On the Influence of Large Scale Forcing and Flow Topology on the Dynamics of Small-Scale Turbulent Transport

Turbulence and turbulent mixing play a key role in a wide range of engineering and scientific applications. One of the major difficulties when simulating these phenomena comes from their multi-scale nature. The range of scales that can be explicitly simulated is still too limited, even with current supercomputers, to study accurately most geophysical or engineering flows. A solution is to model the small scales in order to reduce the computational cost. Unfortunately, current models are of variable accuracy, in particular due to many constraining and sometimes empirical hypotheses. In order to improve the models used in turbulence simulations, and, more generally, to progress in our understanding of turbulence and turbulent mixing, it is crucial to study the behavior of the small-scale motions of turbulent flows. Rather than a traditional statistical approach, a physics-based description of the dynamics of the flow at these scales can lead to a better appreciation of the role of the small-scale motions in turbulence as well as drastically improve their prediction, particularly in regions of strong and fast variations that, currently, most models fail to capture. First, the relation between external forcing and the dissipation rate of turbulent kinetic energy has been studied. Theory represents the energetic equilibrium of turbulence as a cascade of energy from the larger scales to the smaller ones at a constant dissipation rate. A number of turbulence models rely on some sort of prediction of this dissipation rate, mostly based on (semi-)empirical considerations. Analyses of the Navier-Stokes equations show that for a given forcing on the flow, the dissipation rate could be precisely estimated at high enough Reynolds number. The case of a forcing on two low wavenumbers is presented in this dissertation. The low Reynolds number simulations were made for forces of increasing amplitude on the highest of the two wavenumbers. The results confirm the existence of a regime for which the dissipation rate could be precisely estimated and show a dependence on the dominant wavenumber, predicted by the analytical derivations. Second, the small-scale dynamics of a concentration of passive tracers, or passive scalars, is investigated. When advected by a turbulent flow, the passive scalar field for which the scalar diffusivity is smaller than the kinematic viscosity can create scales even smaller than those of the flow itself. The small-scale dynamics is analyzed with regards to the local topology of the flow, which is determined by the second and third invariant of the velocity gradient tensor. The phase-plane defined by these invariants allows an identification of the streamline patterns in the neighborhood of the location where they are computed. Probability density functions and conditioned statistics based on the local flow structure show that large scalar dissipation occurs in biaxial extensional regions located near vortices. Large scalar dissipation fluctuations pose a great challenge for traditional numerical simulations. Their scales, which could be several orders of magnitude smaller than the smallest velocity scales, may cause numerical errors that can significantly affect the accuracy of the solution. The study presented in this dissertation establishes the foundation for a new modeling strategy based on the flow topology and the combination of Eulerian and Lagrangian transport method.