Experimental evidence of chaotic advection in a convective flow

– Lagrangian chaos is experimentally investigated in a convective flow by means of Particle Tracking Velocimetry. The Finite Size Lyapunov Exponent analysis is applied to quantify dispersion properties at different scales. In the range of parameters of the experiment, Lagrangian motion is found to be chaotic. Moreover, the Lyapunov exponent depends on the Rayleigh number as Ra1/2. A simple dimensional argument for explaining the observed power law scaling is proposed. The investigation of transport and mixing of passive tracers is of fundamental importance for many geophysical and engineering applications [1, 2]. It is now well established, and confirmed by several numerical [3] and experimental [4] evidence, that even in very simple Eulerian flow (i.e. laminar flow) the motion of Lagrangian tracers can be very complex due to Lagrangian Chaos [2, 5]. In such a situation, diffusion may be of little relevance for transport which is, on the contrary, strongly enhanced because of chaotic advection [3, 5]. In this letter, we address the problem of quantifying the dispersion of passive tracers in a relatively simple convective flow at various Rayleigh numbers Ra. By applying the Finite Size Lyapunov Exponent (FSLE) [6] analysis to the Lagrangian trajectories obtained from Particle Tracking Velocimetry (PTV) technique, we are able to estimate the dispersion properties at different scales. We find a clear power law dependence of the Lagrangian Lyapunov exponent on the Rayleigh number. This dependence is explained by a dimensional argument which excludes a role of diffusion in the dispersion process. The experiment is performed in a rectangular tank L = 15.0 cm wide, 10.4 cm deep and H = 6.0 cm height, filled with water. Upper and lower surfaces are kept at constant temperature while the side walls are adiabatic. The convection is generated by an electrical circular