On restraining the production of small scales of motion in a turbulent channel flow

Since most turbulent flows cannot be computed directly from the incompressible Navier-Stokes equations, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider nonlinear approximations of the convective term that preserve the symmetry and conservation properties. In particularly, the energy, enstrophy (in 2D) and helicity are conserved. The underlying idea is to restrain the convective production of small scales in an unconditional stable manner, meaning that the approximate solution cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. The resulting simulation method is successfully tested for a turbulent channel flow (Re_τ = 180 and 395).