Velocity and temperature derivatives in high- Reynolds-number turbulent flows in the atmospheric surface layer. Part 3. Temperature and joint statistics of temperature and velocity derivatives

This is part 3 of our work describing experiments in which explicit information was obtained on all the derivatives, i.e. spatial derivatives, ∂/∂x_j, and temporal derivatives, ∂/∂t, of velocity and temperature fields (and all the components of velocity fluctuations and temperature) at the Reynolds number Re_λ ∼ 10⁴. This part is devoted to the issues concerning temperature with the emphasis on joint statistics of temperature and velocity derivatives, based on preliminary results from a jet facility and the main results from a field experiment. Apart from a number of conventional results, these contain a variety of results concerning production of temperature gradients, such as role of vorticity and strain, eigen-contributions, geometrical statistics such as alignments of the temperature gradient and the eigenframe of the rate-of-strain tensor, tilting of the temperature gradient, comparison of the true production of the temperature gradient with its surrogate. Among the specific results of importance is the essential difference in the behaviour of the production of temperature gradients in regions dominated by vorticity and strain. Namely, the production of temperature gradients is much more intensive in regions dominated by strain, whereas production of temperature gradients is practically independent of the magnitude of vorticity. In contrast, vorticity and strain are contributing equally to the tilting of the vector of temperature gradients. The production of temperature gradients is mainly due to the fluctuative strain, the terms associated with mean fields are unimportant. It was checked directly (by looking at corresponding eigen-contributions and alignments), that the production of the temperature gradients is due to predominant compressing of fluid elements rather than stretching, which is true of other processes in turbulent flows, e.g. turbulent energy production in shear flows. Though the production of the temperature gradient and its surrogate possess similar univariate PDFs (which indicates the tendency to isotropy in small scales by this particular criterion), their joint PDF is not close to a bisector. This means that the true production of the temperature gradient is far from being fully represented by its surrogate. The main technical achievement is demonstrating the possibility of obtaining experimentally joint statistics of velocity and temperature gradients.