Batchelor Scaling in Fast-Flowing Soap Films

The dynamics of a passive scalar such as a dye in the far dissipative range of fluid turbulence is a central problem in nonlinear physics. An important prediction for this problem was made by Batchelor over 40 years ago and is known as Batchelor's scaling law. We here present strong evidence in favor of this law for the thickness fluctuations in the flow of a soap film past a flat plate. The results also capture the dissipative range of the scalar which turns out to have universal features. The probability density function of the scalar increments and their structure functions come out in nice agreement with theoretical predictions.