Short communication: Multiscalar roughness length decomposition in fluvial systems using a transform-roughness correlation (TRC) approach

In natural open-channel flows over complex surfaces, a wide range of superimposed roughness elements may contribute to flow resistance. Gravel-bed rivers present a particularly interesting example of this kind of multiscalar flow resistance problem, as both individual grains and bedforms may contribute to the roughness length. In this paper, we propose a novel method of estimating the relative contribution of different physical scales of in-channel topography to the total roughness length, using a transform-roughness correlation (TRC) approach. The technique, which uses a longitudinal profile, consists of (1) a wavelet transform which decomposes the surface into roughness elements occurring at different wavelengths and (2) a "roughness correlation" that estimates the roughness length (ks ) associated with each wavelength based on its geometry alone. When applied to original and published laboratory experiments with a range of channel morphologies, the roughness correlation estimates the total ks to approximately a factor of 2 of measured values but may perform poorly in very steep channels with low relative submergence. The TRC approach provides novel and detailed information regarding the interaction between surface topography and fluid dynamics that may contribute to advances in hydraulics, bedload transport, and channel morphodynamics.