Some fundamental aspects of atmospheric dynamics, with a solar spinoff

Abstract

Abstract Global-scale atmospheric circulations illustrate with outstanding clarity one of the grand themes in physics: the organization of chaotic fluctuations in complex dynamical systems, with nontrivial, persistent mean effects. This is a theme recognized as important not just for classical textbook cases like molecular gas kinetics but also for an increasingly wide range of dynamical systems with large phase spaces, not in simple statistical-mechanical equilibrium or near-equilibrium. In the case of the atmosphere, the organization of fluctuations is principally due to three wave-propagation mechanisms or quasi-elasticities: gravity/buoyancy, inertia/Coriolis, and Rossby/vortical. These enter the fluctuation dynamics along with various forms of highly inhomogeneous turbulence, giving rise to a “wave-turbulence jigsaw puzzle” in which the spatial inhomogeneity—characteristic of “wave-breaking” understood in a suitably generalized sense-exhibits phase coherence and is an essential, leading-order feature as illustrated, also, by the visible surf zones near ocean beaches. Such inhomogeneity is outside the scope of classical turbulence theory, which assumes spatial statistical homogeneity or small departures therefrom. The wave mechanisms induce systematic correlations between fluctuating fields, giving rise to mean fluxes or transports of momentum quite different from those found in gas kinetics or in classical turbulence theory. Wave-induced momentum transport is a long-range process, effective over distances far exceeding the fluctuating material displacements or “mixing lengths” characteristic of the fluid motion itself. Such momentum transport, moreover, often has an “anti-frictional” character, driving the system away from solid rotation, not toward it, as underlined most plainly by the existence of the stratospheric quasi-biennial oscillation (QBO) and its laboratory couunterparts. Wave-induced momentum transport drives the Coriolis-mediated “gyroscopic pumping” of meridional circulations against radiative relaxation, as illustrated by the Murgatroyd-Singleton mesospheric circulation and the Brewer-Dobson (misnamed Hadley) stratospheric circulation. The Brewer-Dobson can be contrasted with the convectively driven tropospheric Hadley circulation and with the oceans' thermohaline circulation. The ocean is an opposite extreme case in the sense that radiative relaxation has no counterpart. If the stratosphere is compared to a tape recorder whose motor is the gyroscopic pump and whose recording head is the tropical tropopause with its seasonal water-vapour signal, then the distribution of radiative-equilibrium temperatures across the tropics may be compared to the guidance wheels influencing the upward path of the tape. In other words, solar heating does not drive the tropical stratospheric upwelling, but does influence the way in which the upwelling mass flux demanded by the wave-driven pumping is distributed across the tropics. Because the tropical mean circulation problem is nonlinear, one cannot think of the tropical part of the circulation as a linear superposition of thermally and mechanically driven “contributions”. Insights into the dynamics of atmospheric circulations have recently led to a breakthrough in an astrophysical problem, that of understanding the differential rotation, meridional circulation, and helium distribution within the sun, with strong implications for helioseismic inversion and the so-called lithium and beryllium problems. This is an example of meteorological understanding informing solar and stellar physics.