Traveling spatially localized convective structures in an inclined porous medium

We analyze the traveling behavior of spatially localized convective structures in a 2D inclined porous layer subject to a fixed bottom temperature and an imperfectly conducting top boundary breaking midplane-reflection symmetry. Direct numerical simulations (DNS) performed for various Biot numbers reveal a nontrivial relationship between the pulse drift velocity c and the symmetry breaking parameter κ (tied to the Biot number). In small domains, the drift velocity c is positive (upslope) and increases monotonically with κ, while in larger domains c takes negative values at small κ and then increases to become positive at large κ. For weak symmetry breaking (small κ), bound states of several pulses exist, while at strong symmetry breaking (large κ), adjacent pulses repel each other and spread out becoming equidistant in the finite computational domain at late times. We show that dominant spatial eigenvalues (SE) accurately predict the spatial growth/decay rate and wavenumber of tails of traveling pulses in DNS. A transition occurs at κ=κ_c>0, where the dominant SE with positive real part shift from complex (oscillatory tails) to real (monotonic tail). Our results shine new light on the dynamics of spatially localized structures in convection in an inclined porous medium.