We derive a system of equations for the statistical moments of a passive scalar dispersed in a turbulent flow from the transport equation of the probability density function. We solve the system through a Green’s function and we obtain a formally exact solution for the statistical moments of the passive scalar concentration. We use this solution to achieve an analytical relationship for the second moment of a passive scalar released from a point source. Comparison with wind-tunnel experiments shows that the relationship is valid also in a neutral turbulent boundary layer if the reflection onto the ground and an appropriate model for the mixing timescale are considered. This approach, combined with a suitable model for the distribution of the concentration, allows the statistics of the passive scalar to be obtained in the whole domain in a closed and ready-to-use form.

Solution for the statistical moments of scalar turbulence / Bertagni, Matteo B.; Marro, Massimo; Salizzoni, PIETRO STEFANO; Camporeale, CARLO VINCENZO. - In: PHYSICAL REVIEW FLUIDS. - ISSN 2469-990X. - ELETTRONICO. - 4:12(2019). [10.1103/PhysRevFluids.4.124701]

Solution for the statistical moments of scalar turbulence

Matteo B. Bertagni;Massimo Marro;Pietro Salizzoni;Carlo Camporeale
2019

Abstract

We derive a system of equations for the statistical moments of a passive scalar dispersed in a turbulent flow from the transport equation of the probability density function. We solve the system through a Green’s function and we obtain a formally exact solution for the statistical moments of the passive scalar concentration. We use this solution to achieve an analytical relationship for the second moment of a passive scalar released from a point source. Comparison with wind-tunnel experiments shows that the relationship is valid also in a neutral turbulent boundary layer if the reflection onto the ground and an appropriate model for the mixing timescale are considered. This approach, combined with a suitable model for the distribution of the concentration, allows the statistics of the passive scalar to be obtained in the whole domain in a closed and ready-to-use form.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2777413