Abstract |
Viscoelastic turbulent flows display intriguing differences
from their Newtonian counterparts. Even familiar flow structures
such as rolls, streaks and hairpin vortices have new origins
and dynamics. A framework based on the evolution of vorticity
and polymer torque is developed in order to explain these differences.
The framework is adopted to study two canonical flow configurations:
(i) roll-streak interactions in Couette flow and (ii) the evolution
of a small-amplitude spanwise vortex in homogeneous shear. Each
of the two problems focuses on different elements of the polymer-torque
equation, and demonstrates the rich variety of behaviors that
ensue depending on the fluid elasticity. Rolls can generate
streaks via an inertial lift-up effect or an elastic polymer-stretch
mechanism which is active even in the absence of inertia. The
most interesting behavior arises when the timescales of viscous
diffusion in the solvent and of polymer relaxation are commensurate,
and the fluid can support the propagation of vorticity waves.
The resulting streaks undergo cycles of amplification and decay
— a unique feature of viscoelastic flows. The evolution of the
spanwise vortex in viscoelastic shear flow defies our intuition
from the Newtonian case entirely. The vortex in a Newtonian
fluid is simply advected by the base flow and decays due to
viscosity, all while energy and enstrophy decay. The Orr mechanism
in that case requires a net tilt in the streamlines against
the shear in order to observe energy amplification. The same
vortex in a polymeric shear flow splits into two co-rotating
and counter-propagating vortices that are stretched by the shear.
In addition, a reverse-Orr mechanism is in effect, whereby perturbations
with a net tilt with the shear amplify. These new findings provide
a theoretical foundation for future analyses of transitional
and turbulent viscoelastic shear flows. |
