Remarks on the Equilibrium Turbulent Boundary Layer

Two similarity laws are known for the mean-velocity profile in turbulent boundary layer with constant pressure. These are 's law of the wall and Karman's momentum-defect law. first law has recently been generalized empirically to flows arbitrary pressure gradient by Ludwieg and Tillmann, and second law to a certain class of equilibrium flows by F. Clauser. the present paper it is shown that the pressure distribution to a given equilibrium flow cam be computed by that a certain parameter D = (τ_w/q)dq/dτ_w is constant, q and τ_w are the dynamic pressure in the free stream and shearing stress at the wall, respectively. The hypothesis = constant is suggested by a study of the integrated continuity and is supported by a rigorous analogy between the of equilibrium flows defined by Clauser and the class of flows studied by Falkner and Skan. The hypothesis = constant is also verified using experimental data for several turbulent flows and is interpreted physically from a point of view. hypothetical limiting cases of equilibrium flow are described. one extreme is the boundary Layer in a sink flow, a completely logarithmic mean-velocity profile outside the . At the other extreme is a continuously separating layer in a dimensionless pressure gradient (x/q)dq/dx twice that for the corresponding laminar flow. shearing-stress profiles are computed for several equilibrium flows, including the two limiting cases.