Publication Date:
1994-09-10
Description:
The linear spin-up 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 Ω. 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 non-diffusive response of the gas outside the Ekman and Stewartson boundary layers on the timescale E-1/2Ω-1for spin-up of a homogeneous fluid. For the case of adiabatic 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 Ω-1. However, if E1/3 ⪡γ — 1 ⪡ 1 and M ~ 1, which characterizes rapidly rotating heavy gases (where y 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 (γ— l)2E-1Ω-1. In such cases, the interior motion splits up into a non-diffusive part of geostrophic character and diffusive boundary layers of thickness (γ — 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 spin-up. © 1994, Cambridge University Press. All rights reserved.
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
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