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Atmospheric Turbulencea molecular dynamics perspective$
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Adrian F. Tuck

Print publication date: 2008

Print ISBN-13: 9780199236534

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780199236534.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 03 March 2021

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Adrian F. Tuck

Oxford University Press

Atmospheric composition played an important part in the development of chemistry, following the work of Priestley, Lavoisier, and Dalton. Since air is a mixture of gases, many of them chemically reactive, see for example Finlayson-Pitts and Pitts (2000) and Graedel et al. (1986), which is subject to solar photons, absorbs and emits infrared photons, experiences temperatures ranging from −100 to 40° C, is exposed to the ocean, encompasses phase changes of water and sustains turbulent flow, it involves significant parts of physical chemistry. Pedagogically, the three-volume set by Berry, Rice, and Ross (2002a, b, c) covers the basic physicochemical material clearly and thoroughly, particularly Chapters 19, 20, 27, 28, 30, and 31. In addition to kinetic molecular theory, chemical kinetics, spectroscopy, and equilibrium statistical mechanics, there are other branches of physical science which are applicable to the atmosphere; in our context they include of course meteorology and turbulence theory. It ought to be recognized that the atmosphere has high complexity arising from a vast number of degrees of freedom, several anisotropies, and morphologically complicated boundaries extending over 15 orders of magnitude in scale from the molecular mean free path to the Earth’s circumference; these factors and the concomitant non-linearities make the application of non-equilibrium statistical mechanics a daunting prospect, but nevertheless one which should be attempted, for the reason that the energy distributions and their transformations in the atmosphere need to be accurately described, particularly in the representation and prognosis of the climatic state. We will also show that vorticity is the fundamental variable, since vortices are generated from molecular populations subjected to an anisotropy, on very short space scales and fast time scales. In this Chapter we will give a skeletal survey connecting these basic subjects, with references to more comprehensive, individual sources. The simplest possible molecular model for a gas is a collection of spherical ‘billiard balls’—the intermolecular potential consists of an infinite repulsive force on contact. This approach, pioneered by Waterston, Maxwell, and Boltzmann, is successful for air as a first approximation. The idea is that collisions are completely elastic, with no interaction between potential collidant molecules until physical contact occurs, whereupon an infinite repulsive potential operates.

Keywords:   Boltzmann equation, Brownian motion, Coriolis force, Gaussian noise, Leonardo da Vinci, Liouville operator, absolute vorticity, atmospheric complexity, autocorrelation

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