Crossflow instability of finite Bodewadt flows: Transients and spiral waves

The flow in in enclosed rotating cylinder with I stationary lower end wall is Investigated numerically. For fast rotation rates. the flow in the interior is primarily in the azimuthal direction. with an angular momentum distribution very close to that corresponding to solid-body rotation for about the inner-half radius The differential rotation Sets Lip a large-scale Circulation that IS primarily, present in the boundary layers oil the rotating top and sidewalls and the stationary bottom) wall. wall a very weak effusive component throughout the bulk interior providing a matching between the boundary layer flows oil the lop and bottom. The top end wall boundary layer has it profile that very closely matches the von Karman solution for,I rotating disk boundary layer. it is stable and very robust to finite disturbances for all rotation rates considered. The boundary layer oil the stationary bottom end wall has it profile that agrees with the Bodewadt Solution for a stationary disk with all ambient flow in solid-body rotation. This boundary layer is not robust. suffering crossflow instability to multiarmed spiral waves via a supercritical Hopf bifurcation, as well as being susceptible to axisymmetric circular waves that travel radially inward where the boundary layer profile is most inflectional In the absence of any external forcing, file circular waves are transitory. but low amplitude forcing call sustain them indefinitely, whereas the spiral waves are essentially unaffected by the external forcing (C) 2009 American Institute of Physics. [doi. 10.1063/1.3262817)