The Oseen-type expansion of Navier-Stokes flows with an application to swimming velocity
Bull. Korean Math. Soc. 2001 Vol. 38, No. 2, 337-346
Sun-Chul Kim
Chung-Ang University
Abstract : A linearization owing to Oseen originally is performed to study the recirculating Navier-Stokes flows at high Reynolds numbers. The procedure is generalized to produce higher order asymptotic expansion for the flow velocity. We call this the {\em Oseen-type expansion }of the given flow. As a concrete example, the velocity of a steady Navier-Stokes flow due to a swimming flexible sheet in two-dimensional infinite strip domain is calculated by an asymptotic expansion technic with two-parameters, the Reynolds number $R$ and the perturbation parameter $\eps$. We here expand the flow in $\eps$ first and then $R$ secondly. The asymptotic result is up to second order in $\eps$.
Keywords : Reynolds number, linearization, boundary layer, recirculating flow
MSC numbers : 76D05, 76D10, 41A60
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