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Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik × Subject: Stokes flow ×

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Now showing 1 - 2 of 2
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    Stokes flows under random boundary velocity excitations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Sabelfeld, Karl
    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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    On the Stokes-type resolvent problem associated with time-periodic flow around a rotating obstacle
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Eiter, Thomas
    Consider the resolvent problem associated with the linearized viscous flow around a rotating body. Within a setting of classical Sobolev spaces, this problem is not well posed on the whole imaginary axis. Therefore, a framework of homogeneous Sobolev spaces is introduced where existence of a unique solution can be guaranteed for every purely imaginary resolvent parameter. For this purpose, the problem is reduced to an auxiliary problem, which is studied by means of Fourier analytic tools in a group setting. In the end, uniform resolvent estimates can be derived, which lead to the existence of solutions to the associated time-periodic linear problem.