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Super‐rotation and diffusion of axial angular momentum: I. ‘Speed limits’ for axisymmetric flow in a rotating cylindrical fluid annulus
Author(s) -
Read P. L.
Publication year - 1986
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49711247113
Subject(s) - momentum diffusion , mechanics , inviscid flow , laminar flow , physics , annulus (botany) , classical mechanics , newtonian fluid , angular momentum , rotational symmetry , streamlines, streaklines, and pathlines , slip (aerodynamics) , no slip condition , boundary layer , boundary layer thickness , turbulence , materials science , thermodynamics , composite material
‘Super‐rotation’ can be defined with respect to the limitations on the magnitude of specific angular momentum, m , in an inviscid fluid. In a viscous fluid, a steady, super‐rotating axisymmetric flow is shown to require diffusion of m against its gradient ∇ m in the meridional plane. The conditions under which m can be diffused in an incompressible fluid by molecular viscosity against ∇ m in a cylindrical system are shown to be consistent with the normal properties of isotropic Newtonian viscosity (i.e. appropriate for the laminar flow of a viscous liquid in the laboratory) when cylindrical curvature is fully represented. A series of numerical simulations of thermally‐driven axisymmetric circulations in a cylindrical fluid annulus, subject to various mechanical boundary conditions, is then presented. The role of diffusion in the angular momentum budget of the simulations is examined by diagnosing m , its diffusive flux F (due to molecular viscosity) and divergence ∇· F from the final equilibrium (steady) flow. Up‐gradient diffusion (with respect to ∇ m ) is found to be particularly important for flows in a system with stress‐free top and side boundaries and a non‐slip base. Similar up‐gradient diffusion can also result in angular momentum expulsion effects in a system confined entirely by stress‐free boundaries. The characteristic dynamics of super‐rotation in a viscous fluid, and the associated limitations upon its magnitude and dependence upon the external conditions and fluid properties, are then explored in a scale analysis for the cylindrical annulus with a non‐slip base (based on a scheme due to Hignett, Ibbetson and Killworth). The most rapid super‐rotation (with zonal Rossby number > 1) is found to be favoured at moderate rotation rates, with strong cylindrical curvature, and a large meridional aspect ratio and Prandtl number. The results of the scale analysis are verified by means of further numerical experiments.