Characteristics of turbulent boundary layers at low Reynolds numbers with and without transpiration

An extension to Coles's (1956) ‘law of the wall–law of the wake’ formulation for incompressible unblown boundary layers with momentum thickness Reynolds number Re θ > 6000. is made for Re θ < 6000. It is found that κ = 0·40, the von Kármán constant for Re θ > 6000, is replaced by Ω = 0·40 ( Re θ /6000) ⅛ for Re θ < 6000. Based upon the data of Simpson (1967) this formulation is extended to injection and undersucked ( d θ/ 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 ε M /ν are used to obtain a continuous expression for ε M /ν as a function of U + , V + w , and Re θ for the wall region. This expression is in reasonable agreement with the generated ε M /ν blowing results and in less agreement with the unblown and suction results. Eddy viscosity and mixing length results confirm that ε M /δ* U ∞ ∝ Ω 2 and l /δ ∝ Ω for the outer region and that ε M /δ* U ∞ and l /δ are substantially independent of blowing and moderate suction, as also reflected by the velocity defect representation for injection and suction.