The local energy flux surrogate in turbulent open-channel flows

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 sheetlike, tube, and filament structures, with large amplitude variations and rotations. This simplified technique can be applied to any measurement of hydrodynamic turbulence.