Similarity solutions of nonlinear diffusion problems related to mathematical hydraulics and the Fokker-Planck equation.


Journal Article

Similarity solutions of the shallow-water equation with a generalized resistance term are studied for open channel flows when both inertial and gravity forces are negligible. The resulting model encompasses various particular cases that appear, in addition to mathematical hydraulics, in diverse physical phenomena, such as gravity currents, creeping flows of Newtonian and non-Newtonian fluids, thin films, and nonlinear Fokker-Planck equations. Solutions of both source-type and dam-break problems are analyzed. Closed-form solutions are discussed, when possible, along with a qualitative study of two phase-plane formulations based on two different variable transformations.

Full Text

Duke Authors

Cited Authors

  • Daly, E; Porporato, A

Published Date

  • November 11, 2004

Published In

Volume / Issue

  • 70 / 5 Pt 2

Start / End Page

  • 056303 -

PubMed ID

  • 15600749

Pubmed Central ID

  • 15600749

Electronic International Standard Serial Number (EISSN)

  • 1550-2376

International Standard Serial Number (ISSN)

  • 1539-3755

Digital Object Identifier (DOI)

  • 10.1103/physreve.70.056303


  • eng