Thursday 15 April 2021, 12:45-13:15 via zoom
Koondanibha Mitra (RU)
The gravity fingering phenomenon in porous media flow: An unsolved problem
In a porous medium like soil, when a wetted layer is above a dry layer, gravity leads to the propagation of water downwards into the medium. However, it is observed from experiments that rather than propagating with a uniform front, certain finger structures appear that move with constant speed. This phenomenon can not be described by standard models for such processes and is not fully understood to this date. We hypothesize that hysteresis effects have to be taken into account to explain such behaviour. In order to explain the stability of the fingered structures over uniform front structures and to specify the propagation speed, we use a travelling wave ansatz and set up a free boundary problem with hysteresis. It is proven that there are only certain speeds at which the solutions can propagate. The solutions for these cases predominantly possess a fingered structure. Our analysis is complemented with numerical results supporting the hypothesis.