Markovian properties of passive scalar increments in grid-generated turbulence

Recent research (Renner, Peinke and Friedrich 2001 J. Fluid Mech. 433 383) has shown that the statistics of velocity increments in a turbulent jet exhibit Markovian properties for scales of size greater than the Taylor microscale, lambda. In addition, it was shown that the probability density functions (PDFs) of the velocity increments, v(r), were governed by a Fokker-Planck equation. Such properties for passive scalar increments have never been tested. The present work studies the (velocity and) temperature field in grid-generated wind tunnel turbulence for Taylor-microscale-based Reynolds numbers in the range 140less than or equal toRlambdaless than or equal to582. Increments of longitudinal velocity were found to (i) exhibit Markovian properties for separations rgreater than or equal tolambda and (ii) be describable by a Fokker-Planck equation because terms in the Kramers-Moyal expansion of order >2 were small. Although the passive scalar increments, ddelta(r), also exhibited Markovian properties for a similar range of scales as the velocity field, the higher-order terms in the Kramers-Moyal expansion were found to be non-negligible at all Reynolds numbers, thus precluding the PDFs of delta(r) from being described by a Fokker-Planck equation. Such a result indicates that the scalar field is less Markovian than the velocity field-an attribute presumably related to the higher level of internal intermittency associated with passive scalars.