The ultimate state of elastic turbulence

Abstract

The asymptotic properties, with vanishing viscosity, of inertial turbulence in Newtonian fluids have been of intense scrutiny over the years. Much less is known about elastic turbulence - a distinct spatio-temporally chaotic state exhibited by viscoelastic fluids. In this work, using direct numerical simulations of turbulence in a triperiodic box, we show that elastic turbulence achieves an ultimate state with increasing polymer relaxation time, i.e., the Deborah number, for two different constitutive models (Oldroyd-B and FENE-P). In the limiting state, various bulk quantities - the fluid dissipation, the polymeric energy transfer, as well as the elastic stresses - are shown to become independent of the polymer relaxation time scale, notwithstanding the microstructure deformation scales distinctly depending on the model.