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

Isoscalar surfaces in turbulent ows are found to be more complex than (selfsimilar) fractals, in both the far eld of liquid-phase turbulent jets and in a realization of Rayleigh-Taylor-instability ow. In particular, they exhibit a scaledependent coverage dimension, D2( ), 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 ow 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 similarD2( ) behavior is found for level-set data of 3-D density-interface behavior in recent direct numerical-simulation studies of Rayleigh-Taylor-instability ow. A comparison of (spatial) spectral and isoscalar coverage statistics will be discussed.