Zhu Xiaojue, Stevens Richard J A M, Verzicco Roberto, Lohse Detlef
Physics of Fluids Group and Max Planck Center Twente, MESA+ Institute and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500AE Enschede, Netherlands.
Dipartimento di Ingegneria Industriale, University of Rome "Tor Vergata," Via del Politecnico 1, Roma 00133, Italy.
Phys Rev Lett. 2017 Oct 13;119(15):154501. doi: 10.1103/PhysRevLett.119.154501. Epub 2017 Oct 11.
In thermal convection, roughness is often used as a means to enhance heat transport, expressed in Nusselt number. Yet there is no consensus on whether the Nusselt vs Rayleigh number scaling exponent (Nu∼Ra^{β}) increases or remains unchanged. Here we numerically investigate turbulent Rayleigh-Bénard convection over rough plates in two dimensions, up to Ra≈10^{12}. Varying the height and wavelength of the roughness elements with over 200 combinations, we reveal the existence of two universal regimes. In the first regime, the local effective scaling exponent can reach up to 1/2. However, this cannot be explained as the attainment of the so-called ultimate regime as suggested in previous studies, because a further increase in Ra leads to the second regime, in which the scaling saturates back to a value close to the smooth wall case. Counterintuitively, the transition from the first to the second regime corresponds to the competition between bulk and boundary layer flow: from the bulk-dominated regime back to the classical boundary-layer-controlled regime. Our study demonstrates that the local 1/2 scaling does not necessarily signal the onset of ultimate turbulence.
在热对流中，粗糙度常被用作增强热传输的一种手段，用努塞尔数来表示。然而，关于努塞尔数与瑞利数的标度指数（Nu∼Ra^{β}）是增加还是保持不变，目前尚无定论。在此，我们对粗糙平板上的二维湍流瑞利 - 贝纳德对流进行了数值研究，最高到Ra≈10^{12}。通过对超过200种组合的粗糙度元素的高度和波长进行变化，我们揭示了两种普适状态的存在。在第一种状态下，局部有效标度指数可达1/2。然而，这不能像先前研究中所建议的那样解释为达到了所谓的最终状态，因为进一步增加瑞利数会导致第二种状态，其中标度会饱和回到接近光滑壁面情况的值。与直觉相反，从第一种状态到第二种状态的转变对应于主体流和边界层流之间的竞争：从主体主导状态回到经典的边界层控制状态。我们的研究表明，局部1/2标度并不一定预示着最终湍流的开始。
