On the geometry of two-dimensional slices of irregular level sets in turbulent flows∗

Isoscalar surfaces in turbulent flows are found to be more complex than (selfsimilar) fractals, in both the far field of liquid-phase turbulent jets and in a realization of Rayleigh-Taylor-instability flow. In particular, they exhibit a scaledependent coverage dimension, D2(λ), for 2-D slices of scalar level sets, that increases with scale, from unity, at small scales, to 2, at large scales. For the jet flow and Reynolds numbers investigated, the isoscalar-surface geometry is both scalarthresholdand Re-dependent; the level-set (coverage) length decreases with increasing Re, indicating enhanced mixing with increasing Reynolds number; and the size distribution of closed regions is well described by lognormal statistics at small scales. A similar D2(λ) behavior is found for level-set data of 3-D density-interface behavior in recent direct numerical-simulation studies of Rayleigh-Taylor-instability flow. A comparison of (spatial) spectral and isoscalar coverage statistics will be discussed.