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Hubert Luce, Lakshmi Kantha, Hiroyuki Hashiguchi, Abhiram Doddi, Dale Lawrence, and Masanori Yabuki

Abstract

Under stably stratified conditions, the dissipation rate ε of turbulence kinetic energy (TKE) is related to the structure function parameter for temperature CT2, through the buoyancy frequency and the so-called mixing efficiency. A similar relationship does not exist for convective turbulence. In this paper, we propose an analytical expression relating ε and CT2 in the convective boundary layer (CBL), by taking into account the effects of nonlocal heat transport under convective conditions using the Deardorff countergradient model. Measurements using unmanned aerial vehicles (UAVs) equipped with high-frequency response sensors to measure velocity and temperature fluctuations obtained during the two field campaigns conducted at Shigaraki MU observatory in June 2016 and 2017 are used to test this relationship between ε and CT2 in the CBL. The selection of CBL cases for analysis was aided by auxiliary measurements from additional sensors (mainly radars), and these are described. Comparison with earlier results in the literature suggests that the proposed relationship works, if the countergradient term γ D in the Deardorff model, which is proportional to the ratio of the variances of potential temperature θ and vertical velocity w, is evaluated from in situ (airplane and UAV) observational data, but fails if evaluated from large-eddy simulation (LES) results. This appears to be caused by the tendency of the variance of θ in the upper part of the CBL and at the bottom of the entrainment zone to be underestimated by LES relative to in situ measurements from UAVs and aircraft. We discuss this anomaly and explore reasons for it.

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Hiromasa Ueda, Tetsuo Fukui, Mizuo Kajino, Mitsuaki Horiguchi, Hiroyuki Hashiguchi, and Shoichiro Fukao

Abstract

Recently, middle- and upper-atmosphere Doppler radar (MU radar) has enabled the measurement of middle-atmosphere turbulence from radar backscatter Doppler spectra. In this work, eddy diffusivities for momentum Km in the upper troposphere and lower stratosphere during clear-air conditions were derived from direct measurements of the Reynolds stress and vertical gradient of mean wind velocity measured by MU radar. Eddy diffusivity for heat Kh below 8 km was determined from measurements of temperature fluctuations by the Radio Acoustic Sounding System (RASS) attached to the MU radar. The eddy diffusivity for momentum was on the order of 10 m2 s−1 in the upper troposphere and decreased gradually in the stratosphere by an order of magnitude or more. The eddy diffusivity for heat was almost of the same order of magnitude as Km.

Estimates of eddy diffusivity from the radar echo power spectral width give fairly good values compared with the direct measurement of Km. Applicability of three turbulence models—the spectral width method, the k–ε model modified for stratified flows, and the algebraic stress model—were also examined, using radar observation values of turbulent kinetic energy k and turbulent energy dissipation rate ε together with atmospheric stability observations from rawinsonde data. It is concluded that the algebraic stress model shows the best fit with the direct measurement of Km, even in the free atmosphere above the atmospheric boundary layer once k and ε values are obtained from observations or a model.

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