On Homogeneous Non-Isotropic Turbulence Connected with a Mean Motion Having a Constant Velocity Gradient. I

Abstract

The statistical theory of turbulence connected with a mean motion has received much less attention thus far than the theory of homogeneous isotropic free turbulence. ²) The circumstance that the field in general will not be homogeneous introduces formidable difficulties, while at the same time the non-isotropic character increases the number of unknowns. In order to cope with the former difficulty the supposition is sometimes made that correlation tensors of the type $\overline {{{u'}_i}{{u''}_j}}$, where u′ _i is a fluctuating velocity component measured at a point S′ with coordinates x′ _h and u″ _j is a fluctuating velocity component measured at a point S″ with coordinates x″ _h = x′ _h + ξ _h , vary only slowly with the x _h if the ξ _h remain unchanged, whereas their variation with the ξ _h in general will be much more rapid.

Sheldon Travelling Fellow, Harvard University. — The two authors had arrived independently at the system of equations (18) and their Fourier transforms (27). A visit of Dr. Mitchner to Delft gave an opportunity for a discussion on this subject. Dr. Mitchner had also worked out the Fourier transforms for a more general case, to be given in the second part of this paper.