The vortex gas scaling regime of baroclinic turbulence

Abstract

The mean state of the atmosphere and ocean is set through a balance between external forcing (radiation, winds, heat and freshwater fluxes) and the emergent turbulence, which transfers energy to dissipative structures. The forcing gives rise to jets in the atmosphere and currents in the ocean, which spontaneously develop turbulent eddies through the baroclinic instability. A critical step in the development of a theory of climate is to properly include the eddy-induced turbulent transport of properties like heat, moisture, and carbon. In the linear stages, baroclinic instability generates flow structures at the Rossby deformation radius, a length scale of order 1,000 km in the atmosphere and 100 km in the ocean, smaller than the planetary scale and the typical extent of ocean basins, respectively. There is, therefore, a separation of scales between the large-scale gradient of properties like temperature and the smaller eddies that advect it randomly, inducing effective diffusion. Numerical solutions show that such scale separation remains in the strongly nonlinear turbulent regime, provided there is sufficient drag at the bottom of the atmosphere and ocean. We compute the scaling laws governing the eddy-driven transport associated with baroclinic turbulence. First, we provide a theoretical underpinning for empirical scaling laws reported in previous studies, for different formulations of the bottom drag law. Second, these scaling laws are shown to provide an important first step toward an accurate local closure to predict the impact of baroclinic turbulence in setting the large-scale temperature profiles in the atmosphere and ocean.

On the Vertical Structure of Oceanic Mesoscale Tracer Diffusivities

“…The eddies responsible for mesoscale mixing are usually coherent and nonlinear in the extratropics (Chelton et al., 2011). These eddies tend to have deep vertical extents (e.g., Zhang et al., 2014), so the distance between coherent eddies, corresponding to the mixing length (Gallet & Ferrari, 2020; Thompson & Young, 2006), is independent of depth—at least in the upper ocean where the eddies are strong (Bates et al., 2014). It is therefore reasonable to expect that the mixing length in Equation is independent of depth where eddies are strong and nonlinear.…”

A Quantitative Scaling Theory for Meridional Heat Transport in Planetary Atmospheres and Oceans

“…However, while the insightful theoretical arguments provide qualitative understanding of the numerical data accumulated over the years (Chang & Held, 2021; Held & Larichev, 1996; Thompson & Young, 2007), they do not provide a quantitative scaling theory for the emergent diffusivity coefficients to the point that one may feel justified to question the very possibility of closing baroclinic turbulence on the basis of simple physical arguments. Building on a recent scaling theory developed for f ‐plane baroclinic turbulence (Gallet & Ferrari, 2020), we turn to the crucial impact of planetary curvature and zonal jets on the ‐plane, with the following motivational questions in mind: Can one express the heat flux driven by baroclinic turbulence on a curved planet using a downgradient diffusive closure? What are the key parameters the turbulent diffusivity coefficient depends on?…”

“…This may be at the origin of the inadequacy of spectral approaches, which ignore the phase information and assume interactions restricted to neighboring wavenumbers in spectral space. In Gallet and Ferrari (2020) (GF in the following), we embraced the physical‐space (as opposed to the spectral‐space) approach. By combining the statistics of isolated vortices and vortex dipoles with energetic arguments, we derived a predictive scaling theory (referred to as the “vortex gas” scaling theory in the following) for the meridional heat transport as a function of external forcing and friction.…”

A quantitative scaling theory for meridional heat transport in planetary atmospheres and oceans

“…However, while the insightful theoretical arguments provide qualitative understanding of the numerical data accumulated over the years (Held & Larichev, 1996;Thompson & Young, 2007;Chang & Held, 2021), they do not provide a quantitative scaling theory for the emergent diffusivity coefficients to the point that one may feel justified to question the very possibility of closing baroclinic turbulence on the basis of simple physical arguments. Building on a recent scaling theory developed for f -plane baroclinic turbulence (Gallet & Ferrari, 2020), we turn to the crucial impact of planetary curvature and zonal jets on the β-plane, with the following motivational questions in mind:…”