The use of stokeslets to describe the arbitrary translation of a disk near a plane wall. (English) Zbl 0881.76027
Summary: A method is presented to describe the fully three-dimensional Stokes flow generated by the translation in any direction of an arbitrarily oriented disk in fluid bounded by a plane wall. The velocity field is represented solely in terms of stokeslet distributions on the disk, modified to take account of the bounding wall according to the century-old idea of Lorentz. Sets of integral equations of the second kind, not all disjoint, are obtained for the Abel transforms in each Fourier mode of the density functions. However, only a few modes need be considered in determining the flow field to order \(D^{-3}\), where \(D\) is the distance of the disk axis from the wall. Less detail is required to evaluate the drag force and torque experienced by the disk.
MSC:
| 76D07 | Stokes and related (Oseen, etc.) flows |
Keywords:
velocity field; integral equations of second kind; Abel transforms; Fourier mode; density functions; drag force; torqueReferences:
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