On the isotropy of temperature fluctuations in passive scalar turbulence

We use direct numerical simulation to investigate the scalar gradient skewness downstream of a square grid element. The passive scalar is generated by applying a constant heat flux on the grid element. We primarily focus on the far-downstream grid-element centerline, where the scalar turbulence is homogeneous, and there are no mean velocity or scalar gradients. In this region, some discrepancy exists in the literature concerning the isotropy of the scalar. To the best of our knowledge, this is the first study that measures scalar gradients in all three directions. We detect nonzero skewness for the lateral scalar gradients, while in the streamwise direction, the skewness is zero. We show, through statistical analysis, that the nonzero values are solely due to steep gradients called cliffs. The cliffs originate from the bars of the grid-element that generate sharp mean scalar gradients along the lateral directions in the near wake. These mean gradients decay as the flow develops downstream, but the convected cliffs remember the generating upstream conditions and, in particular, the direction of the mean scalar gradient. Due to this memory effect, the cliffs align preferentially along a specific direction despite the absence of a local mean scalar gradient, thus making the homogeneous scalar field anisotropic. We also report some hitherto undocumented properties of cliffs and ramps through conditional statistical analysis. Finally, we corroborate our conclusions with two additional simulations, one involving grid-element turbulence in the presence of a transverse mean scalar gradient and the other scalar turbulence due to a heated cylinder.