Abstract
A Lagrangian stochastic model of two-point displacements which includes explicitly the effects of molecular diffusion and viscosity is developed from the marked-particle model of Durbin (1980) and used to study the influence of these molecular processes on scalar fluctuations in stationary homogeneous turbulence. It is shown that for the homogeneous scalar field resulting from a uniform-gradient source distribution or for a cloud produced by a source large compared with the Kolmogorov microscale, the variance of scalar fluctuations but not as much as the effect of reducing Pr to a finite value. A finite sampling volume and infinite Pr is not necessarily equivalent to a finite value of Pr and a point sample.Timescales for important stages in the development of the scalar field in a cloud or downwind of a continuous source (for example, the onset of dissipation or the stage at which fluctuations are dominated by internal structure or ‘streakiness’ within the cloud rather than bulk motion or ‘meandering’) have been estimated. For small sources and large Re these timescales are significantly less than the integral timescale tL. Many real flows evolve on the timescale tL, so that the present results for stationary homogeneous turbulence should apply to such flows for small sources and large Re, a situation typical of the atmosphere.
Published Version
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