Explict-scales projections of the partitioned non-linear term in direct numerical simulation of the Navier-Stokes equation

In this paper we consider the properties of the internal partitions of the nonlinear term, obtained when a filter with a sharp cutoff is introduced in wavenumber space. We see what appears to be some degree of independence of the choice of the position of the cutoff wavenumber for both instantaneous and time-integrated partitioned nonlinearities. We also investigate the basic idea of an eddy-viscosity model for subgrid terms and have found that while phase modelling will be very poor, amplitude modelling can be far more successful.