Benjamin-Feir turbulence in convective binary fluid mixtures

Binary mixtures of water and alcohol or ³He and ⁴He provide an excellent vehicle for studying the onset of a rich variety of dynamical behavior. For different values of the separation ratio, these systems exhibit both steady and oscillatory convection, competition between the two, and in another parameter range, a weakly turbulent state. In this paper we develop a general theory which is valid near onset and which can account for each of these features. A universal equation of Ginzburg-Landau type with complex coefficients obtains and is investigated numerically and analytically in one and two spatial dimensions. The most novel prediction is that some of the a periodic behavior seen in experiment is due to the universal Benjamin-Feir instability and we call this phenomenon Benjamin-Feir turbulence. Although the possibility of this effect has been discussed theoretically in the literature for over ten years, binary mixture convection provides the first vehicle in which the prediction can be quantitatively tested. We also discuss mean drift effects and the consequences of fixed lateral boundaries.