The dynamical parameters of turbulence theory as they apply to middle atmosphere studies

Abstract

The study of turbulent heating and diffusion in the middle atmosphere is complicated by some subtle points relating to the application of existing theory. Incorrect interpretation of turbulent spectra can result, leading to errors in estimates of the strengths of turbulence by factors of 5 and more. In this short review, the relevant turbulent spectra and equations are considered, and their applications in middle atmosphere studies are outlined. New developments with regard to some of this theory, and especially new understandings about the dynamical parameters used in some of these applications (often referred to as the "constants" of the equations) are described. Current areas of uncertainty are also considered, both in relation to turbulent energy dissipation as well as diffusion over various scales.

Characterization and Parametrization of Reynolds Stress and Turbulent Heat Flux in the Stably-Stratified Lower Arctic Troposphere Using Aircraft Measurements

“…For example, Cho et al (2003) and Dehghan et al (2014) analyze aircraft measurements of turbulence using structure functions to derive dissipation rates ( ) in clear-air turbulence, and Inoue et al (2005) measured the heat flux over sea-ice using aircraft observations. However, these statistics do not reliably estimate turbulent diffusion coefficients (K m , K h ), which are relevant to turbulent flux parametrizations in the atmosphere (Hocking 1999). In addition, turbulence measurements using instrumentation on aircraft under stable conditions pose many difficulties due to weak turbulence and non-stationary or heterogeneous conditions.…”

“…Figure 10 shows the absolute value of the cospectrum of the heat flux for n = 920 spectra on a logarithmic scale and the cospectrum of the heat flux separated into the boundary layer (n = 74) and the free troposphere (n = 846) on a logarithmic-inear scale. The absolute value is used in the logarithmic scale to consolidate all spectra on the same plot in order to observe the regimes associated with the buoyancy flux and the Kolmogorov inertial subrange (Hocking 1999;Pope 2000;Stull 2003;Lovejoy et al 2007). The cospectrum at small scale (inertial subrange) occurs at approximately κ > 0.01 m −1 , while the cospectrum at large scale (buoyancy range) occurs at approximately κ < 0.01 m −1 .…”

“…4.5 a sensitivity analysis is also performed and reported to show the effect of varying f c from 0.0125 to 0.2 Hz. Turbulent dissipation rate ( ) for each leg is calculated using structure functions based on the methodology of Hocking (1999) and Dehghan et al (2014). Spectral analysis is performed for the heat flux using fast Fourier transform (FFT) (Stull 2003).…”

The structure of turbulence in the middle and lower atmosphere seen by and deduced from MF, HF and VHF radar, with special emphasis on small-scale features and anisotropy

“…Thus, the rate of vertical diffusion over scales deeper than the typical layer depths depends on factors including the depth of the layers, and the frequency of occurrence of the layers, (as well as the strength of turbulence within the layers). More details about this process can be found in Dewan (1981), Woodman and Rastogi (1984), and Hocking (1991Hocking ( , 1999, among others. This understanding of turbulent diffusion has been developed, in part, due to the contributions of radar observations which offer one of the best tools to implement calculations of diffusion in this manner, as described by Woodman and Rastogi (1984).…”

“…for reviews of these methods, which involve both absolute power measurements and spectral-width determinations, see Hocking and Mu, 1997;Hocking, 1999). Radars can also be used to parameterize the processes of diffusion in the atmosphere.…”