Secondary instabilities of hexagonal patterns in a Bénard-Marangoni convection experiment.

We have identified experimentally secondary instability mechanisms that restrict the stable band of wave numbers for ideal hexagons in Bénard-Marangoni convection. We use "thermal laser writing" to impose long wave perturbations of ideal hexagonal patterns as initial conditions and measure the growth rates of the perturbations. For epsilon=0.46 our results suggest a longitudinal phase instability limits stable hexagons at a high wave number while a transverse phase instability limits low wave number hexagons.