| Abstract: |
| We introduce a new nonlocal model for gravitational fingering and study its wave propagation dynamics. Gravitational fingering is an instability in the displacement of miscible fluids in porous media, governed by Darcy's law, which occurs when a lighter fluid lies below a heavier one and gravity drives an exchange of positions. Our main result establishes the existence of a propagating terrace consisting of infinitely many traveling waves in a semi-discrete Transverse Flow Equilibrium (TFE) model. The talk is based on ongoing joint work with Sergey Tikhomirov (PUC-Rio, Brazil) and extends earlier results on two-tubes models of gravitational fingering (SIMA, arxiv:2401.05981) |
|