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ON THE INITIAL CONDITIONS FOR BOUNDARY LAYER EQUATIONS,
NEW YORK UNIV N Y
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A three dimensional boundary layer with two components of velocity, v, w, much smaller than the third component, u, which is along the inviscid stream line, the x-coordinate, is studied. It is shown that the boundary layer equations lead to a compatibility equation on the four initial data of the three velocity components and the density, while the enthalpy is related to density by the equation of state. When the four initial data prescribed at a station, x 0, are inconsistent with the compatibility equation, the solution in a thin initial strip near x 0 will not fulfill the usual boundary layer equations. In this thin initial strip, a new set of governing equations are derived by stretching all three coordinates. By the examination of the general properties of the solutions in the thin strip and by the standard matching procedures, it is shown that the three proper initial conditions to be imposed on the boundary layer equations are the density profile, the velocity component u and a third quantity which is neither v nor w but a combination of the four prescribed initial data. An alternate derivation of these proper initial conditions and their physical interpretation is presented by the direct balance of mass, momentum and energy across the thin initial strip. Author
APPROVED FOR PUBLIC RELEASE