Internal Report

Studies in classical turbulence theory

Author Document Type Year Download File size
Erik Lindborg Doctoral thesis 1996 Not available
ISSN 0348-467X


The thesis deals with various problems in classical turbulence theory. The kinematical theory of homogeneous axisymmetric turbulence is given a simple and concise formulation. A representation of two-point correlation tensors of homogeneous axisymmetric turbulence is developed, such that each measurable correlation corresponds to a single scalar function, and moreover such that the equations of continuity take the most simple form. The Poisson equation for the pressure-strain tensor is solved in terms of measurable velocity correlations. Kolmogorov's third order structure function law is derived from an equation where the pressure terms and mean flow gradient terms are retained. A new inertial range law, relating the two-point pressure-velocity correlation to the single-point pressure-strain tensor, is derived. This law shows that the two-point pressure-velocity correlation, just as the third order structure function, grows linearly with the separation distance in the inertial range. An inertial range law is also derived for the third order velocity-enstrophy structure function of two-dimensional turbulence. The turbulence closure problem is analysed, starting from the hierarchy of single time Fourier moment equations. The geometric properties of the equation hierarchy are investigated. The number of independent components of the n:th order isotropic correlation tensor of Fourier velocity components is proved to be n+1 for n>=4 . It is shown that a closure on the fourth order level would lead to inconsistencies. It is argued that the energy spectrum decreases slower than E(k)=exp(-bk) in the dissipation range. Here, b is any positive constant. A comparison between EDQNM and DNS calculations of axisymmetric low Reynolds number turbulence is presented. The agreement between the results is found to be rather good. However, it is argued that this does not permit us to draw any conclusion for the high Reynolds number case. The prediction capability of pressure-strain models, within the context of RST-closures, is investigated. Severe difficulties are found when the antisymmetric, rotational part of the mean flow gradient tensor, has a stronger influence than the symmetric part.