SPIN-UP OF A RAPIDLY ROTATING HEAVY GAS IN A THERMALLY INSULATED ANNULUS

The linear spin-up problem for a rapidly rotating viscous diffusive id eal gas is considered in the limit of vanishing Ekman number E. Partic ular attention is given to gases having a large molecular weight. The gas is enclosed in a cylindrical annulus, with flat top and bottom wal ls, which is rotating around its axis of symmetry with rotation rate O mega. The walls of the container are adiabatic. In a rotating gas (of any molecular weight), the Ekman layers on adiabatic walls are weak, w hich implies that there is no distinct non-diffusive response of the g as outside the Ekman and Stewartson boundary layers on the timescale E (-1/2)Omega(-1) for spin-up of a homogeneous fluid. For the case of ad iabatic walls, it is shown that the spin-up 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(-1)Omega(-1). However, i f E(1/3) much less than gamma-1 much less than 1 and M similar to 1, w hich characterizes rapidly rotating heavy gases (where gamma is the ra tio of specific heats of the gas and M the Mach number), it is shown t hat the gas spins up mainly by Ekman suction on the shorter timescale (gamma-1)(2) E(-1)Omega(-1). In such cases, the interior motion splits up into a non-diffusive part of geostrophic character and diffusive b oundary layers of thickness (gamma-1) outside the Ekman and Stewartson layers. The motion approaches the steady state of rigid rotation alge braically instead of exponentially as is usually the case for spin-up.