An explicit method to determine Casimirs in 2D geophysical flows

Erwin Luesink; Bernard Geurts

doi:10.1007/978-3-031-40094-0_8

An explicit method to determine Casimirs in 2D geophysical flows

Erwin Luesink, Bernard Geurts

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

Conserved quantities in geophysical flows play an important role in the characterisation of geophysical dynamics and aid the development of structure-preserving numerical methods. A significant family of conserved quantities is formed by the Casimirs i.e., integral conservation laws that are in the kernel of the underlying Poisson bracket. The Casimirs hence determine the geometric structure of the geophysical fluid equations among which the enstrophy is well known. Often Casimirs are proposed on heuristic grounds and later verified to be part of the kernel of the Poisson bracket. In this work, we will explicitly construct Casimirs by rewriting the Poisson bracket in vorticity-divergence coordinates thereby providing explicit construction of Casimirs for 2D geophysical flow dynamics.

Original language	English
Title of host publication	Stochastic Transport in Upper Ocean Dynamics II
Subtitle of host publication	STUOD 2022 Workshop, London, UK, September 26–29
Publisher	Springer
Pages	193-206
ISBN (Electronic)	978-3-031-40094-0
ISBN (Print)	978-3-031-40093-3
DOIs	https://doi.org/10.1007/978-3-031-40094-0_8
Publication status	Published - 4 Aug 2023
Event	3rd Stochastic Transport in Upper Ocean Dynamics Annual Workshop, STUOD 2022 - London, United Kingdom Duration: 26 Sept 2022 → 29 Sept 2022 Conference number: 3

Publication series

Name	Mathematics of Planet Earth
Publisher	Springer
Volume	11

Workshop

Workshop	3rd Stochastic Transport in Upper Ocean Dynamics Annual Workshop, STUOD 2022
Abbreviated title	STUOD 2022
Country/Territory	United Kingdom
City	London
Period	26/09/22 → 29/09/22

Keywords

physics.flu-dyn

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10.1007/978-3-031-40094-0_8Licence: CC BY

978-3-031-40094-0_8Final published version, 384 KBLicence: CC BY

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An explicit method to determine Casimirs in 2D geophysical flows
Luesink, E. & Geurts, B., 23 Feb 2023, ArXiv.org.
Research output: Working paper › Preprint › Academic

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Cite this

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title = "An explicit method to determine Casimirs in 2D geophysical flows",

abstract = "Conserved quantities in geophysical flows play an important role in the characterisation of geophysical dynamics and aid the development of structure-preserving numerical methods. A significant family of conserved quantities is formed by the Casimirs i.e., integral conservation laws that are in the kernel of the underlying Poisson bracket. The Casimirs hence determine the geometric structure of the geophysical fluid equations among which the enstrophy is well known. Often Casimirs are proposed on heuristic grounds and later verified to be part of the kernel of the Poisson bracket. In this work, we will explicitly construct Casimirs by rewriting the Poisson bracket in vorticity-divergence coordinates thereby providing explicit construction of Casimirs for 2D geophysical flow dynamics. ",

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author = "Erwin Luesink and Bernard Geurts",

note = "11 pages, no figures, second version. All comments are welcome; 3rd Stochastic Transport in Upper Ocean Dynamics Annual Workshop, STUOD 2022, STUOD 2022 ; Conference date: 26-09-2022 Through 29-09-2022",

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language = "English",

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Luesink, E & Geurts, B 2023, An explicit method to determine Casimirs in 2D geophysical flows. in Stochastic Transport in Upper Ocean Dynamics II: STUOD 2022 Workshop, London, UK, September 26–29. Mathematics of Planet Earth, vol. 11, Springer, pp. 193-206, 3rd Stochastic Transport in Upper Ocean Dynamics Annual Workshop, STUOD 2022, London, United Kingdom, 26/09/22. https://doi.org/10.1007/978-3-031-40094-0_8

An explicit method to determine Casimirs in 2D geophysical flows. / Luesink, Erwin; Geurts, Bernard.
Stochastic Transport in Upper Ocean Dynamics II: STUOD 2022 Workshop, London, UK, September 26–29. Springer, 2023. p. 193-206 (Mathematics of Planet Earth; Vol. 11).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AU - Geurts, Bernard

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N2 - Conserved quantities in geophysical flows play an important role in the characterisation of geophysical dynamics and aid the development of structure-preserving numerical methods. A significant family of conserved quantities is formed by the Casimirs i.e., integral conservation laws that are in the kernel of the underlying Poisson bracket. The Casimirs hence determine the geometric structure of the geophysical fluid equations among which the enstrophy is well known. Often Casimirs are proposed on heuristic grounds and later verified to be part of the kernel of the Poisson bracket. In this work, we will explicitly construct Casimirs by rewriting the Poisson bracket in vorticity-divergence coordinates thereby providing explicit construction of Casimirs for 2D geophysical flow dynamics.

AB - Conserved quantities in geophysical flows play an important role in the characterisation of geophysical dynamics and aid the development of structure-preserving numerical methods. A significant family of conserved quantities is formed by the Casimirs i.e., integral conservation laws that are in the kernel of the underlying Poisson bracket. The Casimirs hence determine the geometric structure of the geophysical fluid equations among which the enstrophy is well known. Often Casimirs are proposed on heuristic grounds and later verified to be part of the kernel of the Poisson bracket. In this work, we will explicitly construct Casimirs by rewriting the Poisson bracket in vorticity-divergence coordinates thereby providing explicit construction of Casimirs for 2D geophysical flow dynamics.

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DO - 10.1007/978-3-031-40094-0_8

M3 - Conference contribution

SN - 978-3-031-40093-3

T3 - Mathematics of Planet Earth

SP - 193

EP - 206

BT - Stochastic Transport in Upper Ocean Dynamics II

PB - Springer

T2 - 3rd Stochastic Transport in Upper Ocean Dynamics Annual Workshop, STUOD 2022

Y2 - 26 September 2022 through 29 September 2022

ER -

An explicit method to determine Casimirs in 2D geophysical flows

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Workshop

Keywords

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Research output

An explicit method to determine Casimirs in 2D geophysical flows

Cite this