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

Abstract

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), Dairayet al.(J. Fluid Mech., vol. 781, 2015, pp. 166–195), Goto & Vassilicos (Phys. Lett. A, vol. 379 (16), 2015, pp. 1144–1148) and Obligadoet 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.