A heuristic estimation of the smallest transition Reynolds number in wall bounded flows

The aim of this paper is to present an estimation of the smallest Reynolds number in wall flows. A variational principle -which can be derived from large deviation principles or which can be seen as a variant of the recent introduced escape rate formalism in the nonequilibrium statistical mechanics context- is a means to an end. It is remarkably that the Kolmogorov and the Karman constants can be calculated by suitable assumptions and by a physical interpretation of the variational principle. These two constant determine the extend of the buffer layer and by it the smallest critical Reynolds number. These will be done for the pipe-, the Blasius- and the Couette-flow.