| Fri January 11th 2008 11:00 | Seminar | Turbulent Dispersion from a Line Source: Further Lessons from a Simple Flow Steven Pope |
Details:This talk is part historical, part tutorial, and in part describes recent research. The history of turbulent dispersion extends back to Taylor’s classic 1921 paper, and the modeling tools now used extend back further to Langevin (1908). Dispersion from a line source was studied extensively in the 1980s (e.g., Warhaft 1984, Anand & Pope 1985), and more recently by Sawford (2004). Although this dispersion problem is in some sense very simple, the relatively small length scale of the initial thermal wake poses a challenge to statistical models. For the mean temperature field, a standard turbulent diffusion model is qualitatively incorrect. A PDF model based on the Langevin equation is successful in describing the mean field; but (with the standard “interaction by exchange with the mean” (IEM) mixing model) the predictions of the temperature variance are qualitatively incorrect. Sawford (2004) showed that both the mean and variance can be accurately described using the IECM model (in which mixing is conditioned on velocity), but only if the mixing time scale is radically altered in an empirical way close to the source. In recent work (Viswanathan & Pope 2008), we obtain an exact expression for the appropriate time scale close to the source. Combining this with the known far-field behavior, we obtain a PDF model which accurately describes the whole temperature field with a minimum of empirical input. This model is applied to arrays of line sources and is shown to yield excellent agreement with Warhaft’s experimental data. | ||
