Wall roughness induces asymptotic ultimate turbulence

Abstract

Turbulence is omnipresent in Nature and technology, governing the transport of heat, mass, and momentum on multiple scales. For real-world applications of wall-bounded turbulence, the underlying surfaces are virtually always rough; yet characterizing and understanding the effects of wall roughness for turbulence remains a challenge, especially for rotating and thermally driven turbulence. By combining extensive experiments and numerical simulations, here, taking as example the paradigmatic Taylor-Couette system (the closed flow between two independently rotating coaxial cylinders), we show how wall roughness greatly enhances the overall transport properties and the corresponding scaling exponents. If only one of the walls is rough, we reveal that the bulk velocity is slaved to the rough side, due to the much stronger coupling to that wall by the detaching flow structures. If both walls are rough, the viscosity dependence is thoroughly eliminated in the boundary layers and we thus achieve asymptotic ultimate turbulence, i.e. the upper limit of transport, whose existence had been predicted by Robert Kraichnan in 1962 (Phys. Fluids 5, 1374(1962) and in which the scalings laws can be extrapolated to arbitrarily large Reynolds numbers.

Controlling secondary flow in Taylor–Couette turbulence through spanwise-varying roughness

“…pressure drag dominates), the scaling asymptotes to the ultimate regime predicted by Kraichnan, i.e. Nu ω ∝ Ta 0.5 (Kraichnan 1962;Zhu et al 2018). In Zhu et al (2018), the closest configuration to our study is the case of rough IC and smooth OC, for which an effective exponent α = 0.43 was found.…”

“…Zhu et al (2016) investigated the influence of grooves for large Ta (O(10 10 )), and find that at the tips of the grooves, plumes are preferentially ejected. In a more recent work, Zhu et al (2018) find that by using a similar configuration of rough walls as van den Berg et al (2003), the scaling Nu ω ∝ Ta 1/2 predicted by the so-called asymptotic ultimate regime can be achieved. They attribute this to a dominance of the pressure drag over the viscous drag on the cylinders.…”

“…We perform interpolation in the spatial direction preferential to the normal surface vector to transfer the boundary conditions to the momentum equations. The IBM has been validated previously (Fadlun et al 2000;Iaccarino & Verzicco 2003;Stringano et al 2006;Zhu et al 2016Zhu et al , 2017Zhu et al , 2018. Hatched regions indicate axially translated copies of the same data (including averages) -possible due to the periodic boundary condition in the axial direction -to allow for straightforward comparison.…”

Heat transfer in rough-wall turbulent thermal convection in the ultimate regime

“…The near-wall velocity and temperature profiles are logarithmic in the ultimate regime [7,9] [48,62]. Within the asymptotic fully rough regime, viscous effects are negligible and the pressure (or form) drag is dominant [47,63,64]. Note that k s must be determined dynamically for a given rough surface and is not a simple geometric length scale of the roughness.…”

“…For that flow, indeed the ultimate regime with the corresponding Nusselt number N u ω (the dimensionless angular velocity transport [44]) scaling N u ω ∝ T a 0.38 (where the Taylor number T a is the dimensionless mechanical driving strength) can be achieved both in experiments and in numerical simulations, see the review article [42]. In TC flow with a rough wall, even the asymptotic ultimate regime N u ω ∝ T a 1/2 can be achieved, both experimentally [45][46][47] and numerically [47]. This regime corresponds to fully rough pipe or channel flow in which the friction factor becomes Reynolds number independent [47][48][49][50].…”