Wall-roughness induced ultimate Taylor-Couette turbulence

We use direct numerical simulations to examine the Taylor number ($Ta$) dependence of the torque required to drive rotating cylinders with smooth and/or rough walls in Taylor-Couette turbulence. With the introduction of both inner {\it{and}} outer wall roughness, the scaling of the dimensionless torque $Nu_\omega$ becomes $Nu_\omega \propto Ta^{0.5 \pm 0.01}$. We interpret this through an extension of the Grossmann-Lohse theroy [Phys. Fluids 23, 045108 (2011)], by accounting for the log-law of the wall in the presence of roughness. The logarithmic correction $L(Re)$ in the relation $Nu_\omega \propto Ta^{1/2} \times L(Re)$, which leads to the effective scaling $Nu_\omega \propto Ta^{0.38}$ in the ultimate regime for the smooth case, gets canceled out and Kraichnan's pure ultimate scaling $Nu_\omega \propto Ta^{1/2}$ [R. H. Kraichnan, Phys. Fluids 5, 1374 (1962)] is recovered.