The Boltzmann- and the Klimontovich formalisms with reference to turbulence resolution

The Navier-Stokes equation expressed in terms of Klimontovich microscopic density is compared with the conventional one based on the Boltzmann formalism. Their difference is described by the two-point BBGKY equation. An implication is given that the averaging procedure from the Klimontovich to the Boltzmann formalism wipes out not only thermal agitation, but also a certain hydrodynamic turbulence. This is substantiated by agreement with measurements due to Schubauer and Klebanoff.