Instantaneous viscous flow in a corner bounded by free surfaces

We study the instantaneous Stokes flow near the apex of a corner of angle 2a formed by two plane stress free surfaces. The fluid is under the action of gravity with gW parallel to the bisecting plane, and surface tension is neglected. For 2a.126.28°, the dominant term of the solution as the distance r to the apex 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 depends on the far flow field. Within this angular domain, the instantaneous 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, there may be eddies in the flow. The situation is substantially different for 2a,126.28°, as the dominant term is related to gravity and not to the far flow. It has the character of a self-similar solution of the first kind, with the exponent of r being given by dimensional analysis. The solution cannot be continued in time since it leads to the curling of the boundaries. Nevertheless, it provides information on how such a cornered contour may evolve. When 2a,180°, the corner angle does not vary as the flow develops; on the other hand, if 2a.180° the corner must round or tend to a narrow cusp, depending on the far flow. These predictions are supported by simple experiments. © 1996 American Institute of Physics. @S1070-6631~96!01407-9#