the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Dependence of the critical Richardson number on the temperature gradient in the mesosphere
Michael N. Vlasov
Michael C. Kelley
Abstract. Maximum upper atmospheric turbulence results in the mesosphere from convective and/or dynamic instabilities induced by gravity waves. For the first time, by comparing the vertical accelerations induced by wind shear and the buoyancy force, it is shown that the critical Richardson number Ric can be estimated. Dynamic instability is developed for Ri < Ric. This new approach, for the first time, makes it is possible to establish and estimate the temperature gradient impact on dynamic instability development. Regarding our results, Ric increases from 0.25 to 0.38 as the negative temperature vertical gradient increases from ∂T/∂z = 0 to ∂T/∂z ≤ −9 K/km. However, Ric for the temperature, independent of altitude, is 0.25, coinciding exactly with the Ric commonly used and estimated in classical studies (Miles, 1961; Howard, 1961) and subsequent papers without the temperature impact. The increase in the Ric value strongly influences cooling, inducing the cooling rate increase. Also, our results show that criterion Ric < 0.25 can only be used for the turbulent diffusion, which is characterized by eddies with sizes much smaller than the scale height of the atmosphere. The Ric value increases with the increasing size of the eddies, but the term eddy diffusion
cannot be applied to transport due to the large-scale eddies (Vlasov and Kelley, 2015).
Michael N. Vlasov and Michael C. Kelley


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RC1: 'questionable contribution to science', Anonymous Referee #1, 21 Sep 2018
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AC1: 'Response to the Comments of Reviewer 1', Michael Vlasov, 01 Nov 2018
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AC1: 'Response to the Comments of Reviewer 1', Michael Vlasov, 01 Nov 2018
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RC2: 'Review of the paper " Dependence of the critical Richardson number on the temperature gradient in the mesosphere"', Anonymous Referee #2, 20 Nov 2018
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AC2: 'Author Response to Reviewer 2', Michael Vlasov, 18 Dec 2018
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AC2: 'Author Response to Reviewer 2', Michael Vlasov, 18 Dec 2018


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RC1: 'questionable contribution to science', Anonymous Referee #1, 21 Sep 2018
-
AC1: 'Response to the Comments of Reviewer 1', Michael Vlasov, 01 Nov 2018
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AC1: 'Response to the Comments of Reviewer 1', Michael Vlasov, 01 Nov 2018
-
RC2: 'Review of the paper " Dependence of the critical Richardson number on the temperature gradient in the mesosphere"', Anonymous Referee #2, 20 Nov 2018
-
AC2: 'Author Response to Reviewer 2', Michael Vlasov, 18 Dec 2018
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AC2: 'Author Response to Reviewer 2', Michael Vlasov, 18 Dec 2018
Michael N. Vlasov and Michael C. Kelley
Michael N. Vlasov and Michael C. Kelley
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