Nonlinearity and complexity in gravel bed dynamics

Arvind Singh, Stefano Lanzoni, Efi Foufoula

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21 Scopus citations


The dynamics of river bed evolution are known to be notoriously complex affected by near-bed turbulence, the collective motion of clusters of particles of different sizes, and the formation of bedforms and other large-scale features. In this paper, we present the results of a study aiming to quantify the inherent nonlinearity and complexity in gravel bed dynamics. The data analyzed are bed elevation fluctuations collected via submersible sonar transducers at 0.1 Hz frequency in two different settings of low and high discharge in a controlled laboratory experiment. We employed surrogate series analysis and the transportation distance metric in the phase-space to test for nonlinearity and the finite size Lyapunov exponent (FSLE) methodology to test for complexity. Our analysis documents linearity and underlying dynamics similar to that of deterministic diffusion for bed elevations at low discharge conditions. These dynamics transit to a pronounced nonlinearity and more complexity for high discharge, akin to that of a multiplicative cascading process used to characterize fully developed turbulence. Knowing the degree of nonlinearity and complexity in the temporal dynamics of bed elevation fluctuations can provide insight into model formulation and also into the feedbacks between near-bed turbulence, sediment transport and bedform development.

Original languageEnglish (US)
Pages (from-to)967-975
Number of pages9
JournalStochastic Environmental Research and Risk Assessment
Issue number7
StatePublished - 2009

Bibliographical note

Funding Information:
This research was supported by the National Center for Earth-surface Dynamics (NCED), a Science and Technology Center funded by NSF under agreement EAR-0120914. The support by the Joseph T. and Rose S. Ling Professorship in Environmental Engineering at the University of Minnesota is also gratefully acknowledged. A series of experiments (known as StreamLab06) were conducted at the St. Anthony Falls Laboratory as part of an NCED program to examine physical-biological aspects of sediment transport ( ). Computer resources were provided by the Minnesota Supercomputing Institute, Digital Technology Center at the University of Minnesota. The authors are grateful to David Olsen for his assistance in the preparation of the manuscript.


  • Bedforms
  • Complexity
  • Diffusion
  • Finite size Lyapunov exponent (FSLE)
  • Nonlinearity


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