

Article
Spin up of a rapidly rotating gas in thermallyh insulated container.
Authors: 
Lindblad, I., Bark, F.H., Zahrai, S. 
Document Type: 
Article 
Pubstate: 
Published 
Journal: 
J. Fluid Mech. 
Volume: 

Year: 
1993 
AbstractThe linear spinup problem for a rapidly rotating viscous diffusive ideal gas is considered in the limit of vanishing Ekman number E. Particular attention is given to gases having a large molecular weight. The gas is enclosed in a cylindrical annulus, with flat top and bottom walls, which is rotating around its axis of symmetry with rotation rate Omega . The walls of the container are adiabatic. In a rotating gas (of any molecular weight), the Ekman layers on adiabatic walls are weak, which implies that there is no distinct nondiffusive response of the gas outside the Ekman and Stewartson boundary layers on the timescale E/sup 1/2/ Omega /sup 1/ for spinup of a homogeneous fluid. For the case of adiabatic walls, it is shown that the spinup mechanisms due to viscous diffusion and Ekman suction are, from a formal point of view, equally strong. Therefore, the gas will adjust to the increased rotation rate of the container on the diffusive timescale E/sup 1/ Omega /sup 1/. However, if E/sup 1/3/<< gamma 1<<1 and M approximately 1, which characterizes rapidly rotating heavy gases (where gamma is the ratio of specific heats of the gas and M the Mach number), it is shown that the gas spins up mainly by Ekman suction on the shorter timescale ( gamma 1)/sup 2/E/sup 1/ Omega /sup 1/. In such cases, the interior motion splits up into a nondiffusive part of geostrophic character and diffusive boundary layers of thickness ( gamma 1) outside the Ekman and Stewartson layers. The motion approaches the steady state of rigid rotation algebraically instead of exponentially as is usually the case for spinup.

