REALIZABILITY OF 2ND-MOMENT CLOSURE VIA STOCHASTIC-ANALYSIS

It is shown that realizability of second-moment turbulence closure mod els can be established by finding a Langevin equation for which they a re exact. All closure models currently in use can be derived formally from the type of Langevin equation described herein. Under certain cir cumstances a coefficient in that formalism becomes imaginary. The regi me in which models are realizable is, at least, that for which the coe fficient is real. The present method does not imply unrealizable solut ions when the coefficient;is imaginary, but it does guarantee realizab ility when the coefficient is real; hence, this method provides suffic ient, but not necessary, conditions for realizability. Illustrative co mputations of homogeneous shear flow are presented. It is explained ho w models can be modified to guarantee realizability in extreme non-equ ilibrium situations without altering their behaviour in the near-equil ibrium regime for which they were formulated.