A Scaling Theory for Horizontally Homogeneous, Baroclinically Unstable Flow on a Beta Plane

Abstract

The scaling argument developed by Larichev and Held (1995) for eddy amplitudes and fluxes in a horizontally homogeneous, two-layer model on an f -plane is extended to a β-plane. In terms of the non-dimensional number ξ = U/(βλ 2 ), where λ is the deformation radius and U is the mean thermal wind, the result for the RMS eddy velocity V , the characteristic wavenumber of the energy-containing eddies and of the eddy-driven jets k j , and the magnitude of the eddy diffusivity for potential vorticity D, in the limit ξ ≫ 1, are as follows:

Lagrangian scale of particle dispersion in turbulence

“…The above conclusion about the dominance in the diffusivity of one scale, which is close to the forcing scale, is at odds with results obtained in several studies, which find that the diffusivity is determined by the energy-containing eddy scales [20][21][22][23] . In 2D turbulence, in the presence of the inverse energy cascade, these scales are in the lower-k part of the Eulerian spectrum.…”

Energy pathways and structures of oceanic eddies from the ECCO2 state estimate and simplified models

“…Quite a few recent studies about eddy dynamics are based on the local baroclinic instability hypothesis (e.g. Held and Larichev, 1996;Tulloch et al, 2011;Panetta, 1993;Venaille et al, 2011;Arbic and Flierl, 2004), and these investigations suggest that this hypothesis is useful in many contexts. For example, Smith (2007) and Tulloch et al (2011) found that the eddy scale with the fastest growth rate, based on the local linear instability analysis, is smaller than the observed eddy scales and they concluded that inverse cascade is important in setting the observed eddy scales.…”

“…Robinson and McWilliams, 1974;Held and Larichev, 1996;Venaille et al, 2011;Smith, 2007;Tulloch et al, 2011). This hypothesis has two aspects: (1) each region in the ocean is assumed to be horizontally homogeneous and thus all the energy released from the baroclinically unstable mean flow is used to sustain the local eddy energy growth, which is balanced by other terms in the eddy energy budget (e.g.…”

CLIMBER-2: a climate system model of intermediate complexity. Part I: model description and performance for present climate

“…) are obtained in the model applying the conventional method of deriving a set of equations for synoptic-scale components similar to Saltzman and Vernekar (1972). Stone and Yao (1990), and Held and Larichev (1996). The assumption that synoptic components are a Gaussian process in space and time (Hasselmann 1976;Lemke 1977) allows us to reduce an in®nite set of equations to a set of equations for the second moments only.…”