# The stagnation point von Kármán coefficient - Physics > Fluid Dynamics

Abstract: On the basis of various DNS of turbulent channel flows the following pictureis proposed. i At a height y from the y = 0 wall, the Taylor microscale\lambda is proportional to the average distance l s between stagnation pointsof the fluctuating velocity field, i.e. \lambday = B 1 l sy with B 1constant, for \delta u << y \lesssim \delta. ii The number density n s ofstagnation points varies with height according to n s = C s y +^{-1} -\delta u^3 where C s is constant in the range \delta u << y \lesssim\delta. iii In that same range, the kinetic energy dissipation rate per unitmass, \epsilon = 2-3 E + u \tau^3 - \kappa s y where E + is the total kineticenergy per unit mass normalised by u \tau^2 and \kappa s = B 1^2 - C s is thestagnation point von K\-arm\-an coefficient. iv In the limit of exceedinglylarge Re \tau, large enough for the production to balance dissipation locallyand for - ~ u \tau^2 in the range \delta u << y << \delta, dU +-dy ~ 2-3E +-\kappa s y in that same range. v The von K\-arm\-an coefficient \kappais a meaningful and well-defined coefficient and the log-law holds only if E +is independent of y + and Re \tau in that range, in which case \kappa ~\kappa s. The universality of \kappa s = B 1^2 - C s depends on theuniversality of the stagnation point structure of the turbulence via B 1 andC s, which are conceivably not universal. vi DNS data of turbulent channelflows which include the highest currently available values of Re \tau suggestE + ~ 2-3 B 4 y +^{-2-15} and dU +-dy + ~ B 4-\kappa s y +^{-1 - 2-15} withB 4 independent of y in \delta u << y << \delta if the significant departurefrom - ~ u \tau^2 is taken into account.

Author: Vassilios Dallas, J. Christos Vassilicos, Geoffrey F. Hewitt

Source: https://arxiv.org/