# Statistical and Geometrical Properties of Turbulent Flows with Viscosity Stratification

**Principal Investigator:** Michael Gauding, Université de Rouen, Rouen (France)

**HPC Platform:** JUQUEEN of JSC

*Viscosity represents the most important property of turbulent flows, and the impact of its variation on the dynamics of turbulence is not yet fully understood. The principal question addressed by the present project is how the dissipation mechanism and self-similarity of turbulent flows is affected by fluctuations of the viscosity. A better understanding of these questions leads to a better modelling of turbulent mixing and, for example, an improved prediction of the pollutant formation in combustion engines. Turbulent flows reveal a tremendous number of degrees of freedom, which makes numerical simulations very challenging. In this project we performed highly resolved direct numerical simulations of turbulent shear flows on the supercomputer JUQUEEN with up to 231 billion grid points.*

Copyright: CNRS UMR 6614 CORIA and JSC

The turbulent motion of fluid flows is a complex, strongly non-linear, multi-scale phenomenon, which poses some of the most difficult and fundamental problems in classical physics. Real turbulent flows encountered in engineering and environmental applications are very often characterized by a spatial or temporal variation of its thermo-physical properties, like viscosity or density. A prominent example from geophysical flows is the convection in the earth's mantle, where the viscosity and density decreases with temperature. An other important case is the turbulent mixing in combustion systems, where a concentration dependent viscosity may affect the efficiency of turbulent mixing. A better understanding of these phenomena leads to a better modelling of turbulent mixing and, for example, an improved prediction of the pollutant formation in combustion engines.

Viscosity represents the most important property of turbulent flows, and the impact of its variation on the dynamics should be addressed in detail. According to Kolmogorov's first hypothesis, the smallest scales of turbulent flows should reveal universal properties, and should depend only on two parameters, namely the viscosity and the mean energy dissipation rate. However, the dissipation is a highly fluctuating quantity with large but rare excursions from its mean value. In the literature this phenomenon is called internal intermittency. The physical mechanism behind internal intermittency is still unresolved, and it is not known whether viscosity gradients enhance or reduce internal intermittency. Figure 1 shows the field of the scalar dissipation which is characterized by very fine filamented structures.

Copyright: CNRS UMR 6614 CORIA and JSC

The principal question that is addressed by the present project is the self-similarity of turbulent flows with variable viscosity. The concept of self-similarity has played an important role in shaping the understanding of turbulent flows. Several problems in turbulence have been approached by self-preservation or self-similarity hypotheses imposing restrictions on the dynamics of the flow. By a combination of theoretical techniques and highly resolved direct numerical simulations, the scientists found two new main results. Firstly, the self-preservation of a turbulent flow is broken by fluctuations of the viscosity, while secondly, the mean dissipation becomes independent of fluctuations of the viscosity (which confirms Taylor's postulate).

From a statistical analysis it was further shown that turbulent flows with variable viscosity are characterized by an enhanced level of small-scale intermittency, which results in the presence of smaller length scales and a modified turbulent mixing.

**References:**

M. Gauding, J. H. Goebbert, C. Hasse and N. Peters, Line Segments in Homogeneous Scalar Turbulence, Physics of Fluids 27, 9, 095102, 2015

J. H. Goebbert, M. Gauding, Direct Numerical Simulations of Fluid Turbulence at Extreme Scale with psOpen, Technical Report of the JUQUEEN Extreme Scaling Workshop, 2015

F. Hunger, M. Gauding, C. Hasse, On the impact of the turbulent/non-turbulent interface on differential diffusion in a turbulent jet flow. Journal of Fluid Mechanics, 10;802:R5, 2016

J. H. Goebbert, M. Gauding, C. Ansorge, B. Hentschel, T. Kuhlen, H. Pitsch, Direct Numerical Simulation of Fluid Turbulence at Extreme Scale with psOpen, Proceedings of the International Conference on Parallel Computing, 2016

N. Peters, J. Boschung, M. Gauding, J.H. Goebbert, R.J. Hill, H. Pitsch, Higher-order dissipation in the theory of homogeneous isotropic turbulence. Journal of Fluid Mechanics, 803:250-74, 2016

M. Gauding, L. Danaila, E. Varea, High-order structure functions for passive scalar with mean gradient, International Journal of Heat and Fluid Flow, 2017

M. Gauding, L. Danaila, E. Varea, Dissipative range statistics of turbulent flows with variable viscosity, Proceedings of the 10th International Symposium on Turbulence and Shear Flow Phenomena, 2017

**Scientific Contact**:

Michael Gauding

CNRS UMR 6614 - CORIA

Université de Rouen

Saint Etienne Du Rouvray, France

michael.gauding [at] coria.fr

Jens Henrik Goebbert

Institute for Advanced Simulation (IAS)

Jülich Supercomputing Centre (JSC)

Forschungszentrum Jülich, Germany

j.goebbert [at] fz-juelich.de

*May 2017*