Scalings and Relative Scalings in the Navier-Stokes Turbulence

Nianzheng Cao; Shiyi Chen; Zhen-Su She

doi:10.1103/PhysRevLett.76.3711

Scalings and Relative Scalings in the Navier-Stokes Turbulence

Nianzheng Cao, Shiyi Chen, and Zhen-Su She

Phys. Rev. Lett. 76, 3711 – Published 13 May 1996

Abstract

High-resolution direct numerical simulations of 3D Navier-Stokes turbulence with normal viscosity and hyperviscosity are carried out. It is found that the inertial-range statistics, both the scalings and the probability density functions, are independent of the dissipation mechanism, while the near-dissipation-range fluctuations show significant structural differences. Nevertheless, the relative scalings expressing the dependence of the moments at different orders are universal, and show unambiguous departure from the Kolmogorov 1941 description, including the $2 / 3$ law for the kinetic energy. Implications for numerical modeling of turbulence are discussed.

Received 28 August 1995

DOI:https://doi.org/10.1103/PhysRevLett.76.3711

Authors & Affiliations

Nianzheng Cao^1,2, Shiyi Chen^1,2, and Zhen-Su She^3,4

¹IBM Research Division, T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598
²Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
³Department of Mathematics, University of Arizona, Tuscon, Arizona 85721
⁴Department of Mathematics, University of California, Los Angeles, California 90095