Velocity and Passive Scalar Cross Spectra in Stably and Unstably Stratified Grid Turbulence

Abstract

The effects of stable and unstable thermal stratifications on the cross spectra between passive scalar (dye concentration) fluctuation c and vertical velocity fluctuation υ in shear-free grid turbulence are investigated using previously published data. The results show that cospectra in the neutral stratification have a slope close to -7/3, as predicted by Lumley (1964). The coherences of υ and c in the neutral stratification have a slope close to -4/3, which implies the absence of a phase shift between υ and c. In the weakly stable stratification, both the cospectrum and the coherence decay due to stable buoyancy force. In the moderately stable stratification, the scaling laws of the cospectrum and coherence collapse in the downstream region. However, in the strongly stable stratification, the negative cospectrum in the countergradient region reconstructs a small but distinct region close to -7/3 after the collapse. In the unstable stratification, despite strong convective motions due to the unstable buoyancy force, the cospectra and the coherences exhibit -7/3 and -4/3 power decay regions, respectively.