Abstract

We investigate the effects of polymer additives on flows that display homogeneous, isotropic turbulence by extensive direct numerical simulations (DNS) of (a) a shell model and (b) the Navier-Stokes equation coupled to an equation for the polymer-conformation tensor (the FENE -P model). Our simulations show that the addition of polymers to such flows leads to dissipation reduction in both decaying and statistically steady turbulence; this dissipation reduction is the analogue of drag reduction in wall-bounded flows. Our numerical results agree well with recent experimental results. In particular, we find that polymers decrease the energy of the turbulent fluid at intermediate length scales but increase it at small length scales; a scale-dependent viscosity provides a natural means of understanding our results. Preliminary studies of the multiscaling of structure functions, in the presence of polymer additives, and shock-capturing schemes for this problem are also discussed.