Abstract: 
We summarize our recent combined experimentaltheoreticalcomputational study of the effects of horizontal heterogeneities on the propagation of viscous gravity currents with applications to porous media flows. Our model geometry is a horizontal channel (specifically, a HeleShaw cell) with variable gap thickness in the streamwise direction in the form of a power law. We demonstrate that two types of selfsimilar behaviors emerge as a result of such horizontal heterogeneity: (a) a ``firstkind`` solution is found using dimensional analysis for currents that propagate away from the origin (a point of zero permeability); (b) a ``secondkind`` solution is found using a phaseplane analysis for viscous gravity currents that propagate toward the origin. Using the phaseplane formalism, we are able to construct the universal secondkind selfsimilar current shape. Additionally, still employing selfsimilar intermediate asymptotics and the phaseplane formalism, we identify selfsimilar behaviors in the postclosure regime, i.e., once the current reaches the geometric origin and begins to fill the model porous medium. The theoretical predictions show good agreement with labscale experiments using HeleShaw cells and also numerical solutions of the governing partial differential equation developed under the lubrication approximation.
Z. Zheng, I.C. Christov, H.A. Stone, {\it J.\ Fluid Mech.}\ {\bf 747} (2014) 218246, doi:10.1017/jfm.2014.148. 
