How much Navier-Stokes dynamics is needed to represent turbulent mixing?*

Turbulent mixing plays a key role in many natural and engineering systems and is typically studied as passive scalars advected by a turbulent velocity field. Phenomenology posits, and previous research shows, some degree of universality in mixing regardless of the details of flow geometry or stirring mechanism. However, some quantities characterizing scalar mixing are known to depend on the details of the advecting velocity. Naturally, a question arises on the sensitivity of mixing characteristics  to the velocity field.

We explore this question in the context of the recently proposed Selected Eddy Simulations (SES). SES velocity fields are obtained from solving Navier-Stokes (NS) in a random subset of modes and evolving the complementary set with trivial dynamics. This enables us to determine the amount of NS dynamics required in the velocity field to accurately capture the physics of turbulent mixing. 

By comparing SES simulations with DNS, we find that most of the mixing  is captured with just 10%-30% of the velocity modes depending on the statistics of interest. The results also show that SES is a suitable alternative tool for studying mixing at high R_λ. We also find that adding more NS dynamics at larger and intermediate scales leads to better results, indicating the importance of these scales to mixing. Trends with Reynolds and Schmidt numbers are also discussed.