Publications [#284214] of Amilcare Porporato
Papers Published
- Daly, E; Porporato, A, Similarity solutions of nonlinear diffusion problems related to mathematical hydraulics and the Fokker-Planck equation.,
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol. 70 no. 5 Pt 2
(November, 2004),
pp. 056303, ISSN 1539-3755 [PhysRevE.70.056303], [doi]
(last updated on 2023/08/08)Abstract:
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.Keywords:
channel flow;creeping flow;diffusion;Fokker-Planck equation;fractals;non-Newtonian flow;non-Newtonian fluids;