Stagnation point flows with freestream turbulence - The matching condition

In many situations, the calculation of stagnation point flows with imbedded freestream turbulence is of practical importance. One example for such a situation is related to the combustor exhaust flow impacting on the nozzle guide vanes in a gas turbine, while another example is concerned with the heat transfer at a rettachment point of a separated turbulent flow. However, a difficulty has recently been encountered in a k-epsilon calculation. This difficulty was related to the attainment of a proper match between the outer freestream flow and the turbulent/laminar viscous sublayer. The present note is concerned with the resolution of this problem for the outer freestream flow. For a special case, an analytical solution is found to link the outer flow with an inner viscous layer flow. The considered case involves a low-speed, two-dimensional, constant-density stagnation point flow with imbedded freestream turbulence.