WIAS Preprint No. 1362, (2008)

Stokes flows under random boundary velocity excitations


  • Sabelfeld, Karl

2010 Mathematics Subject Classification

  • 65C05 65C20 65Z05


  • Stokes flow, Random boundary excitations, Karhunen-Loève expansion, velocity correlation tensor, stress, vorticity, and pressure


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 boundary condition uncertainty dramatically underestimates the variance of the velocity and pressure in the interior/exterior of the domain.

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