On the Closed Motion of a Fluid in a Square Cavity

Abstract

This paper is concerned with two-dimensional, incompressible fluid motion generated within a square cavity (a) by an outer stream and (b) by the action of a flat surface passing over one of its sides. This type of motion (“cavity flow”) is considered to consist of a boundary layer surrounding an inviscid “core.” A solution of a linearised form of von Mises’ equation is obtained for steady flow in the boundary layer for constant pressure and that of a small periodic variation around the walls of the cavity. From this analysis the vorticity imparted to the core is obtained. The motion in the core is then determined on the basis of the persistence of this value of the vorticity. Experimental results are given for (a) and (b) and compared with the theory. A method of solution of the non-linear boundary layer problem is indicated.