Author(s): Alessandro Lenci; Luca Chiapponi; Vittorio Di Federico And Sandro Longo
Linked Author(s): Luca Chiapponi, Vittorio Di Federico, Sandro Longo
Keywords: Gravity currents porous media Forchheimer flow self-similar solutions
Abstract: We consider an axisymmetric gravity current of a Newtonian fluid advancing in a homogeneous porous medium. The flow regime follows Forchheimer’s law, characterized by a quadratic relationship between velocity and the pressure gradient. Assuming a power-law injection of fluid along the vertical axis, we derived a self-similar solution that describes the water table profile, which can be determined by numerically integrating a non-linear ordinary differential equation. In the case of a finite volume of fluid release, the solution is analytical.
Year: 2025