Navier-Stokes equations on the β-plane: Determining modes and nodes

PHYSICA D-NONLINEAR PHENOMENA

卷:386

Article

Miyajima, N.¹  Wirosoetisno, D.¹ 

[1] Univ Durham, Dept Math Sci, Durham DH1 3LE, England

关键词: Navier-Stokes equations;    Beta plane;    Determining modes;    Determining nodes;   

DOI  :  10.1016/j.physd.2018.08.005

来源: Elsevier

【 摘 要 】

We revisit the 2d Navier-Stokes equations on the periodic beta-plane, with the Coriolis parameter varying as beta y, and obtain bounds on the number of determining modes and nodes of the flow. The number of modes and nodes scale as c g(0)(1/2) + c'(M/beta)(1)(/)(2) and c g(0)(2)(/)(3) + c'(M/beta)(1)(/)(2), respectively, where the Grashof number g(0) = vertical bar f(v)vertical bar L-2/(mu(2 )k(0)(2)) and M involves higher derivatives of the forcing f(v). For large beta (strong rotation), this results in fewer degrees of freedom than the classical (non-rotating) bound that scales as c g(0). (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free