# Scales, Growth Rates, and Spectral Fluxes of Baroclinic Instability in the Ocean.

(Tulloch, Ross and Marshall, John and Hill, Chris and Smith, K. Shafer), *JOURNAL OF PHYSICAL OCEANOGRAPHY*, vol. 41, no. 6, pp. pages, 2011.

## Abstract

An observational, modeling, and theoretical study of the scales, growth rates, and spectral fluxes of baroclinic instability in the ocean is presented, permitting a discussion of the relation between the local instability scale; the first baroclinic deformation scale R(def); and the equilibrated, observed eddy scale. The geography of the large-scale, meridional quasigeostrophic potential vorticity (QGPV) gradient is mapped out using a climatological atlas, and attention is drawn to asymmetries between midlatitude eastward currents and subtropical return flows, the latter of which has westward and eastward zonal velocity shears. A linear stability analysis of the climatology, under the “local approximation” yields the growth rates and scales of the fastest-growing modes. Fastest-growing modes on eastward-flowing currents, such as the Kuroshio and the Antarctic Circumpolar Current, have a scale somewhat larger (by a factor of about 2) than R(def). They are rapidly growing (e folding in 1-3 weeks) and deep reaching, and they can be characterized by an interaction between interior QGPV gradients, with a zero crossing in the QGPV gradient at depth. In contrast, fastest-growing modes in the subtropical return flows (as well as much of the gyre interiors) have a scale smaller than R(def) (by a factor of between 0.5 and 1), grow more slowly (e-folding scale of several weeks), and owe their existence to the interaction of a positive surface QGPV gradient and a negative gradient beneath. These predictions of linear theory under the local approximation are then compared to observed eddy length scales and spectral fluxes using altimetric data. It is found that the scale of observed eddies is some 2-3 times larger than the instability scale indicative of a modest growth in horizontal scale. No evidence of an inverse cascade over decades in scale is found. Outside of a tropical band, the eddy scale varies with latitude along with but somewhat less strongly than R(def). Finally, exactly the same series of calculations is carried out on fields from an idealized global eddying model, enabling study in a more controlled setting. Broadly similar conclusions are reached, thus reinforcing inferences made from the data.

doi = 10.1175/2011JPO4404.1