Abstract
Model equations for turbulent flows generally must have the same Galilean transformation properties as the exact transport equations. We examine the transport equation of one-point velocity joint probability density function (JPDF) under Galilean transformations. The JPDF and its transport equation as well as the unclosed terms in the equation are shown to be Galilean invariant. For constant density flows they are also invariant under extended Galilean transformations. It is also shown that conditional statistics of any Galilean invariant variables conditional on velocity are invariant. The present work provides a basis and justification for using such conditional statistics in studying turbulent flows.
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