Experimental Observation of the Area Rule and Bifractality of Circulation in Three Dimensional Newtonian and Polymeric Turbulence

Velocity circulation around closed loops is a fundamental quantity of central interest in the study of the energy cascade in turbulent flows. Recent theoretical and numerical studies have identified circulation as a geometric observable that captures intermittency through the area rule and a distinctive bifractal scaling of its moments in classical and quantum turbulence. One fundamental question is how these statistical characteristics of circulation are altered when an additional agent such as long-chain flexible polymer that can modify the turbulence energy cascade is added to the fluid. Here, through stereo particle image velocimetry measurements in high Reynolds number (Rλ≈393) turbulent flow of pure water and dilute polymer solution in a von Kármán swirling flow system, we provide the first experimental evidence that the area rule and the bifractality of the circulation hold for planar loops in both the 3D Newtonian and polymeric turbulence. These two statistical characteristics of circulation are robust despite strong modifications of the energy cascade and small-scale topology induced by polymer elasticity, except that the Hölder exponent in polymeric turbulence (h≈1.55) is significantly larger than in Newtonian turbulence (h≈1.14), suggesting that the flow is smoother in polymeric turbulence. Our results establish velocity circulation as a more universal and fundamental tool, compared to the very frequently used velocity increments, for unifying intermittency across different turbulent systems from Newtonian to polymeric to quantum turbulence.