Inclined convection in a layer of liquid water with poorly conducting boundaries

Abstract

We investigate pattern formation in an inclined layer of liquid water with poorly conducting boundaries. We show that above the threshold for convection the presence of an inclination larger than 14 mrad determines a transition from a square pattern to longitudinal rolls, a behavior remarkably different than the one reported in the presence of inclined conducting boundaries, where transitions between convective planforms occur at inclination angles of the order of several degrees. The longitudinal rolls are characterized by a dimensionless wave vector k≈1.8, significantly smaller than k≈3.117 reported for conducting boundaries at large Prandtl number. The transition can be triggered by changing dynamically the inclination of the layer of fluid, and does not occur symmetrically in the two directions. By starting in the horizontal configuration, it develops slowly through the demolition of the square structure to form longitudinal rolls, while it develops rapidly in the other direction, through the formation of a cross-roll structure perpendicular to the longitudinal rolls.