Nonlinear Dynamics of Viscoelastic Turbulence in Transitional Channel Flo

Introducing a trace amount of long-chain polymer molecules results in substantial reduction of friction drag in turbulent flows. This phenomenon has been observed for decades, and polymer addition has become a standard practice in industry. The most intriguing phenomenon regarding this is the existence of an upper limit of drag reduction, the maximum drag reduction (MDR) asymptote. The MDR asymptote is universal with respect to the flow geometries and polymer-related properties such as the chemical species, concentration, and molecular weight. MDR is not restricted to high Reynolds number flows; it occurs at Reynolds number near laminar-turbulent transition as well. The universality and the mechanism of how turbulence sustains at MDR still puzzle the researchers. We use direct numerical simulations (DNS) to model the flow and the polymer conformation, to study the dynamics, the flow structures and their interactions, aiming to gain deeper understanding towards MDR. Numerical simulations in minimal domains are conducted to study the temporal dynamics. In minimal channels 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 work illustrates how the statistics of these intervals evolve over the entire range of drag reduction levels. We also addresses the question of whether similar low-drag events arise spatiotemporally in non-minimal domains. The results indicate that the hibernating states found in non-minimal 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. The above-mentioned simulations were based on spectral scheme with non-negligible artificial diffusion found to damp the polymer stress field. We develop the next-generation viscoelastic DNS code adopting a high resolution scheme which guarantees numerical stability without any diffusion. The code is used to model turbulent flows at MDR and lower Reynolds numbers. In this regime, polymer becomes the dominant source feeding turbulent kinetic energy, which may serve as one perspective to understand the sustaining mechanism at MDR.