The Excess Dissipation of Energy in a Turbulent Boundary-Layer and its Departure from Log-Normality

Abstract

We investigate turbulent dissipation in a von Karman flow using PIV and Diffusing Wave Spectroscopy measurements to directly compare bulk and wall dynamics. While bulk dissipation conforms to the dissipative anomaly, wall dissipation exhibits a clear excess that grows with Re, consistent with velocity-gradient dominated scaling. Decomposition into dissipation intensity bands reveals that this excess is mainly driven by progressive redistribution toward high-intensity events, larger than 10 x mean, as Re increases. From these measurements, we infer the skin-friction coefficient, finding a decreasing trend with Re fairly consistent with classical power-law behavior despite increasing dissipation. Statistically, the wall shows strong departures from log-normality at low Re that diminishes with increasing Re, reflecting an increase in the effective dimensionality of the near-wall gradient field with Re. In contrast, the bulk dissipation remains near log-normal across all Re with slowly growing log-dissipation variance, consistent with K62 refined similarity. These results suggest distinct origins of log-normal behavior which are multiplicative cascade dynamics in the bulk versus the combined effect of persistent shear and a superposition of an increasing number of independent gradient contributions at the wall.