The calculation of correlation functions in the statistical theory of turbulent flows
Abstract
The field theory of turbulence is developed in a manner that eliminates inconsistencies found in earlier treatments, and leads to new insight into the nature of bounded shear flows. Formal results include the construction of a Ward identity that greatly simplifies analysis at the nonperturbative level, and the specific inclusion of a background field that is not a saddlepoint of the NavierStokes equation of motion. Correlation functions are calculated that correspond to the bare propagator given by a path integral generating functional developed by Domokos, KovesiDomokos and Zoltani. The functions are computed numerically for Gaussian, exponential, and whitenoise forceforce correlations. From these results it appears that an exponential form most closely realizes the observed correlation functions. For the whitenoise case, a simple, but very accurate, analytic form is derived for the xx and yy stresses, and frequency spectra are then obtained. The case of homogeneous isotropic turbulence using the DKDZ formalism is considered, and SchwingerDyson equations are presented for the exact Green's functions through the third order.
 Publication:

Ph.D. Thesis
 Pub Date:
 1990
 Bibcode:
 1990PhDT........46B
 Keywords:

 Shear Flow;
 Statistical Correlation;
 Turbulent Flow;
 Green'S Functions;
 Homogeneous Turbulence;
 Isotropic Turbulence;
 Random Noise;
 White Noise;
 Fluid Mechanics and Heat Transfer