Recovery of atmospheric flow statistics in a general circulation model without nonlinear eddy‐eddy interactions

Abstract

[1] The closure problem of turbulence arises because nonlinear interactions among turbulent fluctuations (eddies) lead to an infinite hierarchy of moment equations for flow statistics. Here we demonstrate with an idealized general circulation model (GCM) that many atmospheric flow statistics can already be recovered if the hierarchy of moment equations is truncated at second order, corresponding to the elimination of nonlinear eddy-eddy interactions. Some, but not all, features of the general circulation remain the same. The atmospheric eddy kinetic energy spectrum retains a À3 power-law range even though this is usually explained in terms of an enstrophy cascade mediated by nonlinear eddy-eddy interactions. Our results suggest that it may be possible to construct fast general circulation models that solve for atmospheric flow statistics directly rather than via simulation of individual eddies and their interactions. Citation: O'Gorman, P. A., and T. Schneider

Statistics of an Unstable Barotropic Jet from a Cumulant Expansion

“…There is evidence, however, that nonlinear eddy-eddy interactions in the earth's atmosphere are weak (Schneider and Walker 2006). O'Gorman and Schneider (2007) have shown that several features of atmospheric flows, such as scales of jets and the shape of the atmospheric turbulent kinetic energy spectrum, can be recovered in an idealized general circulation model in which eddy-eddy interactions are suppressed. In particular, baroclinic jets form spontaneously and are maintained by eddy-mean flow interactions even in the absence of nonlinear eddy-eddy interactions.…”

Baroclinic Adjustment and Dissipative Control of Storm Tracks

“…First, both the global-mean APE and eddy kinetic energy have been observed to increase with radiative forcing of storm tracks (O'Gorman and Schneider 2008;O'Gorman 2010), yet the Ambaum-Novak model predicts that the mean APE should be insensitive to this forcing (and storm-track activity). The mean APE responses have been found to be spatially complex and very sensitive to the choices used to define the baroclinic mixing zone over which the mean APE is averaged.…”

“…For example, Chen et al (2007) have found strong dependency of storm-track activity to eddy frictional dissipation in a dry GCM, while the predictions above are for eddies and eddy friction to be independent. Furthermore, O'Gorman (2010) and O'Gorman and Schneider (2008) find that in an idealized GCM and in more complex climate models the steady-state mean available potential energy is directly proportional to the thermal mean forcing of the meridional temperature gradient, yet the AmbaumNovak model prediction is for these to be independent in the steady state.…”

“…The inverse cascade does not dominate in the midlatitude atmosphere (O'Gorman and Schneider 2007), because of Earth's limited domain size relative to the deformation scale (Zurita-Gotor and Vallis 2009). Baroclinic eddies therefore often interact directly with the mean barotropic flow, in addition to being able to reduce the baroclinicity, and their barotropic feedbacks may substantially intervene with the baroclinic eddy-mean flow interaction.…”

The Relative Humidity in an Isentropic Advection–Condensation Model: Limited Poleward Influence and Properties of Subtropical Minima

“…To gain insights into how the relative humidity is maintained in a more idealized setting, Pierrehumbert et al (2007) introduced a version of advection-condensation modeling in which the advecting winds are taken to be stochastic processes. O'Gorman and Schneider (2006) extended the approach to more general stochastic wind processes and linked the stochastic model to simulations with turbulent velocity fields. They considered a prototype setting with a monotonic saturation specific humidity profile and without spatially inhomogeneous moisture sources.…”