Title: Two scenarios of advective washing-out of localized convective patterns under frozen parametric disorder,
Abstract: The effect of spatial localization of states in distributed parameter systems
under frozen parametric disorder is well known as the Anderson localization and
thoroughly studied for the Schrödinger equation and linear dissipation-free
wave equations. Some similar (or mimicking) phenomena can occur in dissipative
systems such as the thermal convection ones. Specifically, many of these
dissipative systems are governed by a modified Kuramoto-Sivashinsky equation,
where the frozen spatial disorder of parameters has been reported to lead to
excitation of localized patterns. Imposed advection in the modified
Kuramoto-Sivashinsky equation can affect the localized patterns in a nontrivial
way; it changes the localization properties and suppresses the pattern. The
latter effect is considered in this paper by means of both numerical simulation
and model reduction, which turns out to be useful for a comprehensive
understanding of the bifurcation scenarios in the system. Two possible
bifurcation scenarios of advective suppression ("washing-out") of localized
patterns are revealed and characterised.