Experimental Analysis of Lagrangian Coherent Structures and Chaotic Mixing in Rayleigh-Benard Convection

It is known that some fluid particles may be transported chaotically in Lagrangian description although the velocity field seems to be stable in Eulerian description. A typical example can be found in the system of two-dimensional Rayleigh-Benard convection with perturbed velocity fields, which has been investigated as a low dimensional mechanical model of fluid phenomena associated with natural convection in order to clarify the mechanism of fluid transport (see, for instance, [2]). In this study, we make an experimental study on the global structures of chaotic mixing appeared in the two-dimensional perturbed Rayleigh-Benard convection by analyzing Lagrangian coherent structures (LCSs), which correspond to the invariant manifolds of time-dependent mechanical systems. We develop an apparatus to measure the velocity field by Particle Image Velocimetry (PIV) and then show the LCSs which can be numerically detected from the experimental data by computing Finite-time Lyapunov exponent (FTLE) fields. Finally, we show the global structures of chaotic mixing appeared in the perturbed Rayleigh-Benard convection as well as the steady convection by experiments. In particular, we clarify how the LCSs are entangled with each other around the cell boundaries to carry out chaotic Lagrangian transports.