Revisiting nonlinearity in meandering river planform dynamics using Gradual Wavelet Reconstruc­­tion

Friday, 19 December 2014
Jon Schwenk, University of Minnesota Twin Cities, Department of Civil Engineering, Saint Anthony Falls Laboratory, Minneapolis, MN, United States, Efi Foufoula-Georgiou, University of Minnesota Twin Cities, Civil Engineering, Saint Anthony Falls Laboratory, Minneapolis, MN, United States and Stefano Lanzoni, University of Padua, Padua, Italy
Characterizing the intrinsic nonlinearity in meandering river dynamics is important because it dictates river evolution response to perturbations such as bank armoring or channel straightening. Meandering river dynamics have been described in terms of chaos or self-organized criticality—characterizations predicated on the presence of nonlinearity—yet recent studies have found only limited evidence for its existence.

Standard nonlinearity tests are performed by generating a number of linearized surrogate series from a signal of interest. Inherent nonlinearities in the original signal are destroyed in the surrogates via phase randomization in the Fourier domain. Nonlinearity is inferred if a significant difference exists between the original and the surrogates in an appropriately determined phase space. These tests detect the presence or absence of nonlinearity but cannot identify which scales and locations are contributing most to the signal’s nonlinearity. A new surrogate generation method called Gradual Wavelet Reconstruction (GWR) has two key advantages over the standard methodology. First, GWR quantifies the degree of nonlinearity rather than simply detecting its presence or absence, providing a basis for comparisons between river planforms and models of meander migration. Second, because the GWR methodology relies on localized transformations, it can determine the scales and locations primarily contributing to the observed complexity. As a result of those advantages too, GWR has been shown to detect the presence of nonlinearity in signals where standard tests have failed.

We apply GWR methodology to time series of channel sinuosity predicted by two established models of long-time meander migration: a HIPS-type model and that of Zolezzi and Seminara (2001). Although the former model has been shown to capture first-order meander dynamics, it fails to fully couple sediment and flow dynamics; nor does it account for the resonance phenomenon. Using GWR, we show how incorporating these additional physical processes affects the nonlinearity of the signal. We also analyze planform geometries of meandering rivers flowing through different geomorphic settings and develop hypotheses about how scale-dependent nonlinearities relate to the underlying physical environment.