Premium
Linear stability analysis of oscillating Ekman boundary layers
Author(s) -
Withalm Martin,
Röper Jasmin,
Hoffmann Norbert P.
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910217
Subject(s) - floquet theory , reynolds number , physics , oscillation (cell signaling) , ekman layer , instability , boundary layer , mechanics , linear stability , ekman number , amplitude , boundary (topology) , galerkin method , classical mechanics , mathematical analysis , mathematics , nonlinear system , chemistry , flow (mathematics) , optics , quantum mechanics , turbulence , biochemistry
The analysed Ekman layer is generated in a fluid layer rotating around an axis normal to its two bounding rigid plates. One of the plates is stationary, the other moving at certain Reynolds numbers. An additional oscillation is added to the moving plate at different amplitudes and frequencies. The linear stability of this system is determined via a Floquet analysis and a Galerkin‐approximation of the corresponding Navier‐Stokes‐Equations. If the frequencies of the oscillations are small the critical Reynolds numbers of the Type I and Type II instabilities do not differ much from steady Ekman layers. Also for a purely oscillating system the critical values of the instabilities are almost consistent with those for a steady system. Interestingly, for higher frequencies the Type II instability does not appear any more. Instead the boundary layer becomes unstable only in terms of a Type I instability. In comparison with findings of other authors these results seem to be quite reasonable. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)