[GTP] GTP/ESSL/ACD Two-day Seminar--Adrian Tuck

[Silvia Gentile]

ESSL/ACD/GTP Two-day Seminar

A Molecular View of Vorticity & Turbulence

Dr. Adrian Tuck, NOAA
***November 28 AND  29, 2007 ***
1:30 – 4:30 p.m.
(Coffee break from 2:30-3:00)
Room 1001, Foothills Lab 2

Abstract

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.

To view a Powerpoint presentation of this lecture visit: 
http://www.image.ucar.edu/public/Seminars/Tuck07.html