The Stagnation Point Structure of Wall-Turbulence and the Law of the Wall in Turbulent Channel Flow

DNS of turbulent channel flows propose the following picture. (a) The Taylor microscale lambda(y) is proportional to l(s) (y), the average distance between stagnation points of the fluctuating velocity field, i.e. lambda(y) = B(1)l(s)(y) where B-1 is constant, for delta(nu) << y < delta. (b) The number density of stagnation points n(s) varies with height as n(s) = C(s)y(+)(-1)/delta(3)(nu) with Cs constant in the range delta(nu) << y < delta. (c) In that same range, the kinetic energy dissipation rate per unit mass, epsilon = 2/3E+u(tau)(3)/(kappa(s) y) where E+ = E/u(tau)(2) is the normalised total kinetic energy per unit mass, kappa(s) = B-1(2)/C(s)where is the stagnation point von Karman coefficient. (d) For Re-tau >> I, large enough for the production to balance dissipation locally and for -< uv > similar to u(tau)(2), in the range delta v << y << delta, d < u >/dy similar or equal to 2/3 E+u(tau)/(kappa(s) y) in that same range. (e) The von Karman coefficient K is 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 similar to kappa(s). The universality of kappa(s) = B-1(2)/C-s depends on the universality of the stagnation point structure of the turbulence via B-1 and C-s, which are conceivably not universal.