Long frontal waves and dynamic scaling in freely evolving equivalent barotropic flow
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We present a scaling theory that links the frequency of long frontal waves to the kinetic energy decay rate and inverse transfer of potential energy in freely evolving equivalent barotropic turbulence. The flow energy is predominantly potential, and the streamfunction makes the dominant contribution to potential vorticity (PV) over most of the domain, except near PV fronts of width O(LD), where LD is the Rossby deformation length. These fronts bound large vortices within which PV is well-mixed and arranged into a staircase structure. The jets collocated with the fronts support long-wave undulations, which facilitate collisions and mergers between the mixed regions, implicating the frontal dynamics in the growth of potential-energy-containing flow features. Assuming the mixed regions grow self-similarly in time and using the dispersion relation for long frontal waves (Nycander et al., Phys. Fluids A, vol. 5, 1993, pp. 1089–1091) we predict that the total frontal length and kinetic energy decay like t-1/3, while the length scale of the staircase vortices grows like t1/3 . High-resolution simulations confirm our predictions.
Burgess , B H & Dritschel , D G 2019 , ' Long frontal waves and dynamic scaling in freely evolving equivalent barotropic flow ' , Journal of Fluid Mechanics , vol. 866 , R3 . https://doi.org/10.1017/jfm.2019.133
Journal of Fluid Mechanics
Non peer reviewed
© 2019, Cambridge University Press. This work has been made available online in accordance with the publisher's policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1017/jfm.2019.133
DescriptionFunding: Leverhulme Trust Early Career Fellowship (BHB).
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