Remarks on the principles of statistical fluid mechanics

This is an idiosyncratic survey of statistical fluid mechanics centering on the Hopf functional differential equation. Using the Burgers equation for illustration, we review several functional integration approaches to the theory of turbulence. We note in particular that some important contributions have been brought about by researchers working on wave propagation in random media, among which Uriel Frisch is not an exception. We also discuss a particular finite-dimensional approximation for the Burgers equation