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Stokes Flows under Random Boundary Velocity Excitations
Authors:K K Sabelfeld
Institution:(1) Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraśse 39, 10117 Berlin, Germany;(2) Institute of Computational Mathematics and Mathematical Geophysics, Russian Acad. Sci., Lavrentieva str., 6, 630090 Novosibirsk, Russia
Abstract:A viscous Stokes flow over a disc under random fluctuations of the velocity on the boundary is studied. We give exact Karhunen-Loève (K-L) expansions for the velocity components, pressure, stress, and vorticity, and the series representations for the corresponding correlation tensors. Both the white noise fluctuations, and general homogeneous random excitations of the velocities prescribed on the boundary are studied. We analyze the decay of correlation functions in angular and radial directions, both for exterior and interior Stokes problems. Numerical experiments show the fast convergence of the K-L expansions. The results indicate that ignoring the stochastic fluctuations in boundary conditions dramatically underestimates the variance of the velocity and pressure in the interior/exterior of the domain. The support of the RFBR Grant N 06-01-00498 is kindly acknowledged.
Keywords:Stokes flow  Random boundary excitations  Karhunen-Loève expansion  Velocity correlation tensor  Stress  vorticity  and pressure
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