The local energy flux surrogate in turbulent open-channel flows

Abstract

We present a local analysis of turbulence in open-channel flows, using time-series velocity measurements. The method is based on a local form of the Kolmogorov “4/3-law” of homogeneous turbulence for the third-order moment of velocity increments. Following the Duchon and Robert [“Inertial energy dissipation for weak solutions of incompressible Euler and Navier–Stokes equations,” Nonlinearity 13, 249 (2000)] idea, which envisions turbulence dissipation as a lack of smoothness of the Navier–Stokes solutions, we estimate the local energy flux in a laboratory experiment with natural bed flows. Taking advantage of one-dimensional filtering techniques, under reasonable hypothesis, simple expressions of a surrogate of the energy flux are provided. The local energy flux surrogate reveals that, independently of the geometry, turbulence dissipation is highly intermittent. Among a variety of eddies that populate turbulence, dissipative singularities appear in sheet-like, tube, and filament structures, with large amplitude variations and rotations. This simplified technique can be applied to any measurement of hydrodynamic turbulence.