Anshuman Roy

Polymer drag reduction in exact coherent structures of plane shear flow

Recently discovered traveling-wave solutions to the Navier–Stokes equations in plane shear geometries provide model flows for the study of turbulent drag reduction by polymer additives. These solutions, or “exact coherent states” (ECS), qualitatively capture the dominant structure of the near-wall buffer region of shear turbulence, i.e., counter-rotating pairs of streamwise-aligned vortices flanking a low-speed streak in the streamwise velocity. The optimum length scales for the ECS match well the length scales of the turbulent coherent structures and evidence suggests that the ECS underlie the dynamics of these structures. We study here the effect of viscoelasticity on these states. The changes to the velocity field for the viscoelastic ECS, where the FENE-P model calculates the polymer stress, mirror the modifications seen in experiments of fully turbulent flows of polymer solutions at low to moderate levels of drag reduction: drag is reduced, streamwise velocity fluctuations increase while wall-normal ...

Fall and rise of a viscoelastic filament

When a viscoelastic fluid blob is stretched out into a thin horizontal filament, it sags and falls gradually under its own weight, forming a catenary-like structure that evolves dynamically. If the ends are brought together rapidly after stretching, the falling filament tends to straighten by rising. These two effects are strongly influenced by the elasticity of the fluid and yield qualitatively different behaviours from the case of a purely viscous filament analysed previously (Teichman & Mahadevan, J. Fluid Mech. vol. 478, 2003, p. 71). Starting from the bulk equations for the motion of a viscoelastic fluid, we derive a simplified equation for the dynamics of a viscoelastic filament and analyse this equation in some simple settings to explain our observations.

Publisher’s Note: “Polymer drag reduction in exact coherent structures of plane shear flow” [Phys. Fluids 16, 3470 (2004)]

This article was originally published with three typographical errors. On p. 3471, in the seventh line from the bottom of the right-hand column, the subscript to t should be “wall,” rather than “watt.” In the top line of the right-hand column on p. 3473, the sentence should read: “This difference is negligible in the present situation, where b.103.” On p. 3478, in the sentence above Eq. (10), the partial derivatives should be with respect to x, not to t. AIP apologizes for these errors. All online versions of the article have been corrected. Author to whom correspondence should be addressed. Electronic mail: graham@engr.wisc.edu PHYSICS OF FLUIDS VOLUME 16, NUMBER 12 DECEMBER 2004