Eddy diffusion coefficients and their upper limits based on application of the similarity theory

Abstract

Abstract. The equation for the diffusion velocity in the mesosphere and the lower thermosphere (MLT) includes the terms for molecular and eddy diffusion. These terms are very similar. For the first time, we show that, by using the similarity theory, the same formula can be obtained for the eddy diffusion coefficient as the commonly used formula derived by Weinstock (1981). The latter was obtained by taking, as a basis, the integral function for diffusion derived by Taylor (1921) and the three-dimensional Kolmogorov kinetic energy spectrum. The exact identity of both formulas means that the eddy diffusion and heat transport coefficients used in the equations, both for diffusion and thermal conductivity, must meet a criterion that restricts the outer eddy scale to being much less than the scale height of the atmosphere. This requirement is the same as the requirement that the free path of molecules must be much smaller than the scale height of the atmosphere. A further result of this criterion is that the eddy diffusion coefficients K ed , inferred from measurements of energy dissipation rates, cannot exceed the maximum value of 3.2 × 10 6 cm 2 s −1 for the maximum value of the energy dissipation rate of 2 W kg −1 measured in the mesosphere and the lower thermosphere (MLT). This means that eddy diffusion coefficients larger than the maximum value correspond to eddies with outer scales so large that it is impossible to use these coefficients in eddy diffusion and eddy heat transport equations. The application of this criterion to the different experimental data shows that some reported eddy diffusion coefficients do not meet this criterion. For example, the large values of these coefficients (1 × 10 7 cm 2 s −1 ) estimated in the Turbulent Oxygen Mixing Experiment (TOMEX) do not correspond to this criterion. The K ed values inferred at high latitudes by Lübken (1997) meet this criterion for summer and winter polar data, but the K ed values for summer at low latitudes are larger than the K ed maximum value corresponding to the criterion. Analysis of the experimental data on meteor train observations shows that energy dissipation with a small rate of about 0.2 W kg −1 sometimes can induce turbulence with eddy scales very close to the scale height of the atmosphere. Our results also explain the discrepancy between the large cooling rates calculated by Vlasov and Kelley (2014) and the temperatures given by the MSIS-E-90 model because, in these cases, the measured eddy diffusion coefficients used in calculating the cooling rates are larger than the maximum value presented above.

Hough Mode Extensions (HMEs) and Solar Tide Behavior in the Dissipative Thermosphere

“…However, controversy and uncertainty still surround the choice of eddy diffusivity (hereafter K eddy ). In the HME calculations, a single K eddy profile with peak near 200 m 2 s −1 is assumed, a magnitude consistent with the arguments put forth in Forbes (1982), Lindzen and Forbes (1983), and more recent estimates based on similarity theory and measurements of energy dissipation rates (Vlasov & Kelley, 2015). A turbulent Prandtl number of unity is assumed, meaning that the values of momentum eddy diffusivity and heat transfer eddy diffusivity are equal.…”

First Na lidar measurements of turbulence heat flux, thermal diffusivity, and energy dissipation rate in the mesopause region

“…Currently, numerous ground‐based and in situ observational techniques estimate k z z indirectly from measuring the energy dissipation rate ( ϵ ) with uncertainties remain in estimating ϵ and determining the dependence of k z z on ϵ . These uncertainties can affect the measurements of k z z by 2–3 orders of magnitude [ Vlasov and Kelley , , ]. Also, the discrepancies between these observational coefficients and coefficients used in general circulation models suggest the necessity for a more effective way to determine k z z .…”

The Three Regimes of Atmospheric Evaporation for Super-Earths and Sub-Neptunes

“…The ratio approaches 1 at higher magma ocean temperatures and then becomes 0 when the system transitions into regime two. Kirchhoff & Clemesha 1983;Lübken 1997;Vlasov & Kelley 2015). Because horizontal convection also contributes to mixing on hot exoplanets, it is uncertain whether a reversal will occur, so we adopt the eddy diffusion relation proposed by Charnay et al (2015),…”