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Russia Vladivostok
Section Mathematics
Title An asymptotic study of multi-ring pattern formation in axisymmetric two-layer 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 Sciencesa
Abstract The axisymmetric model based on the Stokes equations is proposed to investigate the multi-ring pattern formation in two-layer 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 Fourier-Laplace method, we analyze the small-amplitude 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 multi-ring basins on the Moon. Using parameters of some lunar multi-ring basins we calculate the consecutive crest radii of the unstable wave and compare the results of simulation with the measured ring radii.
Keywords multi-layer 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 multi-ring pattern formation in axisymmetric two-layer creeping flow with variable layer thicknesses, and some geophysical applications, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, issue 4, pp. 95-108.
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