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D. K. Lilly
,
D. E. Waco
, and
S. I. Adelfang

Abstract

Vertical diffusion coefficients in the stratosphere are estimated from data obtained in the High Altitude Clear Air Turbulence (HICAT) investigation. The HICAT data sample was obtained from 285 flights of over 800,000 km distance, containing 24,000 flight kilometers of turbulence between 14 and 21 km MSL, and is the only such collection of fine-scale, true gust velocities in the stratosphere.

One of the HICAT program objectives was to compute power spectral densities from each of the gust velocity component measurements over the wavelength range 30–15,000 m. The square roots of the integrals of these spectra for wavelengths <610 m, designated vi (for the ith component of velocity), were computed and related to the dissipation of kinetic energy, ε by use of the inertial range assumption in the form
υi 2ai ½k
Here k is the lower wavenumber limit of the spectral integration (2π/610 m), and ai is equal to 0.5 for the longitudinal component and 0.65 for the lateral and vertical components, or 1.8 for the total velocity vector. With the aid of an assumption on the flux Richardson number in turbulence, the eddy heat diffusivity Kπ is related to energy dissipation rate by Kπ=ε/(3N 2), where N is the Brunt-Väisälä frequency.

Our calculations indicate that small-scale diffusion coefficients vary from order 4×103 cm2 sec−1 over ocean regions to order 105 cm2 sec−1 over high mountains when averaged over periods of perceptible turbulence, which include from 2.0 to 5.2%, respectively, of the total flight distance. The values decrease rapidly above 17 km except over mountainous terrain, where mixing appears to be pronounced up to and above 19 km in winter. The overall mean value over North America and Greenland is 190 cm2 sec−1, and the global mean is 120 cm2 sec−1, with an uncertainty of about half an order of magnitude.

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