Dependence of the critical Richardson number on the temperature gradient in the mesosphere

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 Ri_c can be estimated. Dynamic instability is developed for Ri < Ri_c. 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, Ri_c 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, Ri_c for the temperature, independent of altitude, is 0.25, coinciding exactly with the Ri_c commonly used and estimated in classical studies (Miles, 1961; Howard, 1961) and subsequent papers without the temperature impact. The increase in the Ri_c value strongly influences cooling, inducing the cooling rate increase. Also, our results show that criterion Ri_c < 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 Ri_c 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).