Abstract
An extension to Coles's (1956) ‘law of the wall–law of the wake’ formulation for incompressible unblown boundary layers with momentum thickness Reynolds numberReθ> 6000. is made forReθ< 6000. It is found that κ = 0·40, the von Kármán constant forReθ> 6000, is replaced by Ω = 0·40 (Reθ/6000)⅛forReθ< 6000. Based upon the data of Simpson (1967) this formulation is extended to injection and undersucked (dθ/dx> 0) flows in ‘law of the wall’ and ‘velocity-defect’ representations. This law of the wall for the logarithmic turbulent region and Reichardt's sublayer variation of εM/ν are used to obtain a continuous expression for εM/ν as a function ofU+,V+w, andReθfor the wall region. This expression is in reasonable agreement with the generated εM/ν blowing results and in less agreement with the unblown and suction results. Eddy viscosity and mixing length results confirm that εM/δ*U∞∝ Ω2andl/δ ∝ Ω for the outer region and that εM/δ*U∞andl/δ are substantially independent of blowing and moderate suction, as also reflected by the velocity defect representation for injection and suction.
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