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

Miyajima, Naoko and Wirosoetisno, Djoko (2019) 'Navier–Stokes equations on the β-plane : determining modes and nodes.', Physica D : nonlinear phenomena., 386-387 . pp. 31-37.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.physd.2018.08.005
Publisher statement:© 2018 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:09 August 2018
Date deposited:09 August 2018
Date of first online publication:22 August 2018
Date first made open access:22 August 2019

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