Turbulence properties and global regularity of a modified Navier-Stokes equation

PHYSICA D-NONLINEAR PHENOMENA

卷:254

Article

Grafke, Tobias¹  Grauer, Rainer¹  Sideris, Thomas C.² 

[1] Ruhr Univ Bochum, Inst Theoret Phys 1, Bochum, Germany

[2] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

关键词: PDEs;    Turbulence;    Navier-Stokes equation;    Burgers equation;    Regularity;   

DOI  :  10.1016/j.physd.2013.03.007

来源: Elsevier

【 摘 要 】

We introduce a modification of the Navier-Stokes equation that has the remarkable property of possessing an infinite number of conserved quantities in the inviscid limit. This new equation is studied numerically and turbulence properties are analyzed concerning energy spectra and scaling of structure functions. The dissipative structures arising in this new equation are curled vortex sheets instead of the vortex tubes arising in Navier-Stokes turbulence. The numerically calculated scaling of structure functions is compared with a phenomenological model based on the She-Leveque approach. Finally, for this equation we demonstrate global well-posedness for sufficiently smooth initial conditions in the periodic case and in R-3. The key feature is the availability of an additional estimate which shows that the L-4-norm of the velocity field remains finite. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free