  Following our first report (A. Groisman and V. Steinberg, $\sl Nature$ $\bf
405$, 53 (2000)) 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 high ratio of
width of the region available for flow to 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. Those include: (i)randomly fluctuating fluid motion excited in a
broad range of spatial and temporal scales; (ii) significant increase in the
rates of momentum and mass transfer (compared to 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.
