When the eddy viscosity is defined by the standard k-ε turbulence model, the equations governing self-similar incompressible plane and radial jets have a solution that is not analytic at the jet edge. A transformation that stretches the similarity variable simplifies the defining set of ordinary differential equations and makes them amenable to efficient numerical integration. Highly resolved solutions for the velocity, turbulent kinetic energy and dissipation rate profiles are tabulated and entrainment, velocity decay rate and growth rate are determined. The growth rate differs by 6 percent from a parabolic marching asymptotic solution to the full partial differential equations.

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The hypersonic viscous interaction is treated by the development of a set of equations valid throughout the boundary layer, shock-wave structure, and inviscid core. Although the primary interest is with the nature of the leading-edge continuum merged layer, where the hypersonic interaction parameter %« is of the order of the square of the Mach number, the theory is applicable for smaller values of %«> as well. Because of the parabolic nature of these equations, finite-difference solutions are attainable. The flow over a flat plate at zero incidence, as well as angle of attack, was considered. Calculated surface pressure, heat transfer, and shock-jump conditions in the merged layer were significantly below their strong-interaction values. These were approached downstream.specific heat at constant pressure and at constant volume, respectively .& = coefficient of thermal conductivity £ = length scale in tangential direction M = Mach number Ni = error terms in Eqs. (2-5) p = pressure R = gas constant Re m = Reynolds number based on freestream conditions T = temperature •u, v = tangential and normal velocity components, respectively x, y = tangential and normal body coordinates, respectively a = angle of attack 7 = ratio of specific heats y = C P /C V 6 = length scale in normal direction e = order of higher approximation in Eq. (5) X = mean free path JUL = coefficient of viscosity p = density a-= Prandtl number Xco = interaction parameter \l/ = stream function to = exponent in temperature-viscosity law Superscripts { ) = dimensional { ) = nondimensional Subscripts Jm = free molecular max = maximum value ref = local reference conditions RH = Rankine-Hugoniot .Y. t Associate Professor of Aerospace Engineering. Associate Member AIAA. s = schock wave si = shock layer stag = stagnation conditions 5 = boundary layer 0 = initial value oo = freestream quantities

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