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The Stability of Flows in a Differentially Heated Rotating Fluid System with Rigid Bottom and Free Top
Author(s) -
O'Neil Elizabeth J.
Publication year - 1969
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1969483227
Subject(s) - inviscid flow , mechanics , ekman number , flow (mathematics) , constant (computer programming) , classical mechanics , taylor number , physics , ekman layer , boundary (topology) , boundary layer , mathematical analysis , mathematics , computer science , programming language
The stability of certain steady flows in a rotating system with rigid bottom and free top surfaces is investigated. The simplest flow states having the essential spatial variations of steady responses of a rotating fluid system to differential heating in the horizontal are studied, that is, those with a constant gradient temperature distribution with both horizontal and vertical components, and the accompanying Coriolis‐balanced constant velocity shear (thermal wind). Ekman boundary layers and intermediate boundary layers are encountered in a systematic asymptotic analysis in two small parameters, the Ekman number and an inverse Richardson number. The resulting neutral stability curves indicate the possibility of instabilities above the inviscid stability criterion due to Eady, for some mean flow configurations. The estimate of the critical Taylor number is numerically close to the values obtained in the most nearly applicable experiments.