Analysis of power law and log law velocity profiles in the overlap region of a turbulent wall jet

The two-dimensional turbulent wall jet on a flat surface without free stream is analysed at a large Reynolds number, using the method of matched asymptotic expansions. The open mean equations of the turbulent boundary layer are analysed in the wall and wake layers by the method of matched asymptotic expansions and the results are matched by the Izakson-Millikan-Kolmogorov hypothesis. In the overlap region, the outer wake layer is governed by the velocity defect law (based on U-m, the maximum velocity) and the inner layer by the law of the wall. It is shown that the overlap region possesses a nonunique solution, where the power law region simultaneously exists along with the log law region. Analysis of the power law and log law solutions in the overlap region leads to self-consistent relations, where the power law index, alpha, is of the order of the non-dimensional friction velocity and the power law multiplication constant, C, is of the order of the inverse of the non-dimensional friction velocity. The lowest order wake layer equation has been closed with generalized gradient transport model and a closed form solution is obtained. A comparison of the theory with experimental data is presented.