PASSIVE SCALAR CONDITIONAL STATISTICS IN A MODEL OF RANDOM ADVECTION

We study numerically a model of random advection of a passive scalar b y an incompressible velocity field of different prescribed statistics. Our focus is on the conditional statistics of the passive scalar and specifically on two conditional averages. the averages of the time der ivative squared and the second time derivative of the scalar when its fluctuation is at a given value. We find that these two conditional av erages can be quite well approximated by polynomials whose coefficient s can be expressed in terms of scalar moments and correlations of the scalar with its time derivatives. With the fitted polynomials for the conditional averages, analytical forms for the probability density fun ction (pdf) of the scalar are obtained. The variation of the coefficie nts with the parameters of the model result in a change in the pdf. Th ree different kinds of velocity statistics, (i) Gaussian, (ii) exponen tial, and (iii) triangular, are studied, and the same qualitative resu lts are found demonstrating that the one-point statistics of the veloc ity field do not affect the statistical properties of the passive scal ar. (C) 1997 American Institute of Physics.