C. F. v. Weizsächer on Quasistationary Isotropic Turbulence Compared With Onsager's Statistical Hydrodynamics

ABSTRACT We present in English Carl Friedrich v. Weizsäcker's historic 1948 derivation of the 5/3 law for energy transfer in turbulence via dimensional analysis in real space. As the relevant standard for comparison, we also present Onsager's derivation of the 5/3 law via dimensional analysis in k ‐space. v. Weizsäcker began by assuming a cubic volume filled with isotropic quasi‐stationary turbulence, where he then introduced a systematic partitioning of that volume into ever smaller nested cubes. Weizsäcker's dimensional analysis in real space parallels Onsager's 1949 derivation in k ‐space and also foreshadows the fractal beta model. We compare several steps in Onsager's and Weizsäcker's approaches and then discuss the extension of Weizsäcker's dimensional analysis to the beta model. The more recent experimental violations of the assumptions of homogeneity and isotropy are then discussed, and a practical measure is offered to test for ‘weak isotropy’ in data.