Related Experiment Video
Updated: Aug 1, 2026

Visualizing Hyporheic Flow Through Bedforms Using Dye Experiments and Simulation
Published on: November 18, 2015
Similarity solutions of nonlinear diffusion problems related to mathematical hydraulics and the Fokker-Planck
Edoardo Daly1, Amilcare Porporato
1Dipartimento di Idraulica, Trasporti ed Infrastrutture Civili, Politecnico di Torino, Torino, Italy.
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.
Related Concept Videos
Navier–Stokes Equations
Steady, Laminar Flow Between Parallel Plates
Modeling and Similitude
Typical Model Studies
Linear Differential Equations
Partial Differential Equations

