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On the spacing of meandering jets in the strong-stair limit

Published online by Cambridge University Press:  11 November 2021

R.K. Scott Open the ORCID record for R.K. Scott [Opens in a new window] ,
B.H. Burgess Open the ORCID record for B.H. Burgess [Opens in a new window]  and
D.G. Dritschel Open the ORCID record for D.G. Dritschel [Opens in a new window]
R.K. Scott*
Affiliation:
School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
B.H. Burgess
Affiliation:
School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
D.G. Dritschel
Affiliation:
School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
*
†Email address for correspondence: rks4@st-andrews.ac.uk
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Abstract

Based on an assumption of strongly inhomogeneous potential vorticity mixing in quasi-geostrophic $\beta$-plane turbulence, a relation is obtained between the mean spacing of latitudinally meandering zonal jets and the total kinetic energy of the flow. The relation applies to cases where the Rossby deformation length is much smaller than the Rhines scale, in which kinetic energy is concentrated within the jet cores. The relation can be theoretically achieved in the case of perfect mixing between regularly spaced jets with simple meanders, and of negligible kinetic energy in flow structures other than in jets. Incomplete mixing or unevenly spaced jets will result in jets being more widely separated than the estimate, while significant kinetic energy outside the jets will result in jets closer than the estimate. An additional relation, valid under the same assumptions, is obtained between the total kinetic and potential energies. In flows with large-scale dissipation, the two relations provide a means to predict the jet spacing based only on knowledge of the energy input rate of the forcing and dissipation rate, regardless of whether the latter takes the form of frictional or thermal damping. Comparison with direct numerical integrations of the forced system shows broad support for the relations, but differences between the actual and predicted jet spacings arise both from the complex structure of jet meanders and the non-negligible kinetic energy contained in the turbulent background and in coherent vortices lying between the jets.

JFM classification

Geophysical and Geological Flows: Geostrophic turbulence Geophysical and Geological Flows: Quasi-geostrophic flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 930 , 10 January 2022 , A20
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

*

The online version of this article has been updated since original publication. A notice detailing the change has also been published.

References

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