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The approach to and development of turbulence of low-Prandtl-number fluids in the Rayleigh-B\'enard geometry is studied with truncated Boussinesq equations. Semiquantitative agreement is found with experimental results on helium for the turbulent threshold, and for the intensity and frequency spectrum of fluctuations at slightly higher Rayleigh numbers. It is argued that this transition conforms with abstract mathematical proposals of Ruelle and Takens, but that other transitions violate their picture.
McLaughlin et al. (1974) studied this question.