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

Miyajima, Naoko; Wirosoetisno, Djoko

Abstract

We revisit the 2d Navier–Stokes equations on the periodic β-plane, with the Coriolis parameter varying asβy, and obtain bounds on the number of determining modes and nodes of the flow. The number of modesand nodes scale as c G1/20+ c′(M/β)1/2and c G2/30+ c′(M/β)1/2, respectively, where the Grashof numberG0= |fv|L2/(µ2κ20) and M involves higher derivatives of the forcing fv. For large β (strong rotation), thisresults in fewer degrees of freedom than the classical (non-rotating) bound that scales as c G0.

Citation

Miyajima, N., & Wirosoetisno, D. (2019). Navier–Stokes equations on the β-plane: Determining modes and nodes. Physica D: Nonlinear Phenomena, 386-387, 31-37. https://doi.org/10.1016/j.physd.2018.08.005

• Journal Article Type: Article
• Acceptance Date: Aug 9, 2018
• Online Publication Date: Aug 22, 2018
• Publication Date: Jan 1, 2019
• Deposit Date: Aug 9, 2018
• Publicly Available Date: Aug 22, 2019
• Journal: Physica D: Nonlinear Phenomena
• Print ISSN: 0167-2789
• Electronic ISSN: 1872-8022
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 386-387
• Pages: 31-37
• DOI: https://doi.org/10.1016/j.physd.2018.08.005
• Public URL: https://durham-repository.worktribe.com/output/1323883
• Related Public URLs: https://arxiv.org/abs/1802.08644