The ultimate state of turbulent permeable-channel flow

Direct numerical simulations have been performed for heat and momentum transfer in internally heated turbulent shear flow with constant bulk mean velocity temperature, $u_{b}$ $\theta_{b}$, between parallel, isothermal, no-slip permeable walls. The wall-normal transpiration on the walls $y=\pm h$ is assumed to be proportional local pressure fluctuations, i.e. $v=\pm \beta p/\rho$ (Jim\'enez et al., J. Fluid Mech., vol. 442, 2001, pp.89-117). temperature supposed a passive scalar, Prandtl number set unity. Turbulent permeable-channel $\beta u_{b}=0.5$ has found exhibit distinct states depending Reynolds $Re_b=2h u_b/\nu$. At $Re_{b}\lesssim 10^4$, classical Blasius law of friction coefficient its similarity Stanton number, $St\approx c_{f}\sim Re_{b}^{-1/4}$, are observed, whereas at $Re_{b}\gtrsim so-called ultimate scaling, $St\sim Re_b^0$ $c_{f}\sim Re_b^0$, found. state attributed appearance large-scale intense spanwise rolls length scale $O(h)$ arising from Kelvin-Helmholtz type shear-layer instability over can induce large-amplitude fluctuations $O(u_b)$ as free layers, so that Taylor dissipation $\epsilon\sim u_{b}^{3}/h$ (or equivalently Re_b^0$) holds. In spite strong turbulence promotion there no separation, thus $O(\theta_b)$ also induced similarly. As consequence, achieved, i.e., wall flux scales $u_{b}\theta_{b}$ independent thermal diffusivity, although dominated by conduction.