On the concentration distribution in turbulent thermals

The preprint operates within the dominant paradigm of turbulent thermal theory, specifically focusing on the established understanding of entrainment, self-similarity, and the influence of Reynolds and Péclet numbers.

This preprint investigates the concentration distribution within turbulent thermals, a topic that has not been systematically explored before. While the study confirms existing theoretical predictions regarding the moments of concentration and observes self-similar behavior in the concentration distributions (normalized by the mean), it also presents some nuanced findings that do not fully align with previous interpretations of self-similarity in thermals. Notably, the study suggests the cores of the thermals may not adhere to the same self-similar evolution as the overall thermal, possibly due to the slower decrease in maximum concentration. Furthermore, the study reveals a surprising insensitivity of the concentration distribution to variations in Schmidt number over a large range. These observations remain within the existing paradigm of turbulent thermal theory but raise questions about the precise nature of self-similarity and the role of diffusivity, motivating further investigations within this paradigm. This work can therefore be classified as "normal science," where research is conducted within the framework of the established paradigm.