Prandtl and the G\"ottingen School

TL;DR

This paper provides a historical review of Ludwig Prandtl's contributions to boundary layer theory and turbulence, highlighting his early derivation of the Kolmogorov length scale before Kolmogorov's work.

Contribution

It uncovers Prandtl's independent derivation of turbulence scales prior to Kolmogorov, based on historical analysis of original notes and correspondence.

Findings

Prandtl developed an energy cascade model for turbulence in 1945.

Prandtl's work predated Kolmogorov's K41 theory.

Historical analysis reveals Prandtl's early insights into turbulence scales.

Abstract

This is a historical review of "Prandtl and the G\"ottingen School" from his first work in 1898 to after WWII. We report the development of the boundary layer theory and the investigations that lead Ludwig Prandtl in the spring of 1945 to use a energy cascade model to derive for fully developed turbulence the Kolmogrov length scale. Working at the end of WWII he was not aware of the work by Kolmogorov. Thus Ludwig Prandtl was before Onsager, von Weiz\"acker, and Heisenberg in rederiving parts of K41 theory. In our historical analysis we rely heavily on exchanges between Ludwig Prandtl with Theodore von K\'arm\'an and Goeffrey Ingram Taylor and on the original notes by Ludwig Prandtl and others.