Robustness of vortex populations in the two-dimensional inverse energy cascade
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We study how the properties of forcing and dissipation affect the scaling behaviour of the vortex population in the two-dimensional turbulent inverse energy cascade. When the flow is forced at scales intermediate between the domain and dissipation scales, the growth rates of the largest vortex area and the spectral peak length scale are robust to all simulation parameters. For white-in-time forcing the number density distribution of vortex areas follows the scaling theory predictions of Burgess & Scott (J. Fluid Mech., vol. 811, 2017, pp. 742–756) and shows little sensitivity either to the forcing bandwidth or to the nature of the small-scale dissipation: both narrowband and broadband forcing generate nearly identical vortex populations, as do Laplacian diffusion and hyperdiffusion. The greatest differences arise in comparing simulations with correlated forcing to those with white-in-time forcing: in flows with correlated forcing the intermediate range in the vortex number density steepens significantly past the predicted scale-invariant A-1 scaling. We also study the impact of the forcing Reynolds number Rej, a measure of the relative importance of nonlinear terms and dissipation at the forcing scale, on vortex formation and the scaling of the number density. As Rej decreases, the flow changes from one dominated by intense circular vortices surrounded by filaments to a less structured flow in which vortex formation becomes progressively more suppressed and the filamentary nature of the surrounding vorticity field is lost. However, even at very small Rej, and in the absence of intense coherent vortex formation, regions of anomalously high vorticity merge and grow in area as predicted by the scaling theory, generating a three-part number density similar to that found at higher Rej. At late enough stages the aggregation process results in the formation of long-lived circular vortices, demonstrating a strong tendency to vortex formation, and via a route distinct from the axisymmetrization of forcing extrema seen at higher Rej. Our results establish coherent vortices as a robust feature of the two-dimensional inverse energy cascade, and provide clues as to the dynamical mechanisms shaping their statistics.
Burgess , B H & Scott , R K 2018 , ' Robustness of vortex populations in the two-dimensional inverse energy cascade ' Journal of Fluid Mechanics , vol. 850 , pp. 844-874 . https://doi.org/10.1017/jfm.2018.473
Journal of Fluid Mechanics
© 2018, 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 may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1017/jfm.2018.473
DescriptionFunding: Leverhulme Early Career Fellowship from the Leverhulme Trust, the Natural Environment Research Council grant NE/M014983/1 (B.H.B.).
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