Energy exchange in a stably stratified flow with laterally distorting duct

Abstract

The long-time evolution of the grid-generated turbulence in a stably stratified air flow is investigated using a duct that has both a vertical contraction and a lateral expansion. Through this duct a Brunt–Väisälä frequency N increases, while a constant mean velocity U is maintained, so that a nondimensional buoyancy time (Nt/2π≈1.3) longer than any other previous wind tunnel experiments is obtained. Two complete cycles of the normalized vertical buoyancy flux −wθ¯/w′θ′ oscillation have been observed for the first time experimentally. The present experiments show that the period of the vertical buoyancy flux oscillation is independent of the initial conditions, Prandtl number, Froude number, and Reynolds number, showing that it is determined by the linear processes as described by rapid distortion theory. Initial anisotropy produced by the distorting duct also does not change this period. At a stratification with N⩽2.5 s−1, we found that the oscillation of the vertical buoyancy flux with the higher Reynolds number and the Froude number decays faster, which may be explained by the nonlinear effect. Combination of the strongest stratification (N=3.0 s−1) with the smallest mesh size (M=2.54 cm) gave an internal wave behavior which could be identified by the phase spectra of Phwθ≈90° and by the vertical buoyancy flux of −wθ¯≈0. The ratio of potential energy to vertical kinetic energy becomes about 0.8 at the most downstream measuring point. The effect of mean strain on the stratified turbulence is investigated by comparing the present experiment for laterally distorted flow with the previous experiments for the nondistorted or longitudinally distorted flow. Strong countergradient flux is observed in both the laterally and longitudinally distorted flows. We found that the maximum value of the ratio of potential energy to vertical kinetic energy of the distorted flow becomes three times as large as that of the nondistorted flow. The spectral analysis shows that this large ratio has a significant effect on the strong countergradient flux in the distorted flow.