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Influence of Thermal Stratification on the Stability of Ekman‐Couette‐Flow
Author(s) -
Withalm Martin,
Hoffmann Norbert P.
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110286
Subject(s) - stratification (seeds) , ekman layer , mechanics , prandtl number , shear flow , couette flow , instability , shear (geology) , ekman number , physics , thermal stratification , ekman transport , boundary layer , convection , classical mechanics , geology , flow (mathematics) , turbulence , petrology , seed dormancy , botany , germination , oceanography , dormancy , upwelling , biology
The Ekman‐Couette‐System consists of two infinitely extended plates which are sheared in opposite directions over a fluid and are additionally rotated about their normal axis. In the case of angular velocities which tend to zero, the system becomes the classical Couette‐System, whereas for high angular velocities the boundary layers of the upper and lower plate are separated and represent Ekman boundary layers. For both limit cases the influence of thermal stratification on the stability of the base flow has been a subject of research for some time, but not so for moderate angular velocities. This was the motivation for doing a linear stability analysis for that case, including both stable and unstable stratification for a Prandtl number equal to unity. The results show, that as expected, stable stratification is suppressing the emergence of stationary as well as Type I‐ and Type II‐shear‐instabilities, while unstable stratification is supporting them. For unstable stratification, the system can also become unstable to a convection instability with all its properties known from other systems, except for that their orientation angle is not coincidental but determined due to the influence of the shear and Coriolis forces. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)