The Generation of Clear Air Turbulence by Nonlinear Waves

Abstract

The structure of the critical layer in a stratified shear flow is investigated for finite‐amplitude waves at high Reynolds numbers. Under such conditions, which are characteristic of the Clear Air Turbulence environment, nonlinear effects will dominate over diffusive effects. Nevertheless, it is shown that viscosity and heat‐conduction still play a significant role in the evolution of such waves. The reason is that buoyancy leads to the formation of thin diffusive shear layers within the critical layer. The local Richardson number is greatly reduced in these layers and they are, therefore, likely to break down into turbulence. A nonlinear mechanism is thus revealed for producing localized instabilities in flows that are stable on a linear basis. The analysis is developed for arbitrary values of the mean flow Richardson number and results are obtained numerically.

Momentum and buoyancy transfer in atmospheric turbulent boundary layer over wavy water surface – Part 2: Wind–wave spectra

“…This effect has already been discussed in Part 1. It is known that the resonant interaction of waves with stratified shear flows in the viscous and thermal-transfer media leads to the irreversible reduction of the density gradient in the region with closed streamlines -the critical layers (see, e.g., Maslowe, 1972;Haberman, 1973;Troitskaya, 1991) -which leads to a positive wave mass-flux τ ρwave (η) in Eq. (29) and to a reduction of the average density gradient.…”

Turbulent Layers Associated with a Critical Level in the Planetary Boundary Layer

“…Thus the unstable regions would be filled with small scale turbulence. Maslowe (1972) proposed that the unstable regions are originated from the viscous effect associated with strong shear formed around Cat's eyes. However, such layers are too thick to be affected by kinematic viscosity in the actual atmosphere.…”

Momentum and buoyancy transfer in atmospheric turbulent boundary layer over wavy water surface – Part 1: Harmonic wave

“…The point is that the resonant interaction of waves with stratified shear flows in the presence of eddy viscosity and conductivity leads to irreversible reduction of the density gradient in the critical layers, i.e. regions with closed streamlines (see, e.g., Maslowe, 1972;Haberman, 1973;Troitskaya, 1991), which leads to the positive wave mass flux P wave (η) in Eq. (6).…”

“…The decrease in the mass flux depends on the eddy conductivity K ρ ; while K ρ tends to zero, the density gradient in the critical layer also tends to zero. This effect is the main subject of the Maslowe (1972) theorem, which is an analog of the Batchelor (1956) theorem on the constant vorticity in a region with closed streamlines. In its turn, reducing the mean density gradient associated with this effect leads to reducing the density difference between the sea surface and reference level.…”