The influence of Viscous Boundary Layers on Transient Motions in a Stratified Rotating Fluid. Part I

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  • 1 Massachusetts Institute of Technology, Cambridge, Mass.
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Abstract

The transient motion resulting when a rotating cylinder containing a stably stratified fluid system has its rotation rate impulsively changed is examined theoretically and in the laboratory for both a continuously stratified system and a two-layer system. It is shown that the primary effect of viscosity is to force a meridional circulation in the interior of the fluid as a result of convergence in the Ekman boundary layers. The time scale of the meridional circulation as well as the vertical shear of the relative zonal motion which it creates are shown to be functions of the internal rotational Froude number (a measure of the ratio of the Coriolis force to the buoyancy force). For neutral stability the time scale is given by the rotation period times the ratio of the depth of the cylinder to the depth of the Ekman boundary layer, and the zonal motion induced in the interior is solid body rotation at the new rotation rate. Static stability acts to suppress vertical motion, and hence the meridional circulation is confined closer to the boundaries as the stability is increased. It is shown that increasing the static stability decreases the time scale of the transient circulation and also increases the vertical shear of the resulting relative zonal velocity.

Abstract

The transient motion resulting when a rotating cylinder containing a stably stratified fluid system has its rotation rate impulsively changed is examined theoretically and in the laboratory for both a continuously stratified system and a two-layer system. It is shown that the primary effect of viscosity is to force a meridional circulation in the interior of the fluid as a result of convergence in the Ekman boundary layers. The time scale of the meridional circulation as well as the vertical shear of the relative zonal motion which it creates are shown to be functions of the internal rotational Froude number (a measure of the ratio of the Coriolis force to the buoyancy force). For neutral stability the time scale is given by the rotation period times the ratio of the depth of the cylinder to the depth of the Ekman boundary layer, and the zonal motion induced in the interior is solid body rotation at the new rotation rate. Static stability acts to suppress vertical motion, and hence the meridional circulation is confined closer to the boundaries as the stability is increased. It is shown that increasing the static stability decreases the time scale of the transient circulation and also increases the vertical shear of the resulting relative zonal velocity.

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