Flow past cylindrical obstacles on a beta-plane

Michael A. Page, E.R. Johnson

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Abstract

The flow past a cylindrical obstacle in an enclosed channel is examined when the entire configuration is rotating rapidly about an axis which is aligned with that of the obstacle. When viewed from a frame of reference which is rotating with the channel, Coriolis forces dominate and act to constrain the motion to be two-dimensional. The channel is considered to have depth varying linearly across its width, producing effects equivalent to the so-called β-plane approximation and permitting waves to travel away from the obstacle, both upstream and downstream. For the eastward flow considered in this paper, this leads to the formation of a lee-wavetrain downstream of the obstacle and, under some conditions, a region of retarded, or ‘blocked’, flow upstream of the obstacle. The flow regime studied is essentially inviscid, although one form of frictional effect on the flow, introduced through the Ekman layers, isincluded. The properties of this system are examined numerically and compared with the theoretical predictions from other studies, which are applicable in asymptotic limits of the parameters. In particular, the relevance of ‘Long's model’ solutions is considered.

Original languageEnglish
Pages (from-to)349-382
Number of pages34
JournalJournal of Fluid Mechanics
Volume221
DOIs
Publication statusPublished - 1 Jan 1990

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