We analyze here the flow in a horizontal closed cylinder of aspect ratio 2, induced by both an axial temperature gradient and the rotation about its axis. A Prandtl number representative of molten metals at high temperature is considered. We have characterized the symmetric basic states and analyzed their stability when the temperature gradient increases in a region of moderate values of rotation rates, in which the two driving effects, natural convection and rotation, are comparable.
The bas...
We analyze here the flow in a horizontal closed cylinder of aspect ratio 2, induced by both an axial temperature gradient and the rotation about its axis. A Prandtl number representative of molten metals at high temperature is considered. We have characterized the symmetric basic states and analyzed their stability when the temperature gradient increases in a region of moderate values of rotation rates, in which the two driving effects, natural convection and rotation, are comparable.
The basic state consists in a center-symmetric longitudinal flow, tilted with respect to the vertical plane and steady in the laboratory frame. Results characterizing the basic states as the rotation rate increases, in comparison with the non-rotating case previously studied (Mercader et al, 2014), are presented. As rotation increases, temperature becomes more uniform in space and the strength of the flow due to buoyancy in the vertical direction reduces. As it occurred in the non-rotating case for higher values of the Prandtl number, two curves of steady states with the same symmetric character coexist for moderate values of the Rayleigh number. In the range of values of rotation rate considered, rotation has a stabilizing effect only for very small values. As the rotation rate approaches to 3.5 and 4.5 values in thermal units (length=diameter), the scenario of bifurcations becomes more complex due to
the existence in both cases of very close bifurcations of codimension 2, which in the latter case involve both curves of symmetric solutions.
For the numerical calculations we use a second order time-splitting method for integrating the equations in time combined with a pseudo-spectral method for the spatial discretization (Mercader et al, 2010). Steady solutions and continuation of them are calculated by using the Stokes preconditioner developed by L Tuckermann (Mamun and Tuckerman, 1995)
The linear stability analysis has been carried on by using an Arnoldi method applied to an approximation of the Jacobian to obtain approximated leading eigenvalues and eigenvectors. To determine them accurately, the estimated eigenvalues and eigenvectors are used as initial guess to solve the nonlinear system derived from the eigenvalue problem.