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

Miyajima, Naoko; Wirosoetisno, Djoko

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


Authors

Naoko Miyajima



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
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 386-387
Pages 31-37
DOI https://doi.org/10.1016/j.physd.2018.08.005
Related Public URLs https://arxiv.org/abs/1802.08644

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