STABILITY AND FLUCTUATIONS OF A SPATIALLY PERIODIC CONVECTIVE FLOW

The onset of convection for a roll instability is analyzed using a model equation. The wavelength increase follows from a variational approach. For certain wavelengths, phase diffusion turns out to be unstable against compression (or dilatation) and torsion of the rolls. Thermal phase fluctuations induce a tiny brownian motion of the structure which should be observable in carefully designed experiments such as Rayleigh-Benard in liquid helium or Carr-Helfrich in nematic liquid crystals.