Porous media plumes: transient filling box solutions

We examine the transient flow of a negatively buoyant, laminar plume in an emptying filling box filled with porous medium. As the system reaches steady state, the box is partitioned into two uniform layers of different densities. However, the approach towards steady state is characterized by a contaminated layer that is continuously stratified. Whereas the presence of a continuous stratification in the contaminated layer for finite time poses nontrivial analytical challenges, we show that it is possible to derive bounds on the range of possible solutions, The validity of this approach is confirmed by drawing a comparison with the turbulent free plume case. A separate component of our study considers time-variable forcing where the laminar plume source strength changes with time. We focus particular attention on cases where the source buoyancy or volume fluxes are either abruptly altered or else turned on and off with non-dimensional half-period ∆τ .