Multitude scaling laws in axisymmetric turbulent wake

We establish theoretically multitude scaling laws of a self-similar (statistical) axisymmetric turbulent wake. At infinite Reynolds number limit, the flow evolves as general power law and a new exponential law of streamwise distance, consistent with the criterion of equilibrium similarity hypothesis. We found power law scalings for components of the homogeneous dissipation rate (epsilon) obeying the non-Richardson- Kolmogorov cascade as epsilon(u) similar to k(u)(3/2) = (lRe(l)(m)), epsilon(v) similar to k(v)(3/2)/l, k(v) similar to k(u)/Re-l(2m), 0 < m < 3. Here k(u) and k(v) are the components of the Reynolds normal stress, l is the local length scale, and Re-l is the Reynolds number. The Richardson-Kolmogorov cascade corresponds to m = 0. For m approximate to 1, the power law agrees with non-equilibrium scaling laws observed in recent experiments of the axisymmetric wake. On the contrary, the exponential scaling law follows the above dissipation law with different regions of existence for power index m = 3. At finite Reynolds number with kinematic viscosity nu, scalings obey the dissipation laws epsilon(u) similar to nu k(u)/l(2) and epsilon(v) similar to nu k(v)/l(2) with k(v) similar to k(u)/Re-l(n). The value of n is preferably 0 and 2. Different possibilities of scaling laws and symmetry breaking process are discussed at length. Published by AIP Publishing.