Scale-by-scale turbulent energy budget in the intermediate wake of two-dimensional generators

It is first established, on the basis of new X-wire measurements, that the equilibrium similarity of the terms in the scale-by-scale (s-b-s) budget of the turbulent energy q²¯ is reasonably well approximated on the axis of the intermediate wake of a circular cylinder. The similarity, which scales on the Taylor microscale λ and q²¯, is then used to determine s-b-s energy budgets from the data of Antonia, Zhou, and Romano [“Small-scale turbulence characteristics of two-dimensional bluff body wakes,” J. Fluid Mech.459, 67–92 (2002)] for 5 different two-dimensional wake generators. In each case, the budget is reasonably well closed, using the locally isotropic value of the mean energy dissipation rate, except near separations comparable to the wavelength of the coherent motion (CM). The influence of the initial conditions is first felt at a separation L_c¯ identified with the cross-over between the energy transfer and large scale terms of the s-b-s budget. When normalized by q²¯ and L_c , the mean energy dissipation rate is found to be independent of the Taylor microscale Reynolds number. The CM enhances the maximum value of the energy transfer, the latter exceeding that predicted from models of decaying homogeneous isotropic turbulence.