Maji Maheswar, Eswaran Karthik Subramaniam, Ghosh Sourangshu, Seshasayanan Kannabiran, Shukla Vishwanath
Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur-721 302, India.
Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur-721 302, India.
Phys Rev E. 2023 Jul;108(1-2):015102. doi: 10.1103/PhysRevE.108.015102.
We examine the conjecture of equivalence of nonequilibrium ensembles for turbulent flows in two dimensions in a dual-cascade setup. We construct a formally time-reversible Navier-Stokes equation in two dimensions by imposing global constraints of energy and enstrophy conservation. A comparative study of the statistical properties of its solutions with those obtained from the standard Navier-Stokes equations clearly shows that a formally time-reversible system is able to reproduce the features of a two-dimensional turbulent flow. Statistical quantities based on one- and two-point measurements show an excellent agreement between the two systems for the inverse- and direct-cascade regions. Moreover, we find that the conjecture holds very well for two-dimensional turbulent flows with both conserved energy and enstrophy at finite Reynolds number.
我们在双级联设置中研究二维湍流中非平衡系综等价性的猜想。通过施加能量和涡量守恒的全局约束，我们构建了一个二维形式上时间可逆的纳维 - 斯托克斯方程。对其解的统计特性与从标准纳维 - 斯托克斯方程获得的统计特性进行的比较研究清楚地表明，一个形式上时间可逆的系统能够再现二维湍流的特征。基于一点和两点测量的统计量表明，在反向和正向级联区域，这两个系统之间具有极好的一致性。此外，我们发现对于在有限雷诺数下能量和涡量都守恒的二维湍流，该猜想非常成立。
