Continuous wavelet characterization of the wavelengths and regularity of meandering rivers

Meanders are oscillatory systems characterized with multiple spatial frequencies in their planforms. Although the concept of dominant meander wavelength (DMW) is central to morphodynamic research on river meandering, shorter and longer spatial scales of oscillations are also relevant. Using Continuous Wavelet Transform (CWT), we present an objective quantitative characterization of the relevant wavelengths of meandering rivers. Analysis of synthetic meanders generated through Kinoshita curves and real meandering rivers show that DMW can be better detected by applying CWT to the spatial series of the direction-angle, instead of curvature, because the latter shifts the meander oscillation energy toward shorter harmonics. This is related to the typical observed high ratio of meander arclength to channel width, as emerging from field observations and from morphodynamic modeling of meanders, implying the dimensionless wavenumber of meander oscillations to be an O(10−1)O10−1 number. The capability of CWT of capturing local as well as global information in a spatial series is exploited by analyzing two CWT-based indicators, which express the relevance of other wavelengths with respect to the local DMW within the same reach (Mλ) and the variability of the local DMW with respect to the global DMW (Sλ). Thresholding the Mλ indicator shows that the global DMW corresponds to local DMW for only the most regular meanders. At longer scales, the Sλ indicator also reveals the existence of spatial modulations of the direction-angle oscillations in real meandering rivers, which have been previously detected only in synthetic planforms generated by morphodynamic models. This correspondence between observations and modeling indicates the potential of CWT analysis of meanders to provide further insight into the connections between the form and processes of channel meandering, as it suggests that spatial modulations might be inherent in meander-planform dynamics and related to the tendency of meanders to evolve in wavegroups, a potential cause of the so called ‘cutoff avalanches’ observed in natural and modeled meandering streams.