Symmetry-preserving regularization of turbulent channel flow

We propose to regularize the convective term in the Navier-Stokes equations in such a manner that the symmetries that correspond to the invariance of the energy, the enstrophy (in 2D) and helicity are preserved. The underlying idea is to restrain the convective production of smaller and smaller scales of motion by means of vortex stretching in an unconditional stable manner, meaning that the solution can not blow up (in the energy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry properties too. The simulation shortcut is successfully tested for a turbulent channel flow (Re-tau = 180).