Critical geometry of two-dimensional passive scalar turbulence

Passive scalars advected by a magnetically driven two-dimensional turbulent flow are analyzed using methods of statistical topography. The passive tracer concentration is interpreted as the height of a random surface, and the scaling properties of its contour loops are analyzed. Various exponents that describe the loop ensemble are measured and compared to a scaling theory. This leads to a geometrical criterion for the intermittency of scalar fluctuations.