Elastic turbulence in curvilinear flows of polymer solutions

Following our first report (A Groisman and V Steinberg 2000 Nature 405 53), we present an extended account of experimental observations of elasticity-induced turbulence in three different systems: a swirling flow between two plates, a Couette-Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had a high ratio of the width of the region available for flow to the radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high-molecular-weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. They include: (i) randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales and (ii) significant increase in the rates of momentum and mass transfer (compared with those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms and parameter dependence of the elastic turbulence are compared with those of the conventional high-Re hydrodynamic turbulence in Newtonian fluids. Some similarities as well as multiple principal differences were found. In two out of three systems (swirling flow between two plates and flow in the curvilinear channel), power spectra of velocity fluctuations decayed rather quickly, following power laws with exponents of about -3.5. It suggests that, being random in time, the flow is rather smooth in space, in the sense that the main contribution to deformation and mixing (and, possibly, elastic energy) is coming from flow at the largest scale of the system. This situation, random in time and smooth in space, is analogous to flows at small scales (below the Kolmogorov dissipation scale) in high-Re turbulence.