INSTANTANEOUS VISCOUS-FLOW IN A CORNER BOUNDED BY FREE SURFACES

We study the instantaneous Stokes flow near the apex of a corner of an gle 2 alpha formed by two plane stress free surfaces. The fluid is und er the action of gravity with (g) over right arrow parallel to the bis ecting plane, and surface tension is neglected. For 2 alpha > 126.28 d egrees, the dominant term of the solution as the distance r to the ape x tends to zero does not depend on gravity and has the character of a self-similar solution of the second kind; the exponent of r cannot be obtained on dimensional grounds and the scale of the coefficient depen ds on the far flow field. Within this angular domain, the instantaneou s flow is deeply related to the (steady) flow in a rigid corner known since Moffatt [J. Fluid Mech. 18, 1 (1964)] and, as in that case, ther e may be eddies in the flow. The situation is substantially different for 2 alpha < 126.28 degrees, as the dominant term is related to gravi ty and not to the far flow. It has the character of a self-similar sol ution of the first kind, with the exponent of r being given by dimensi onal analysis. The solution cannot be continued in time since it leads to the curling of the boundaries. Nevertheless, it provides informati on on how such a cornered contour may evolve. When 2 alpha < 180 degre es, the corner angle does not vary as the flow develops; on the other hand, if 2 alpha > 180 degrees the corner must round or tend to a narr ow cusp, depending on the far flow. These predictions are supported by simple experiments. (C) 1996 American Institute of Physics.