Abstract :
[en] Turbulence is a fluid flow regime observed in a large number of natural and engineering systems involving liquids or gases in motion. When the fluid viscosity is not able to overcome the flow inertia, a random chaotic motion characterized by a wide range of spatial and temporal scales takes place. In many cases, turbulent fluid flows interact with auxiliary physical phenomena such as chemical reactions or electromagnetic fields, to name but a few, resulting in substantial changes in their driving mechanisms. When the auxiliary physics relies on weakly diffusive quantities, the limited effect of diffusion at the Kolmogorov scale, where the smallest turbulent vortices dissipate, can potentially lead to the formation of even smaller structures. Batchelor's theory and subsequent investigations have proved that, in the case of passively advected quantities, structures smaller than the Kolmogorov scale develop in turbulent flow when the Schmidt number is sufficiently large. However, it remains unclear whether generic quantities behave similarly in multi-physics systems, where they play an active role.
In the present work, direct numerical simulations of multi-physics systems involving weakly diffusive quantities are performed to study the interactions between the smallest scales of generic quantities and the mechanisms driving classical (uncoupled) turbulence. In particular, mixed convection flows and viscoelastic turbulence (dilute polymer solutions) are simulated in a periodic channel domain to determine the role of the small temperature or elastic scales in the turbulence production mechanism and their impact on the redistribution of turbulent kinetic energy over the different scales.
The results of the present study show that the role of the smallest scales of generic quantities in the flow dynamics strongly depends on the system considered. In mixed convection flows, the majority of the multi-physics interactions occur at relatively large scales and decreasing the thermal diffusivity tends to limit the influence of thermal convection on the pressure-driven dynamics. In contrast, reducing polymer diffusion in viscoelastic turbulent flows allows thin polymer sheets characterized by very small scales to develop and contribute more actively to the polymer-turbulence interaction mechanism, resulting in a larger amount of turbulence produced in the flow. Although the two systems of interest are driven by multi-physics interactions of different nature, comparing their spectral distributions also reveals that turbulent vortices smaller than the Kolmogorov scale cannot form in any of the two flows and that the size of the smallest temperature/elastic scale is in rather good agreement with the one predicted by Batchelor's theory for the case of passively advected quantities. These findings suggest that simulating viscoelastic turbulence using RANS or LES approaches would most likely require tailored closure models that take into account the production of turbulence resulting from the interaction between the small elastic scales and the flow inertia.
