Stochastic modelling of turbulent flows for numerical simulations

Numerical simulations are a powerful tool to investigate turbulent flows, both for theoretical studies and practical applications. The reliability of a simulation is mainly dependent on the turbulence model adopted, and improving its accuracy is a crucial issue. In this study, we investigated the potential for an alternative formulation of the Navier-Stokes equations, based on the stochastic representation of the velocity field. The new approach, named pseudo-stochastic simulation (PSS), is a generalisation of the widespread classical eddy-viscosity model, where the contribution of the unresolved scales of motion is expressed by a variance tensor, modelled following different paradigms. The PSS models were compared with the classical ones mathematically and numerically in the turbulent channel flow at Reτ = 590. The PSS and the classical models are equivalent when the variance tensor is shaped through a molecular dissipation analogy, while it is more accurate when the tensor is defined by the way of a local variance model. A near-wall damping function derived from recent advancement in the field is also proposed and was successfully validated. The analyses demonstrate the relevance of the approach proposed and provide a basis for the development of an alternative turbulence model.