SOME ASYMMETRIC STOKES FLOWS THAT ARE STRUCTURALLY SIMILAR

This paper considers the creeping flows generated by a disk moving edg ewise parallel to a rigid wall or free surface, a disk oscillating edg ewise in unbounded fluid and a hole in the rigid plane that bounds a s hear flow excited by a parallel moving plane. The analyses for the thr ee cases follow a similar pattern and several simplifying strategies a re introduced to obtain significant improvements on the presentations suggested by previous work on such flows. Indeed, the resulting integr al equations for the first disk problem are similar to those solved fo r the corresponding broadside motion. The drag force is shown to slowl y approach its limit value as the disk is placed nearer to the free su rface. The oscillatory hydrodynamic force is shown to have only Stokes and Basset components. The error in previously assuming the shear flo w to extend to infinity is shown to be of order H-3, where H is the se paration distance between the bounding planes.