary flows. We conclude with a few comments on revisiting the present results within an internal length gradient (ILG) framework accounting for higher order velocity and temperature gradients.