Statistics of Stretching Fields in Experimental Fluid Flows Exhibiting Chaotic Advection

Stretching fields and their statistical properties are studied experimentally for four distinct two-dimensional time-periodic confined fluid flows exhibiting chaotic advection: a random vortex array for two different Reynolds numbers, a set of parallel shear layers, and a vortex lattice. The flows are driven electromagnetically, and they are studied by means of precise particle velocimetry. We find that for a given flow, the probability distributions of log S (where S is the local stretching in N cycles) can be nearly superimposed for different N when log S is rescaled using the geometrical mean of the stretching distribution. The rescaled stretching fields for a given flow at various N are highly correlated spatially when N is large. Finally, the scaled distributions for different flows are similar, though there are some differences connected to the degree of spatial symmetry and time-reversibility of the flows.