ON THE CONTINUITY OF STOCHASTIC-MODELS FOR THE LAGRANGIAN VELOCITY INTURBULENCE

Inertial sub-range statistics of stochastic models for the Lagrangian velocity in turbulent flow have been examined. For Markovian models it is shown that consistency with Kolmogorov's theory of local isotropy requires that the Lagrangian velocity be a continuous function of time . This limits suitable Markov models to those which can be represented by a stochastic differential equation. Markov models in which the vel ocity is discontinuous (and a class of non-Markovian jump models) are not consistent with Kolmogorov's theory. Modifications to Kolmogorov's theory to account for the effects of intermittency are shown to be no n-Markovian, but still correspond to a Lagrangian velocity which is co ntinuous. In Gaussian homogeneous turbulence only continuous Markov mo dels predict that the particle displacement is Gaussian. For a Markovi an jump model, the particle displacement distribution is leptokurtic w ith a maximum excess of about 0.67, which is inconsistent with wind tu nnel data in grid turbulence.