Intermittency and energy fluxes in the surface layer of free-surface turbulence

TL;DR

This study investigates turbulence near a free surface, revealing that the surface layer's energy fluxes and intermittency differ from classical turbulence models, with persistent energy cascades and depleted intermittency.

Contribution

It provides a new definition of surface-layer thickness based on energy flux crossover scales and characterizes turbulence behavior near free surfaces beyond classical theories.

Findings

Surface layer thickness defined by energy flux crossover scale.

Persistent direct energy cascade at scales smaller than the crossover.

Intermittency is strongly depleted in the surface layer.

Abstract

By analyzing hot-wire velocity data taken in an open channel flow, an unambiguous definition of surface-layer thickness is here provided in terms of the cross-over scale between backward and forward energy fluxes. It is shown that the turbulence in the surface layer does not conform to the classical description of two-dimensional turbulence, since the direct energy cascade persists at scales smaller than the cross-over scale, comparable with the distance from the free-surface. The multifractal analysis of the one-dimensional surrogate of the turbulent kinetic energy dissipation rate in terms of generalized dimensions and singularity spectrum indicates that intermittency is strongly depleted in the surface layer, as shown by the singularity spectrum contracted to a single point. The combination of intermittency indicators and energy fluxes allowed to identify the specific nature of the surface layer as alternative to classical paradigms of three- and two-dimensional turbulence which cannot fully capture the global behavior of turbulence near a free-surface.