Fundamentals and Scaling of Passive Scalar Fields in Isotropic Turbulence

Abstract

Turbulence is a compelling subject mainly due to its ubiquitous presence in natural and engineering phenomena. In this thesis, the focus is on temperature as a passive scalar in a turbulent velocity field with an imposed cross-stream mean temperature gradient is explored. The fundamentals of passive scalar dynamics mainly through various dimensional arguments, self-preserving solutions and a combination of numerical and experimental data are investigated.

A novel nano-scale sensor that minimizes measurements limitations of current sensors and enables more accurate and reliable data is presented. The conditions for self-similarity of the spectral equation are derived. Experimental and numerical data are used to validate and verify the conditions related the characteristic length scale of the flow, the spectrum of temperature variance and the co-spectrum of temperature and velocity. In particular, it is shown that self-preserving solutions exist for the temperature spectra. In addition,The new temperature sensor allows for data to be acquired in the dissipation range and therefore, self-similarity and scaling of the dissipation range is explored. The analysis reveals that the temperature field can be independently modeled using temperature variables only, as opposed to conventional models where knowledge of the velocity field is required.

In addition, it has been observed that the scalar PDF in the exponential tails as opposed to the velocity PDF. The exponential tails are more pronounced with the new temperature sensor compared to conventional measurement techniques. Therefore the phenomenon is investigated in this study and in particular following the linear eddy model of Kerstein. The analysis reveals more pronounced exponential tails as the low frequency content of the measured signal is excluded.

Lastly, the thesis highlights the exciting dynamics of scalar advection along with the phenomenological differences with the turbulent velocity field. Furthermore, the findings of this study show for the first time that the turbulent scalar field can be investigated by solely measuring scalar variables with no information about the underlying turbulent velocity field (in this case, temperature).The approach opens a new perspective for analyzing and understanding turbulent flows using scalar measurements that are inherently simpler to conduct.