Reductionist versus holistic approaches to the study of river meandering: An ideal dialogue

We discuss some recent attempts to apply the theory of nonlinear dynamical systems to the interpretation of the long term morphodynamic evolution of meandering rivers. To make the discussion attractive for the reader, we employ the method of a Socratic dialogue between a member of the so called 'reductionist community', who is inclined to support only theories based on physical principles and who is skeptical about fashionable new paradigms, and a member of the 'holistic community', who supports the idea that new paradigms are needed because rivers are complex systems, whose response can only be interpreted using tools that analyze the system "as a whole". The dialogue focuses on a selection of recent contributions which assesses the progress in understanding of meander dynamics achieved by the use of the above new paradigms. The discussion suggests that some consensus has been reached on the fractal nature of meandering patterns, with the fractal dimension playing the role of a morphometric parameter. On the contrary, despite different early suggestions, recent thorough analysis has been unable to detect any clear evidence that the evolution of meanders displays the characters of either a chaotic or a self organized critical process. The dialogue is concluded with some consensus on the perspective that well founded cellular models may possibly help reconciling the reductionist and holistic viewpoints.