Related self-similar statistics of the turbulent/non-turbulent interface and the turbulence dissipation

The scalings of the local entrainment velocity v(n) of the turbulent/non-turbulent interface and of the turbulence dissipation rate are closely related to each other in an axisymmetric and self-similar turbulent wake. The turbulence dissipation scaling implied by the Kolmogorov equilibrium cascade phenomenology is consistent with a Kolmogorov scaling of v(n) whereas the non-equilibrium dissipation scaling reported for various turbulent flows in Vassilicos (Annu. Rev. Fluid Mech., vol. 47, 2015, pp. 95-114), Dairay et al. (J. Fluid Mech., vol. 781, 2015, pp. 166-195), Goto & Vassilicos (Phys. Lett. A, vol. 379 (16), 2015, pp. 1144-1148) and Obligado et al. (Phys. Rev. Fluids, vol. 1 (4), 2016, 044409) is consistent with a different scaling of v(n). We present results from a direct numerical simulation of a spatially developing axisymmetric and self-similar turbulent wake which supports this conclusion and the assumptions that it is based on.