Whirling hexagons and defect chaos in hexagonal non-Boussinesq convection

We study hexagon patterns in non-Boussinesq convection of a thin rotating layer of water. For realistic parameters and boundary conditions we identify various linear instabilities of the pattern. We focus on the dynamics arising from an oscillatory side-band instability that leads to a spatially disordered chaotic state characterized by oscillating (whirling) hexagons. Using triangulation we obtain the distribution functions for the number of pentagonal and heptagonal convection cells. In contrast to the results found for defect chaos in the complex Ginzburg-Landau equation, in inclined-layer convection, and in spiral-defect chaos, the distribution functions can show deviations from a squared Poisson distribution that suggest non-trivial correlations between the defects.