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Localized Roll‐Solutions in the Ekman‐Couette‐System
Author(s) -
Withalm Martin,
Hoffmann Norbert P.
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010237
Subject(s) - homoclinic orbit , bifurcation , convection , physics , classical mechanics , mechanics , quantum mechanics , nonlinear system
Abstract In the Ekman‐Couette‐System, where the usual Couette‐System is additionally rotated about its normal axis, localized single roll solutions have been known for some time. By varying different system parameters, a new localized solution emerging by saddle‐node bifurcations from these known solutions has now been found. This new solution is of the same localized nature like the old solution but with an additional roll. Further bifurcations lead then to an increasing number of rolls, still localized. This behavior is kind of analogous to the so called ‘homoclinic snaking’ which has recently been investigated in conjunction with the Swift‐Hohenberg equation and binary fluid convection. It might link the unstable localized single roll solutions with stable multi roll solutions or even with stable periodic roll solutions, which has to be shown yet. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)