Research Article

The vortex gas scaling regime of baroclinic turbulence

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PNAS March 3, 2020 117 (9) 4491-4497; first published February 18, 2020; https://doi.org/10.1073/pnas.1916272117

  1. Edited by William R. Young, University of California San Diego, La Jolla, CA, and approved January 15, 2020 (received for review September 20, 2019)

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Figures

  • Fig. 1.
    Fig. 1.

    (A) Base state of the 2LQG system with imposed vertical shear. The interface is tilted in the y direction as a consequence of thermal wind balance. The baroclinic stream function is proportional to −h, where h(x,y,t) is the local displacement of the interface. For this reason, the baroclinic stream function is often referred to as the temperature field. Snapshots of the departure of the baroclinic stream function from the base state (τ; B) and of the barotropic vorticity (ζ; C) from a numerical simulation in the low-friction regime (arbitrary units; low values in dark blue, and large values in bright yellow). We model the barotropic flow as a gas of vortices (D) of circulation ±Γ and radius rcore∼λ. The vortex cores move as a result of their mutual interaction, with a typical velocity V∼Γ/ℓiv, where ℓiv is the typical intervortex distance.

  • Fig. 2.
    Fig. 2.

    Heat transport by a barotropic vortex dipole. A is a schematic representation of the heat sources and sinks induced by the dipolar velocity field. B–D show the barotropic vorticity, temperature field, and local meridional heat flux, respectively, at the end time of a numerical solution of [10] where the dipole travels over a distance ℓiv in the meridional direction y.

  • Fig. 3.
    Fig. 3.

    Dimensionless mixing length ℓ* and diffusivity D* as functions of dimensionless drag for both linear and quadratic drag. Symbols correspond to numerical simulations, while the solid lines are the predictions [15–18] from the vortex gas scaling theory.

  • Fig. 4.
    Fig. 4.

    Testing the diffusive closure. Snapshots and meridional profiles of the dimensionless temperature τ/λ2Q1/2. The solid lines are the zonal and time mean from the numerical simulations, while the dashed lines are the theoretical expressions [23] and [24]. (A) Linear drag, with κ/Q1/2=0.5 and λ/L=0.02. (B) Quadratic drag, with μ*=10−2 and λ/L=0.01.

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The vortex gas scaling regime of baroclinic turbulence
Basile Gallet, Raffaele Ferrari
Proceedings of the National Academy of Sciences Mar 2020, 117 (9) 4491-4497; DOI: 10.1073/pnas.1916272117
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Proceedings of the National Academy of Sciences: 117 (9)
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