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 fastestgrowing 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.

[1] The interpretation of surface altimetric signals in terms of Rossby waves is revisited. Rather than make the long-wave approximation, the horizontal scale of the waves is adjusted to optimally fit the phase speed predicted by linear theory to that observed by altimetry, assuming a first baroclinic mode vertical structure. It is found that in the tropical band the observations can be fit if the wavelength of the waves is assumed to be large, of order 600 km or so. However poleward of ±30°, it is more difficult to fit linear theory to the observations, and the fit is less good than at lower latitudes: the required scale of the waves must be reduced to about 100 km, somewhat larger than the local deformation wavelength. It is argued that these results can be interpreted in terms of Rossby wave, baroclinic instability, and turbulence theory. At low latitudes there is an overlap between geostrophic turbulence and Rossby wave timescales, and so, an upscale energy transfer from baroclinic instability at the deformation scale produces waves. At high latitudes there is no such overlap and waves are not produced by upscale energy transfer. These ideas are tested by using surface drifter data to infer turbulent velocities and timescales that are compared to those of linear Rossby waves. A transition from a field dominated by waves to one dominated by turbulence occurs at about ±30°, broadly consistent with the transition that is required to fit linear theory to altimetric observations.

The horizontal spectra of atmospheric wind and temperature at the tropopause have a steep ؊3 slope at synoptic scales, but transition to ؊5͞3 at wavelengths of the order of 500 -1,000 km [Nastrom, G. D. & Gage, K. S. (1985) J. Atmos. Sci. 42, 950 -960]. Here we demonstrate that a model that assumes zero potential vorticity and constant stratification N over a finite-depth H in the troposphere exhibits the same type of spectra. In this model, temperature perturbations generated at the planetary scale excite a direct cascade of energy with a slope of ؊3 at large scales, ؊5͞3 at small scales, and a transition near horizontal wavenumber k t ‫؍‬ f͞NH, where f is the Coriolis parameter. Ballpark atmospheric estimates for N, f, and H give a transition wavenumber near that observed, and numerical simulations of the previously undescribed model verify the expected behavior. Despite its simplicity, the model is consistent with a number of perplexing features in the observations and demonstrates that a complete theory for mesoscale dynamics must take temperature advection at boundaries into account.geophysical turbulence ͉ meteorology ͉ atmospheric dynamics I n the 1970s, the National Aeronautics and Space Administration (NASA) instrumented commercial Boeing 747 airliners to collect atmospheric data during their regular flights (1) in an endeavor called the Global Atmospheric Sampling Program (GASP). The resulting data set consists of thousands of flight tracks, a few hundred of which are Ͼ10,000 km long, collected over a 4-year period. Most flights occurred in the midlatitudes and tropics but span the full range of seasons. Because airliners travel at altitudes between 9 and 14 km, the data largely reflect the upper troposphere and lower stratosphere, near the tropopause. Atmospheric wavenumber spectra of horizontal wind and temperature computed from the GASP data set by Nastrom and Gage (ref. 1; hereafter NG85) show a distinct transition from a steep spectral slope of Ϫ3 at synoptic scales (Ϸ1,000-3,000 km) to a shallower slope of Ϫ5͞3 at mesoscales (Ϸ10-500 km), with a fairly distinct transition centered at a horizontal wavelength of Ϸ600 km. Understanding the source and structure of this spectrum has posed a puzzle in atmospheric science for the past 20 years.The spectrum is intriguing because it agrees so well at large scales with Charney's (3) theory of geostrophic turbulence but deviates from that prediction where it shallows. Moreover, the fact that the small-scale slope is Ϫ5͞3 invites multiple explanations, because that is the theoretical slope both for the forward cascade of energy in isotropic, three-dimensional (3D) turbulence, and for the inverse cascade of two-dimensional (2D) turbulence, as well as other systems. At the large scale, Charney argued (3), rotation and stratification conspire to make the atmosphere quasi-2D. Stirring by baroclinic instability (or any planetary mechanism) will induce a forward cascade of potential enstrophy, reflected in a Ϫ3 kinetic energy spectrum below the stirring scale. Mor...

Observations and theory suggest that lateral mixing by mesoscale ocean eddies only reaches its maximum potential at steering levels, surfaces at which the propagation speed of eddies approaches that of the mean flow. Away from steering levels, mixing is strongly suppressed because the mixing length is smaller than the eddy scale, thus reducing the mixing rates. The suppression is particularly pronounced in strong currents where mesoscale eddies are most energetic. Here, a framework for parameterizing eddy mixing is explored that attempts to capture this suppression. An expression of the surface eddy diffusivity proposed by Ferrari and Nikurashin is evaluated using observations of eddy kinetic energy, eddy scale, and eddy propagation speed. The resulting global maps of eddy diffusivity have a broad correspondence with recent estimates of diffusivity based on the rate at which tracer contours are stretched by altimetric-derived surface currents. Finally, the expression for the eddy diffusivity is extrapolated in the vertical to infer the eddy-induced meridional heat transport and the overturning streamfunction.