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A model of a turbulent boundary layer with a nonzero pressure gradient. (English) Zbl 1030.76022

The paper presents a model of turbulent boundary layer with nonzero pressure gradient. In the first part the authors describe two separate layers which, according to the model, compose the turbulent boundary layer at large Reynolds numbers Re. In the first layer, the scaling law for the mean velocity distribution takes the form \({u\over u_*}= A({u_*y\over\nu})^\alpha\), while in the second one \({u\over u_*}= B({u_* y\over\nu})^\beta\) (\(u_*\) is the friction velocity, \(\nu\) is the kinematic viscosity, and \(y\) is the distance from the wall), \(A\), \(B\), \(\alpha\), \(\beta\) being constants which can be determined by using experimental data. The expressions for \(A\) and \(\alpha\) are identical to those in smooth pipes, once the Reynolds number is defined correctly.
The second part deals with a similarity analysis of the model. Thus, according to the model, the structures of vorticity fields in the two layers are different, although both are self-similar. Taking into consideration that the influence of viscosity is transmitted to the main body of the flow via streaks separating from the viscous sublayer, and that the mean velocity profile is affected by the intermittency of the turbulence, one determines a set of parameters for the coefficient \(B\) and the exponent \(\beta\). Thus \(B\) and \(\beta\) depend on two parameters \(\text{Re}_\Lambda= U\Lambda/\nu\), \(\Lambda\) is the characteristic length, and \(P= {\nu\partial_xp\over \rho u^3}\).
The third section presents a comparison with experimental data for nearly constant effective Reynolds numbers which reveals simple Reynolds number-dependent relations between the parameters of scaling laws for the mean velocity distributions in the upper self-similar layer of turbulent boundary layer.

MSC:

76F40 Turbulent boundary layers
76M55 Dimensional analysis and similarity applied to problems in fluid mechanics
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References:

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