A Theory of Gaps in the Turbulence Spectra of Stably Stratified Shear Flows

Abstract

A gap and adjacent bump is predicted to occur in the velocity spectrum of stratified shear flows when the flux Richardson number Rf, ?1/2. This prediction is based on a straightforward solution of the spectral energy balance equation with the assumption that the turbulence is locally inertial and nearly stationary. The limitations of the locally inertial assumption are examined critically. The gap occurs at Spectral wavelengths varying from 30 m to more than 1 km, depending on Rf, the turbulence intensity, and the Brunt-Väisälä frequency. In general, the gap occurs near a wavenumber where the spectral transfer function ?(k) vanishes. Both the gap and the zero of ?(k) are caused by shear and/or buoyancy production of energy. In addition, an alternative derivation of ?(k) is made from a more general consideration that avoids the locally inertial assumption. Both expressions predict that ?(k) will vanish at a value of k when Rf ?1/2. A comparison is made with the gaps and adjacent peaks frequently observed in the wind spectra of clear air turbulence (CAT).