New scaling laws of passive scalar with a constant mean gradient in decaying isotropic turbulence. (25th September 2020)

• Record Type: Journal Article
• Authors: Sadeghi, Hamed; Oberlack, Martin
• Is Part Of: Journal of fluid mechanics. Volume 899(2020)
• Publication Date: 2020-09-25
• Subjects: turbulence theory, -- isotropic turbulence; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2020.413
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : Abstract : We use the Lie symmetry theory to derive new scaling laws for passive scalar dynamics under the influence of a constant mean gradient of the scalar in decaying homogeneous isotropic turbulence. For this purpose, we apply symmetry analysis to the equations for two-point correlation of the scalar and velocity fluctuations. It is shown that, in contrast to the classical self-similarity approach, the general invariant solutions, respectively scaling laws, of the two-point functions are constructed using the symmetry approach, without requiring an a priori set of similarity scales to carry on the analysis. In the context of the current analysis also, scaling laws for one-point quantities of the scalar variance $\overline{\unicode[STIX]{x1D703}^{2}}$, the transverse scalar flux $\overline{u_{2}\unicode[STIX]{x1D703}}$ and the variance of the turbulent velocity fluctuations $\overline{u^{2}}$ are established, which are essentially related to the scaling symmetries. A key step to derive the scaling laws is the symmetry breaking induced by the constant mean scalar gradient. We use the results of a highly resolved direct numerical simulation of Gauding et al. ( Comput. Fluids, vol. 180, 2019, pp. 206–217) to verify the scaling laws and the self-similarity of the two-point correlation functions. It is shown that the general symmetry solutions obtained from symmetry results provide a very good similarity to these functions.