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We propose a new Eulerian turbulence theory to obtain a closed set ofequations for homogeneous, isotropic turbulent velocity field correlations andpropagator functions by incorporating constraints of random Galileaninvariance. This incorporation generates a few different equations forpropagator and the present theory suggests a way to utilize them into theclosure solutions of two-time and single-time velocity correlations' equationsso as to properly account for random sweeping phenomena. The present theoryyields exact solutions when applied to simple model problem of randomoscillator.

A new Eulerian theory of turbulence constrained by random Galilean invariance