Chang, Chiung-Yin, and Isaac M Held, June 2022: A scaling theory for the diffusivity of poleward eddy heat transport based on Rhines scaling and the global entropy budget. Journal of the Atmospheric Sciences, 79(6), DOI:10.1175/JAS-D-21-0242.11743-1758. Abstract
Diffusive theories for the meridional atmospheric energy transport can summarize our understanding of this central aspect of the general circulation. They can also be utilized in simple models of Earth’s energy balance to help interpret the response of the system to perturbations. A theory for this diffusivity of eddy heat transport is described based on Rhines scaling and the global entropy budget, each of which provides a constraint between the kinetic energy dissipation and the diffusivity. An expression for the diffusivity is then obtained by eliminating the dissipation from this set of two constraints. The theory can be thought of as a generalization of the theories of Held–Larichev and Barry–Craig–Thuburn. The theory is compared to simulations of the Held–Suarez idealized dry atmospheric model. Limitations of the theory are emphasized. The form of the theory allows it to be readily generalized to a moist atmosphere.
We describe an idealized primitive-equation model for studying mesoscale turbulence and leverage a hierarchy of grid resolutions to make eddy-resolving calculations on the finest grids more affordable. The model has intermediate complexity, incorporating basin-scale geometry with idealized Atlantic and Southern oceans and with non-uniform ocean depth to allow for mesoscale eddy interactions with topography. The model is perfectly adiabatic and spans the Equator and thus fills a gap between quasi-geostrophic models, which cannot span two hemispheres, and idealized general circulation models, which generally include diabatic processes and buoyancy forcing. We show that the model solution is approaching convergence in mean kinetic energy for the ocean mesoscale processes of interest and has a rich range of dynamics with circulation features that emerge only due to resolving mesoscale turbulence.
Although classical theories of midlatitude momentum fluxes focus on the wave–mean flow interaction, wave–wave interactions may be important for generating long waves. It is shown in this study that this nonlinear generation has implications for eddy momentum fluxes in some regimes. Using a two-layer quasigeostrophic model of a baroclinic jet on a β plane, statistically steady states are explored in which the vertically integrated eddy momentum flux is divergent at the center of the jet, rather than convergent as in Earthlike climates. One moves toward this less familiar climate from more Earthlike settings by reducing either β, frictional drag, or the width of the baroclinic zone, or by increasing the upper bound of resolvable wavelengths by lengthening the zonal channel. Even in Earthlike settings, long waves diverge momentum from the jet, but they are too weak to compete with short unstable waves that converge momentum. We argue that long waves are generated by breaking of short unstable waves near their critical latitudes, where long waves converge momentum while diverging momentum at the center of the jet. Quasi-linear models with no wave–wave interaction can qualitatively capture the Earthlike regime but not the regime with momentum flux divergence at the center of the jet, because the nonlinear wave breaking and long-wave generation processes are missing. Therefore, a more comprehensive theory of atmospheric eddy momentum fluxes should take into account the nonlinear dynamics of long waves.
Chang, Chiung-Yin, and Isaac M Held, June 2019: The control of surface friction on the scales of baroclinic eddies in a homogeneous quasigeostrophic two-layer model. Journal of the Atmospheric Sciences, 76(6), DOI:10.1175/JAS-D-18-0333.1. Abstract
In idealized models of the extratropical troposphere, both β and surface friction can control the equilibrated scales of baroclinic eddies by stopping the inverse cascade. A scaling theory on how surface friction alone sets these scales is proposed by Held (1999) in the case of a quadratic drag law. However, the theory breaks down when friction is modeled by linear damping, and there are other reasons to suspect that it is oversimplified. An ideal system to test the theory is the homogeneous two-layer quasigeostrophic model in the β = 0 limit with quadratic damping. This study investigates some numerical simulations of the model to analyze two causes of the theory’s breakdown. They are 1) the asymmetry between two layers due to confinement of friction to the lower layer, and 2) deviation from a spectrally local inverse energy cascade due to the spread of wavenumbers over which energy is input into the barotropic mode. The former is studied by comparing the simulations with drag appearing asymmetrically or symmetrically between the two layers. The latter is addressed with a heuristic modification of the theory. A regime where eddies equilibrate without an inverse cascade is also examined. A comparison is then made between quadratic and linear drag simulations. The connection to a competing theory based on the dynamics of equivalent barotropic vortices with thermal signatures is further discussed. Finally, we present an example of an inhomogeneous statistically steady state to argue that the diffusivity obtained from the homogeneous model has relevance to more realistic configurations.
