Instability of the non-isothermal flow between a rotating and a stationary disks

Both theoretical linear stability analysis and direct numerical simulation are performed to study the transition flow between rotating discs. The paper reports three-dimensional spiral and annular patterns computed with a high-order (spectral) numerical method in the Bodewadt layer of a cylindrical rotor/stator cavity. The characteristic parameters of these boundary layer instabilities are compared with the theoretical results and interpreted in terms of type I and type II generic instabilities. The absolute instability regions are theoretically identified and critical Reynolds numbers of the convective/absolute transition in both layers are given. The absolute or convective nature of the flows is determined by examining the branch-point singularities of the dispersion relation.