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Grid-based calculation of the Lagrangian mean

Published online by Cambridge University Press:  08 April 2022

Hossein A. Kafiabad Open the ORCID record for Hossein A. Kafiabad [Opens in a new window]
Hossein A. Kafiabad*
Affiliation:
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, EdinburghEH9 3FD, UK
*
†Email address for correspondence: h.kafiabad@ed.ac.uk
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Abstract

Lagrangian averaging has been shown to be more effective than the Eulerian mean in separating waves from slow dynamics in two time scale flows. It also appears in many reduced models that capture the wave feedback on the slow flow. Its calculation, however, requires tracking particles in time, which imposes several difficulties in grid-based numerical simulations or estimation from fixed-point measurements. To circumvent these difficulties, we propose a grid-based iterative method to calculate the Lagrangian mean without tracking particles in time, which also reduces computation, memory footprint and communication between processors in parallelised numerical models. To assess the accuracy of this method several examples are examined and discussed. We also explore an application of this method in the context of shallow-water equations by quantifying the validity of wave-averaged geostrophic balance – a modified form of geostrophic balance accounting for the effect of strong waves on slow dynamics.

JFM classification

Geophysical and Geological Flows: Waves in rotating fluids Mathematical Foundations: Computational methods Geophysical and Geological Flows: Ocean circulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 940 , 10 June 2022 , A21
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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