## 2001 Progress Report: Buoyant Plume Dispersal in the Convective Boundary Layer: Analysis of Experimental Data and Lagrangian Modeling

**EPA Grant Number:**R826160

**Title:**Buoyant Plume Dispersal in the Convective Boundary Layer: Analysis of Experimental Data and Lagrangian Modeling

**Investigators:**Weil, Jeffrey C.

**Institution:**

**University of Colorado at Boulder**

**EPA Project Officer:**Shapiro, Paul

**Project Period:**February 3, 1998 through February 2, 2001 (Extended to February 2, 2003)

**Project Period Covered by this Report:**February 3, 2001 through February 2, 2002

**Project Amount:**$244,000

**RFA:**Exploratory Research - Physics (1997) RFA Text | Recipients Lists

**Research Category:**Water , Land and Waste Management , Air , Engineering and Environmental Chemistry

### Objective:

This research project will improve our knowledge and predictive capability of buoyant plume dispersion from elevated sources in the convective boundary layer (CBL). The focus is on modeling the mean and root-mean-square (rms) concentration fields due to such sources. There are three major objectives of this research project. The first is to increase our understanding of highly buoyant plumes that loft or remain near the CBL top and disperse downwards slowly; this includes developing an improved gravity current model for the lofting plume spread. The second objective is to enhance a hybrid Lagrangian dispersion model for predicting concentrations in buoyant plumes by including the gravity current model and other new features. The third objective is to further develop a simple analytical probability density function (PDF) model for the mean and rms concentration fields; this model is useful in air quality applications.

### Progress Summary:

During the first year of the grant, we modified our model of a buoyant plume lofting near the CBL capping inversion based on dispersion data from laboratory experiments. In the new model, we assumed the elevated plume to be embedded within the entrainment layer, capping the CBL and spreading laterally as a gravity current. We also assumed that the plume lost buoyancy and pollutant mass due to CBL turbulence entrainment. The entrainment velocity estimates obtained from the plume data showed that it decreased inversely with the source buoyancy; an empirical relationship deduced from the data agreed with previous experiments on heat entrainment at the CBL top.

We adopted a gravity current model for the lateral spread, which predicts the advancement of one fluid into another, due to the density difference between them. For a plume with a conserved buoyancy flux, an equation for the lateral spread led to a simple power law dependence of spread on distance. We accounted for the buoyancy loss for a lofting plume that was slowly eroded by the CBL turbulence from below. Comparisons between the modeled lateral dispersion and the laboratory data showed that the predicted spread followed the data trends with consistency. The results with the buoyancy loss model were more favorable than those for the constant buoyancy model.

During the second year of the grant, we modified the hybrid Lagrangian model to: (1) treat dispersion by the motion of buoyant particles rather than by a meandering plume as used earlier; (2) account for environmental turbulence effects on plumes through detrainment (or removal) of plume material by the ambient turbulence; and (3) incorporate the gravity current plume spreading at the CBL capping inversion. We included the treatment of dispersion by a large number of buoyant particles to improve the modeling of the plume interaction with the elevated inversion.

In the modified model, we tracked particles by superposing the plume rise velocity and the local ambient turbulence velocity, which was treated stochastically. We obtained the plume properties using equations for mass, momentum, and buoyancy conservation. Plume snapshots from convection tank experiments supported the detrainment concept. We made a preliminary evaluation by comparing model predictions of the mean plume height and crosswind-integrated concentration (CWIC) distribution with data from convection tank experiments. Our initial comparisons for a non-buoyant plume showed consistency with the laboratory data.

During the third year of the grant, we further developed the hybrid model by establishing consistency between the plume rise/entrainment model and the particle model. We required the number of particles detrained from the active plume core to be consistent with the equations governing the plume fluxes. For the plume sections in the mixed layer, the total probability of particles remaining in the plume at any distance was estimated from the plume momentum flux with and without considering detrainment. For the lofting plume, we estimated the probability from an integral of the entrainment velocity over distance.

We compared the model with laboratory data; it showed that the mean plume height and the vertical dispersion were consistent with the data, both as a function of distance and plume buoyancy. The maximum predicted plume heights were somewhat less than the laboratory data, a result that we attributed to the neglect of wind speed fluctuations in the model. One of the significant improvements of the modified Lagrangian model over the earlier model was the shape of the CWIC vertical profile. The profile showed a peak CWIC near the CBL top, and it was maintained over a considerable distance consistent with the laboratory data. However, for large distances, the model overestimated the concentrations in the mixed layer, due to an entrainment velocity deficiency. Finally, the predicted surface CWIC, which is of much practical interest and value, exhibited consistency with the laboratory data.

During the fourth year of the grant, we investigated the effect of light and variable winds on the concentration field by including longitudinal wind fluctuations. Such fluctuations are neglected in most plume models, but they can increase the along-wind dispersion, particularly near the source. As a first step, we investigated two analytical approaches: (1) a plume model with a randomly-varying wind speed; and (2) a time-integrated puff model with a similar wind. In both approaches, we determined the mean concentration by obtaining the average of concentration over the probability density function (PDF) of the wind speed. The PDF was characterized by its mean and rms fluctuation.

For the plume model, the results including the rms fluctuations yielded a slightly higher mean concentration near the source, but the effect was generally small. However, for the integrated puff approach, the results showed that for a low buoyancy plume, there was a systematic change in the maximum concentration and a shift in its location closer to the source. The changes were similar to the differences between the Lagrangian particle model (without rms wind fluctuations) and the laboratory data, and they help to explain these differences. The puff model is a more realistic representation of the variable wind effects than the plume model. As a result of this work, we modified the Lagrangian particle model to include a randomly-varying wind speed and more general dispersion formulations. We have begun testing the numerical code, and it will be completed in the next year.

### Future Activities:

A 1-year, no-cost extension was requested and granted to complete several modeling aspects that require further attention. These include modifications to: (1) incorporate the effects of longitudinal wind fluctuations; (2) improve the modeling of the plume interaction with the CBL top and stable layer interface; and (3) revise/enhance the entrainment velocity formulation for the lofting plume. Furthermore, we plan to enhance the PDF model by including the gravity current approach for lofting plumes. We also plan to prepare papers for journal publication.

### Journal Articles:

No journal articles submitted with this report: View all 3 publications for this project### Supplemental Keywords:

*atmospheric dispersion, Lagrangian stochastic modeling, mean and fluctuating concentrations, peak concentration estimates, buoyant plume modeling.*, Scientific Discipline, Air, Physics, Atmospheric Sciences, Ecological Risk Assessment, Engineering, Chemistry, & Physics, risk assessment, hazardous air pollutants, air pollution modeling system, ambient emissions, buoyant plume dispersal, Langraian modeling, atmospheric dispersion, probablility density function, ecological risk, mean and fugitive concentrations, convective boundry layers