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On the Theory of Turbulence in the Buoyancy Subrange of Stably Stratified Flows

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  • 1 Aeronomy Laboratory, NOAA, Boulder, Colo. 80302
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Abstract

A theoretical investigation is made of turbulence in the buoyancy subrange of stably stratified sheer flows. This theory is based on a new calculation of the buoyancy flux spectrum B (k). In the Lumley-Shur theory, it was assumed that B (k) had a universal form which could be determined by a simple dimensional consideration. That assumption is shown to be incorrect. One new result of the present calculation is that B (k) has a fairly sharp transition at a wavenumber kB = 0.8½ωB/vm, where ωB is the Brunt-Väisälä frequency and vm the root-mean-square velocity in the equilibrium range. Physically, this transition is “interpreted” as an emission of incoherent gravity waves fed by the kinetic energy of vertically fluctuating air particles. When k < kB, the emitted gravity waves are undamped and absorb a good part of an air particle's energy. When, however, k > kB, the gravity waves are strongly damped and consequently contain very little energy. The transition of the energy spectrum E(k) at kB is found usually to be gradual. It is also found that the power law governing E (k) in the buoyancy subrange is not universal. It depends on the flux Richardson number Rf and upon the rms velocity, and is quite variable. Such variability seems to conform with several observations of E(k) made in the stratosphere and upper troposphere. Present theory is compared with a previous theory and with observations in the atmosphere.

Abstract

A theoretical investigation is made of turbulence in the buoyancy subrange of stably stratified sheer flows. This theory is based on a new calculation of the buoyancy flux spectrum B (k). In the Lumley-Shur theory, it was assumed that B (k) had a universal form which could be determined by a simple dimensional consideration. That assumption is shown to be incorrect. One new result of the present calculation is that B (k) has a fairly sharp transition at a wavenumber kB = 0.8½ωB/vm, where ωB is the Brunt-Väisälä frequency and vm the root-mean-square velocity in the equilibrium range. Physically, this transition is “interpreted” as an emission of incoherent gravity waves fed by the kinetic energy of vertically fluctuating air particles. When k < kB, the emitted gravity waves are undamped and absorb a good part of an air particle's energy. When, however, k > kB, the gravity waves are strongly damped and consequently contain very little energy. The transition of the energy spectrum E(k) at kB is found usually to be gradual. It is also found that the power law governing E (k) in the buoyancy subrange is not universal. It depends on the flux Richardson number Rf and upon the rms velocity, and is quite variable. Such variability seems to conform with several observations of E(k) made in the stratosphere and upper troposphere. Present theory is compared with a previous theory and with observations in the atmosphere.

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