A Molecular View of Vorticity & Turbulence

The material in these lectures draws on work published in the literature during the previous seven years, applying Schertzer and Lovejoy’s theory of generalized scale invariance to a large body of airborne data which clearly showed atmospheric variability well above instrumental noise levels but which could not be described adequately by Gaussian PDFs and second moment power spectra.
The atmosphere is molecules in motion but a lacuna exists as regards explicit discussion or treatment of this fact in the meteorological literature and among standard texts on dynamic meteorology, fluid mechanics, turbulence, multifractals, non-equilibrium statistical mechanics and kinetic molecular theory. While texts on atmospheric chemistry of course deal in molecular behaviour, the step from kinetic molecular theory to atmospheric motion is made often without comment, usually via application of the law of mass action on scales many orders of magnitude larger than the mean free path and on which true diffusion cannot be dominant. Discussions of the progression from molecular to fluid motion are found mainly in the statistical mechanics literature but with no consideration of complicated anisotropic large-scale flows within morphologically irregular boundaries, such as those the atmosphere exhibits. There are few examples of attempts to examine the molecular roots of turbulence. These lectures aim to point out the need to address this situation, and to offer suggestions about how to proceed.
The central point of these lectures is that molecular dynamics, via the generation of vorticity in the presence of anisotropies such as gravity, planetary rotation and the solar beam, influences the structure of turbulence, temperature, radiative transfer and chemistry in the atmosphere. Because energy is deposited in the atmosphere by molecules absorbing photons, energy must propagate upward from the smallest scales. Analyses are presented of observations by the statistical multifractal methods developed by Schertzer and Lovejoy, which show generalized scale invariance in the atmosphere. The need to unite molecular dynamics, turbulence theory, fluid mechanics and non-equilibrium statistical mechanics is reinforced by the fact that core wind speeds in jet streams can exceed one third of the most probable velocity of air molecules, a breach of the conditions under which standard derivations of the Navier-Stokes equation are made. Note that in saying this I do not intend to imply that continuum fluid mechanics needs major reformulation in the context of the meteorological simulation of the large-scale flow by numerical process on computers for weather forecasting; the enterprise is too demonstrably successful for that to be the case. Indeed, some understanding of the success of this operation emerges naturally from analyzing high-resolution observations in a statistical multifractal framework. However, for representing the smaller scales, and for accurate accounting of the detailed energy distribution in the atmosphere, required for climate prediction, turbulence must be properly understood and formulated. It is my contention that it will not be achieved without explicit recognition of the fact that fluid mechanical behavior emerges spontaneously in the molecular dynamics simulation of a population of Maxwellian molecules subject to an anisotropy (Alder and Wainwright, 1970); turbulence has molecular roots.
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