Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1034, USA.
Phys Rev Lett. 2011 Jun 17;106(24):244501. doi: 10.1103/PhysRevLett.106.244501. Epub 2011 Jun 14.
Rigorous upper limits on the vertical heat transport in two-dimensional Rayleigh-Bénard convection between stress-free isothermal boundaries are derived from the Boussinesq approximation of the Navier-Stokes equations. The Nusselt number Nu is bounded in terms of the Rayleigh number Ra according to Nu≤0.2891Ra(5/12) uniformly in the Prandtl number Pr. This scaling challenges some theoretical arguments regarding asymptotic high Rayleigh number heat transport by turbulent convection.
从无应力等温边界的纳维-斯托克斯方程的玻尔兹曼近似出发，推导出二维瑞利-贝纳德对流中垂直热输运的严格上限。根据努塞尔数 Nu≤0.2891Ra(5/12)，在普朗特数 Pr 中均匀地用瑞利数 Ra 来限制努塞尔数 Nu，这一标度对一些关于湍流对流在高瑞利数下的渐近热输运的理论观点提出了挑战。
