On the Statistical Theory of Turbulence

Citation

Chuang, Feng-Kan (1950) On the Statistical Theory of Turbulence. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2TJM-BK44. https://resolver.caltech.edu/CaltechETD:etd-10302003-154021

Abstract

The present work starts with a study of isotropic turbulence which was introduced by G. I. Taylor in 1935. The different notions of averages are critically examined. The notion of stochastic average is then introduced and the general transport equation is developed. After a detailed study of kinematics of turbulence, the concept of correlation and spectrum, the correspondence between the Karman-Howarth equation and the spectrum equation is made. The turbulence decay is studied. A theory for turbulence decay at large Reynolds number is proposed. In the study of turbulence spectrum, different assumptions on the transfer function are critically discussed and the solution using Heisenberg's assumption is obtained explicitly. The spectrum is further studied by trying to fit the turbulence phenomenon into a general scheme of stochastic processes. In the second part of the work, an entirely different approach to the statistical theory is made. Linearized vorticity transport theory is developed and finally the non-linear effects in turbulence are studied.

Thesis Files