Onsager's Contribution to Turbulence Theory: Vortex Dynamics and Turbulence in Ideal Flow

Onsager's contribution to turbulence theory is concentrated in a brief abstract and a short paper; it is dense, bold, and important; its full significance is only now beginning to be seen. It opened two important lines of inquiry, on the relation between the physical phenomenology of turbulence and the analytical properties of its equations of motion, and on the role of vortices in the dynamics of turbulence. Both topics are related to Onsager's other interests; the first to his work on irreversible processes, and the second to his work on electrolytes and superfluids.

Onsager's note on the distribution of energy in turbulence [28] is a one-paragraph rederivation of the Kolmogorov spectral law. Kolmogorov's work dates to the late thirties but was not known in the west until after the war; it is one of Kolmogorov's greatest achievements, and Onsager's independent derivation is no mean feat. The argument can be readily summarized: Turbulence is typically stirred on scales much larger than the scales where energy is dissipated; in three-dimensional space, the important "inertia!" range of scales that mediate between stirring and dissipation has a spectrum of universal form, which can be deduced from a few simple assumptions…