Turbulence laws in natural bed flows

Characterization of turbulence in natural bed streams is one of the most fascinatingproblems of fluid dynamics. In this study, a statistical description of turbulence in anatural pebble bed flow is presented applying the laws of turbulence. A laboratoryexperiment was conducted to measure the three-dimensional instantaneous velocitycomponents in a flow over heterogeneous coarse sediments that simulated a naturalbed. The analysis reveals that the spectra (in Fourier space) show a power-law scaling,E.k/ k, suggesting the presence of inertial range turbulence. The exponent isslightly shallower than the Kolmogorov 5=3 scaling law, with this deviation possiblydue to the bed roughness heterogeneity and to fluctuation anisotropy. The Taylorfrozen-in approximation is broken at smaller scales towards the roughness crest level;therefore, a new statistical tool for the validation of this approximation is proposed.The Kolmogorov 4=5-law for the longitudinal increments and simultaneously theMonin–Yaglom 4=3-law for the nonlinear normal fluxes (both in physical space) arepreserved, providing an accurate estimation of the turbulent kinetic energy dissipationrate. The heterogeneity of the bed acts to induce the transport of finite kinetic helicityto the outer layer through persistently prolonged vortices. An associated 2=15-law forthe cascade of helicity has been locally found. These findings open a new directionin turbulence research for flows over highly rough beds.