On Similar Solutions of the Unsteady Quasi-Two-Dimensiona1 Incompressible Laminar Boundary-Layer Equations

概要

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Unsteady three-dimensional boundary-layer equations can be reduced to two-dimensional type, if one component of the velocity and the pressure gradient in that direction are negligible throughout the boundary layer. Conditions for the existence of similar solutions for such quast-two-dimensional boundary layer are obtained. In particular it is found that the velocity at the outer edge of the boundary layer must be proportional to Y_1 exp (at/Y), Y_1(bt+Y)^<a/b> or (x+Y_1)/(bt+Y), where a and b are constants, Y and I Y_1 are arbitrary functions of y. Here a, y, z are geodesic normal plane coordinates (the a-axis being the geodesic of the body surface z = 0). New similar solutions are found, and velocity distributions for various cases are calculated. All the known similar solutions, being two-dimensional, are only special cases of our results. Axisymmetric similar solutions are also among our results.
社団法人日本物理学会の論文
1961-11-05