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- W2788492622 abstract "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 $cG_0^{1/2} + c'(M/beta)^{1/2}$ and $cG_0^{2/3} + c'(M/beta)^{1/2}$ respectively, where the Grashof number $G_0=|f_v|_{L^2}^{}/(mu^2kappa_0^2)$ 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 $cG_0$." @default.
- W2788492622 created "2018-03-06" @default.
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- W2788492622 date "2019-01-01" @default.
- W2788492622 modified "2023-09-27" @default.
- W2788492622 title "Navier–Stokes equations on the <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=mml1 display=inline overflow=scroll altimg=si1.gif><mml:mi>β</mml:mi></mml:math>-plane: Determining modes and nodes" @default.
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- W2788492622 doi "https://doi.org/10.1016/j.physd.2018.08.005" @default.
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