Statistical Mechanics of a Continuous Medium (Vibrating String with Fixed Ends)
UNIVERSITY OF MARYLAND College Park United States
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For the past twenty years there has been much discussion in fluid mechanics about the statistical theory of turbulence. It was J. Boussinesq 1872 and 0. Reynolds 1895, in their pioneering work, who expressed the idea that the turbulent velocity fluctuations of a fluid were much too complicated changing rapidly from one time and one point to another to be known in all their details we must be satisfied to study only some convenient mean values. The systematic use of statistical methods has led, since 1930, to very important results, in the fundamental works of Sir Geoffrey Taylor, Th. von Karman and A. N. Kolmogoroff, for instance. But, if we look carefully at all the results so far obtained, we see at first glance that they are not at all in the same close relation with the theoretical equations of fluid mechanics as the classical statistical mechanics bears to the Hamilton-Jacobie quations for a dynamical system having a finite number of degrees of freedom.
- Statistics and Probability