Predicting macroturbulence energy and timescales for flow over a gravel bed: Experimental results and scaling laws

Abstract

The fluvial science community lacks predictive equations for macroturbulence energy and timescales, which may serve useful for predicting sediment transport in rivers. Therefore, we investigated the systematic variation of macroturbulence scales by varying hydraulic parameters in an experimental facility, collecting velocimetry data and measuring macroturbulence scales with spectral analyses, and testing scaling laws for macroturbulence prediction that consider inner variables, outer variables, and turbulence kinetic energy. Experiments spanned across 11 energy gradients and aspect ratio combinations including 116 testing conditions each with 30 minute instantaneous turbulence time-series collected. Results showed velocimetry data and time-average turbulence parameters supported the presence of an equilibrium outer region and coherent double-layer assumed in the experimental design. Macroturbulence and bursting wavenumbers were constant in the outer region when scaled with the flow depth, and were independent of distance above the boundary, aspect ratio, energy gradient, Froude number, or Shields parameter. Data results agreed with the derivation herein and showed macroturbulence energy scales with the streamwise turbulence kinetic energy. Semi-theoretical equations for turbulence kinetic energy scaled macroturbulence energy reasonably well. A novel equation is presented for the macroturbulence period, and the equation's transferability is supported by consistency with past macroturbulence studies, bursting formula, and flow visualization studies. Novel equations are presented for macroturbulence energy, and transferability is supported on theoretical and empirical grounds; however open questions remain regarding a universal function for streamwise turbulence kinetic energy and the net contribution of macroturbulence to total turbulence energy. Results showed the macroturbulence wavenumber required a relatively long duration of data (i.e., 17 min) to stabilize. Results were used to formulate a time scale for minimum measurement length of turbulence data when information about macroturbulence is sought after. We discuss macroturbulence linkages with sediment transport, including, prediction of the sediment carrying capacity via macroturbulence formula as one application to help close the gap between turbulence and fluvial sediment transport.