Patterns of Dirt

  • N.J. Balmforth
  • A. Provenzale
Part of the Lecture Notes in Physics book series (LNP, volume 582)


Many natural patterns appear when a simply structured equilibrium state is no longer preferred in comparison to a more complicated restructuring or rearrangement of the system. Our goal is typically a theoretical explanation or rationalization of the physical process, and invariably proceeds by way of mathematics; we formulate equations that describe the physical processes and seek to solve them in the appropriate context. Many standard techniques are available for the purpose to aid our analysis. For example, sometimes, hints about the patterns that will form can be extracted from a study of disturbances of infinitesimal amplitude, and so linear stability theory and decomposition into normal modes are our tools. Often, however, the ultimate, nonlinear mechanism of saturation is critical to selecting or shaping the forming pattern, and this cannot be revealed by linear stability analysis alone. Instead, we must advance into the nonlinear regime where we can use ideas from weakly nonlinear and dynamical systems theory complemented by numerical simulation.


Sediment Transport Froude Number Suspended Load Linear Instability Bedload Transport 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • N.J. Balmforth
    • 1
  • A. Provenzale
    • 2
    • 3
  1. 1.Department of Applied Mathematics and Statistics, School of EngineeringUniversity of California at Santa CruzUSA
  2. 2.Istituto di CosmogeofisicaTorinoItaly
  3. 3.ISI FoundationTorinoItaly

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