Spatiotemporal dynamics of viscoelastic turbulence in transitional channel flow

Abstract

Direct numerical simulations (DNS) of viscoelastic turbulence in channel flow are performed in minimal and large domains and the dynamics in the two cases are compared. Friction Reynolds numbers ranging from 70 to 100 and in the zero to moderate (40%) drag reduction (DR) regimes are studied. In minimal domains, there are occasional time intervals when the flow exhibits features such as weak vortices, low Reynolds shear stress, lower friction drag and larger log-law slope; these have been denoted as “hibernating turbulence” in contrast to the “active turbulence” that occurs otherwise. The present study addresses the question of whether similar low-drag events arise spatiotemporally in large domains. Image analysis algorithms and conditional sampling techniques are applied to the extended domains to identify and quantify the spatially local low-drag or hibernating regions. The results indicate that the hibernating states found in large domains share many similarities with those in minimal domains. Not only are their flow structures similar, but how they evolve with Reynolds number and viscoelasticity is qualitatively identical. In both large and minimal domains, structures in hibernating intervals/regions remain virtually unaltered with increasing viscoelasticity and the polymer molecules are less stretched than in active regions. At fixed Weissenberg number the hibernating regions/intervals vanish as friction Reynolds number increases; however they reappear as viscoelasticity is introduced, and gradually dominate the flow fields at sufficiently high Weissenberg number.