Quantifying Flow Resistance of Mountain Streams Using the HHT Approach

Abstract:

This study quantifies the flow resistance of mountain streams with gravel bed and remarkable bed forms. The motivation is to follow the previous ideas (Robert, A. 1990) that the bed surface can be divided into micro-scale and macro-scale roughness, respectively. We processed the field data of longitudinal bed profiles of the Longxi River, Sichuan Province, China, using the Hilbert-Huang Transformation Method (HHT). Each longitudinal profile was decomposed into a set of curves with different frequencies of spatial fluctuation. The spectrogram was accordingly obtained. We supposed that a certain high and low frequency curves correspond to the micro- and macro-roughness of stream bed, respectively. We specified the characteristic height and length with the spectrogram, which represent the macro bed form accounting for bed form roughness. We then estimated the bed form roughness as being proportional to the ratio of the height to length multiplied by the height(Yang et al,2005). We also assumed the parameter, Sp, defined as the sinuosity of the highest frequency curve as the measure of the micro-scale roughness. We then took into account the effect of bed material sizes through using the product of d₅₀/R and Sp, where d₅₀ is the sediment median size and R is the hydraulic radius. The macro- and micro-scale roughness parameters were merged together nonlinearly to evaluate the flow resistance caused by the interplaying friction and form drag forces. Validation results show that the square of the determinant coefficient can reach as high as 0.84 in the case of the Longxi River. Future studies will focus on the verification against more field data as well as the combination of skin friction and form drag.

Key words: flow resistance; roughness; HHT; spectrogram; form drag

Robert, A. (1990), Boundary roughness in coarse-grained channels, Prog. Phys. Geogr., 14(1), 42–69.

Yang, S.-Q., S.-K. Tan, and S.-Y. Lim. (2005), Flow resistance and bed form geometry in a wide alluvial channel, Water Resour. Res., 41, W09419.