Experimental evidence for power-law wave number spectra of fractal tracer distributions in a complicated surface flow

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Abstract
Fractal tracer distributions, experimentally observed in surface flows, have previously been successfully modeled as the snapshot attractors of a random dynamical system. The accompanying paper by Namenson, Antonsen, and Ott [Phys. Fluids 8, 2426 (1996)] suggests that the wave number spectra of such snapshot attractors should exhibit power law dependence on wave number, where the power is given in terms of the correlation dimension of the fractal spatial pattern. Their theoretical and numerical results, while supporting the power‐law result, also caution that the power law may be obscured in an experimental situation. This paper demonstrates that, with proper averaging, the predicted power‐law scaling can be observed in a real experiment.