A detailed examination is performed of the relationship between stocha
stic Lagrangian models-used in PDF methods-and second-moment closures.
To every stochastic Lagrangian model there is a unique corresponding
second-moment closure. In terms of the second-order tensor that define
s a stochastic Lagrangian model, corresponding models are obtained for
the pressure-rate-of-strain and the triple-velocity correlations (tha
t appear in the Reynolds-stress equation), and for the pressure-scramb
ling term in the scalar flux equation. There is an advantage in obtain
ing second-moment closures via this route, because the resulting model
s automatically guarantee realizability. Some new stochastic Lagrangia
n models are presented that correspond (either exactly or approximatel
y) to popular Reynolds-stress models.