Abstract
Equations for layer-integrated energy and Richardson number tendencies are formulated in isentropic co-ordinates. This formulation leads to the Roach equation for the rate of energy dissipation due to clear air turbulence (CAT). The equation governing the ln(Ri) tendency is applied diagnostically to grids from an objective isentropic analysis of archived soundings for a well documented field study of CAT. The Richardson number tendency equation is cast in prognostic form. Using a semi-language advection scheme, it is applied as a mechanistic model to examine the evolution of the Richardson number fields over 12-hour time periods for several cases. These include the field study and two much more recent cases supported by pilot reports.
Heuristic arguments show that the Roach equation for the turbulent dissipation rate should be more restricted in its application than originally presented. Analyses of meso-alpha scale Richardson number and Richardson number tendency fields reveal a phase relationship which is consistent with that expected theoretically based on dynamic coupling. Model experiments are presented which support these subjective interpretations. Consistent with the Roach equation for the turbulent energy dissipation rate, CAT is often encountered when air characterized by relatively small Richardson numbers propagates into areas of significant nonturbulent scale deformation forcing.
