Experimental Investigation of Turbulence Spectra for Flow over Gravel Beds: Spectral Scaling and Macroturbulence Streampower

The $-1$ power region of the turbulence spectrum is a constant energy region responsible for energy production. However, its scaling and their implications are underreported. Experiment results show that the production region comprises 42% of turbulence kinetic energy for open-channel flows over fine gravel and very coarse gravel beds. Energy of the production region scales similarly for these gravel bed types, and enables its prediction using logarithmic and exponential equations. Similarity scaling is evidenced for the production region’s low and high wavenumber boundaries, defined as the macroturbulence and bursting wavenumbers. The macroturbulence and bursting wavenumbers have similar functions, suggesting that the production region is controlled by the same phenomena across its extent. These results are contrary to those of previous research, in which low and high wavenumber boundaries were hypothesized to be scaled by outer and inner scales, respectively. The authors introduce the macroturbulence streampower, which is derived using the energy similarity and macroturbulence wavenumber. The macroturbulence streampower is distributed across the flow depth, is dependent on roughness element, and agrees with Bagnold’s streampower near the channel half-height.