Nonlinear model for Marangoni convection

A Lorenz-like model for Marangoni convection with finite wave number in large aspect ratio situations is constructed. There is exchange of stabilities at the onset of convection. Due to the presence of surface fluctuations, there is onset of oscillations. As the Marangoni number is increased, the oscillations become chaotic. It is shown that the principle of stability is true for the large aspect ratio system. The cylindrical rolls undergo a Hopf bifurcation as the first secondary instability.