J. PZuid zyxwvutsrq Mech. zyxwvutsrq (1969), vol. 38, part 4, pp. 817-831 Printed zyxwvutsrq in. Great Britain zyxwvutsr 817 Sink zyxw flow turbulent boundary layers By B. E. LAUNDER AND W. P. JONES Department of Mechanical Engineering, Imperial College, London, S.W. 7 (Received 7 January 1969) The study of sink flow turbulent boundary layers is of particular relevance to the problem of laminarization. The reason lies in the fact that the acceleration parameter which principally determines when a turbulent boundary layer will begin to revert towards laminar is, in these flows,constant from station to station. The paper presents theoretical solutions to this class of boundary layer by making use of the Prandtl mixing-length formula to relate the turbulent shear stress to the mean velocity gradient. Near the wall the Van Driest recommendation for mixing length is adopted and the Van Driest function, A+, is chosen such that the skin friction coefficient does not exceed a certain maximum value. The predicted solutions, which are in good agreement with available experi- mental data, display a plausible shift from the turbulent towards the laminar solution as the acceleration parameter is increased. 1. Introduction The flow that develops in a convergent channel between intersecting planes is one that has attracted considerable attention over the years. For laminar flow, similar solutions of the complete Navier-Stokes equations have been obtained (Jeffrey 1915; Hamel 1917; Rosenhead 1940; and Millsaps zyx & Pohlhausen 1953) and, in the limit of very high Reynolds numbers, these reduce to the exact boundary-layer solution of Pohlhausen (1921). In turbulent flow, it is the only flow configuration with a varying free-stream velocity in which the characteristic viscous and turbulence length scales may develop at the same rate; thus, since similar laminar flows are attainable, com- pletely similar turbulent flows may also be achieved. For both laminar and turbulent flow these sink flow similar boundary layers have skin friction co- efficients and local Reynolds numbers which are invariant with zy x. For these sink flows, the acceleration parameter K (defined as (v/U2) dU/dx) is also a constant at all stations in the flow. Launder (1964a, 1964b), Moretti & Kays (1965), Pate1 (1965), Schraub & Kline (1965) found experimentally that the parameter K provided a useful indication of when an accelerated turbulent boundary layer would undergo reversion towards laminar. To the accuracy that K determines the onset of laminarization, the critical value may be taken as 2-5 zyxwvut x A number of authors have attempted to derive from simple theoretical arguments the parameter which controls laminarization. The most popular ‘local’ parameter is (v/pu:)dp/dx (which, except for a multiplicative constant, 52 Fluid Mech. 38