The models under location uncertainty (henceforth referred to as stochastic models) recently introduced by Memin [1] provide a new outlook on LES modelling for turbulence studies. These models are derived from the stochastic conservation equations using stochastic calculus (see [1] for the derivation). The resulting conservation equations maintain a similarity with the filtered Navier Stokes equation wherein we observe a sub-grid scale dissipation term. However, in the stochastic version, an extra term appears, termed as “velocity bias”, which can be treated as a biasing/modification of the velocity by the small scales. This velocity bias was introduced first in stochastic models by [2] albeit artificially, however, in this approach it appears automatically through the stochastic derivation. All sub-grid contributions for the stochastic models are defined by the small scale velocity auto-correlation (a = (σσ)T) which can be modelled through a Smagorinsky equivalency (StSm) or by a local variance calculation (StSp). In this study, we have worked towards verifying the applicability and accuracy of these models in the well-studied case of flow over a cylinder. Flow over a cylinder at Re ~ 3900 provides a good case study for comparison of turbulence models. At this Re, the flow displays numerous important characteristics of turbulence flows that needs to be captured efficiently by the model. The shear layer instabilities and the length of the recirculation zone are all definitive aspects that affect flow statistics making this the ideal flow for model study. A comparison of the models indicates a statistical improvement in the stochastic models (StSm and StSp) compared with classic Smagorinsky (Smag) using [3] as reference. The flow reconstruction is also better with the stochastic models where the large scale and small scale vorticity are well represented.

REFERENCES

[1] Mémin E. Fluid flow dynamics under location uncertainty. Geophysical & Astrophysical Fluid Dynamics, 108, 119-146 2014.

[2] MacInnes, J. M. and Bracco, F. V. Stochastic particle dispersion modeling and the tracer-particle limit. Physics of Fluids A: Fluid Dynamics, 4(12):2809, 1992.


[3] Parnaudeau P, Carlier J, Heitz D and Lamballais E. Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900, Physics of Fluids (1994-present) 20, no. 8: 08510 2008.