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Russia Vladivostok
Section  Mathematics 
Title  An asymptotic study of multiring pattern formation in axisymmetric twolayer creeping flow with variable layer thicknesses, and some geophysical applications 
Author(s)  Pak V.V.^{a} 
Affiliations  Pacific Oceanological Institute, Far Eastern Branch of the Russian Academy of Sciences^{a} 
Abstract  The axisymmetric model based on the Stokes equations is proposed to investigate the multiring pattern formation in twolayer creeping flow with variable thickness of layers. Each layer has uniform density and viscosity. The upper layer is lighter than the lower layer. The flow is generated by both surface and interface geometry. The effect of surface tension is supposed to be negligible. We apply the method of multiple scales to obtain the governing equations describing instability in the form of wave in the flow. Using the FourierLaplace method, we analyze the smallamplitude leading behavior of the instability. The asymptotic study reveals that this kind of instability manifests itself as axisymmetric wave which length is comparable with layer thickness; moreover, layer thicknesses play a major role in spatial distribution of wave extrema. The other model parameters alter mostly the wave amplitude. The equation relating extrema distribution to layer thicknesses is derived. We apply the obtained results to study a ring spacing rule observed for most multiring basins on the Moon. Using parameters of some lunar multiring basins we calculate the consecutive crest radii of the unstable wave and compare the results of simulation with the measured ring radii. 
Keywords  multilayer creeping flow, Stokes equations, method of multiple scales, inertialess instability, ring basins 
UDC  532.5.032 
MSC  76D50 
DOI  10.20537/vm140408 
Received  10 September 2014 
Language  Russian 
Citation  Pak V.V. An asymptotic study of multiring pattern formation in axisymmetric twolayer creeping flow with variable layer thicknesses, and some geophysical applications, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, issue 4, pp. 95108. 
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