Viscous gravity currents: similarity solutions, numerical approaches and applications

Gravity currents (GCs) are ubiquitous in nature. They appear whenever a fluid moves primarily horizontally into a fluid of different density and the motion is driven by gravitational forces. Carbon dioxide geological storage or mine tailings contamination are examples of GC propagation in porous media and in free surface, respectively. In the first part of the thesis, the classical literature results are reviewed and reconstructed. In particular, the GC flow in homogeneous porous media, for Newtonian fluids, and in free surface, for Newtonian and non-Newtonian fluids, are discussed. The classical approach to solve the GC flow problem, which is described by partial differential equations (PDEs), is to introduce similarity variables to transform the initial PDE into an ordinary differential equation. Then, an original contribution to the spreading of axisymmetric GCs in porous media under Darcy-Forchheimer flow is developed in the second part of the work. The introduction of the non-linear Forchheimer term in the flow equation, which in the classical theory is described by the Darcy's law, results in the need for numerical integration to solve the initial PDE, which is amenable to similarity solutions only under particular flow regimes (low- and high-Forchheimer). An original numerical scheme is developed to solve the non-linear flow problem. Results are then compared with the ones obtained under the Darcyan flow regime and the high-Forchheimer regime. The comparison is made by considering the real case of a CO2 current that spreads into a porous medium, which characteristics resemble those of the Sleipner field. Results highlight the validity of the high-Forchheimer regime at early times and of the Darcyan regime in the long run. Finally, the results obtained for the free surface case for non-Newtonian fluids are applied to the real case of mine tailings contamination after a dam failure. The spread of two different suspensions is discussed and compared.