Exponential tails and skewness of density-gradient probability density functions in stably stratified turbulence

We have measured the probability density functions (PDFs) of density fluctuations and of density-gradient fluctuations in decaying stratified turbulence, using a thermally stratified wind tunnel. The turbulence was generated by passing the flow through a biplanar grid at the entrance to the test section. The linear mean vertical temperature gradient could be adjusted to produce different stratification strengths. The PDFs of the density-gradient fluctuations exhibit extended exponential tails, while those for the density fluctuations are nearly Gaussian. As the turbulence decays away from the grid the exponential tails of the density gradient PDFs become steeper and the central rounded part of the distribution widens. The tail steepness scales approximately as $Re \lambda{-\frac{1}{2}}$. Buoyancy forces are not the cause of the exponential tails, since when normalized in r.m.s. units the behaviour of the tails is independent of stratification strength. The vertical temperature gradients [partial partial differential]θ/[partial partial differential]z (measured using two cold wires) show a strong positive skewness close to the grid where the turbulence is most vigorous. This skewness is not caused by non-Boussinesq effects and is present for all stratification strengths. We propose a simple phenomenological model (similar to that of Budwig etal. 1985), based on stirring of fluid parcels advected in the mean gradient, to explain the presence of this skewness. The skewness observed by other researchers and their interpretations are discussed in the context of this model. The buoyancy flux PDF also shows strong exponential tails and is very strongly skewed. Both of these properties are consistent with joint-Gaussian statistics of the vertical velocity and temperature fluctuations.