ON SLOW VISCOUS FLOW

Abstract : A new linearization is considered for the problem of the flow of a viscous fluid past an obstacle at low Reynolds number. The linearization results from the conjecture that there may exist a function c(epsilon), 0 less than c less than 1, such that the solution of Delta Delta Chi = Chi sub y Delta Chi sub x - Chi sub x Delta Chi sub y under suitable boundary conditions can be replaced by a solution of Delta Delta Chi = c sub 1 Delta Chi sub x with c sub 1 replaced by c(epsilon), where c depends only upon epsilon and Chi denotes the stream function. This linearization is discussed for the problems of the flow past a long flat plate, a cylinder, a sphere, and a finite flat plate as well as for the flow in wedge-shaped region. For these problems a successful prediction of the macroscopic feature of the flow is obtained by the linearized theory with c = 0.43. Equally successful results are anticipated for other similar flows. No conclusion can be drawn for more complicated flows, and it is not clear whether the range of applicability can be increased by finding a c(epsilon) for larger epsilon than those considered.