## 1999 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, 1999 through February 2, 2000

**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:

The aim of this research program is to improve our knowledge and predictive capability of buoyant plume dispersion from elevated sources in the convective boundary layer (CBL). The focus is on modeling of the mean and root-mean-square (rms) concentration fields due to such sources. There are three major objectives. 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 develop further 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:

This is a summary of the project to date including an overview of Year 1, but with focus on Year 2. In Year 1, we modified our model of a buoyant plume lofting near the CBL capping inversion based on dispersion data from laboratory experiments obtained under another project. In the new model, the elevated plume was assumed to be embedded within the entrainment layer capping the CBL and to spread laterally as a gravity current. The plume was assumed to lose buoyancy and pollutant mass due to entrainment by the CBL turbulence. Estimates of the entrainment velocity deduced from the plume data showed that it decreased inversely with the source buoyancy flux and also inversely with a Richardson number based on the entrainment layer thickness. The empirical relationship obtained was in agreement with previous experiments on heat entrainment at the CBL top.For the lateral spread, we adopted a gravity current model, which predicts the advancement of one fluid into another as a result of the density difference between each of 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. For a lofting plume that was slowly eroded by the CBL turbulence, the buoyancy loss was included using a buoyancy conservation equation. Comparisons between the modeled lateral dispersion and the laboratory data showed that the predicted spread followed the data trends quite well. The results with the buoyancy loss included were indeed better than those for the constant buoyancy model. This lends credibility to the concept of buoyancy and mass loss from the lofting plume through CBL entrainment.

In Year 2, we modified the hybrid Lagrangian dispersion 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. The treatment of dispersion by a large number of buoyant particles was included to improve the modeling of the plume interaction with the elevated inversion.

In the modified model, particles were tracked by superposing the plume rise velocity and the local ambient turbulence velocity, which was treated stochastically. The buoyant plume properties were obtained using equations for mass, momentum, and energy (or buoyancy) conservation. The detrainment concept was supported by plume snapshots from convection tank experiments, which showed segments of tracer material becoming detached from the "active" plume core.

A preliminary evaluation was made by comparing model predictions of the mean plume height and crosswind-integrated concentration (CWIC) distribution with dispersion data from convection tank experiments. The initial focus was on a nonbuoyant plume driven by source momentum. The magnitude of the detrainment coefficient was found to be far smaller than the usual entrainment coefficient. In addition, the mean plume height increased rapidly and attained a maximum value slightly greater than the equilibrium height before subsiding to the latter farther downstream. The model trajectory and surface CWIC agreed well with the laboratory data; the predictions were typically within 15 percent of the measurements. Furthermore, the vertical profiles of the CWIC matched their laboratory counterparts rather well.

For the buoyant sources, the mean plume height increased more rapidly, with the maximum heights ranging from 70 to 85 percent of the CBL depth and occurring closer to the source. The predicted heights were somewhat less than the laboratory data, but the plume trajectories exhibited trends similar to the data. The predicted surface CWIC profiles were qualitatively similar to the data, but the CWIC exceeded the measurements near the source. This behavior was probably due to the neglect of longitudinal wind fluctuations in the model.

### Future Activities:

Our plans for Year 3 are to extend the modified hybrid Lagrangian model by: (1) including the effects of longitudinal wind fluctuations, (2) ensuring a continuous treatment of detrainment as the plume passes from the mixed layer into the elevated inversion layer, and (3) improving the plume interaction with the CBL top and stable layer interface. In addition, we seek a model extension to allow for the calculation of the rms concentration fluctuation. Furthermore, we plan to enhance the PDF model by including the gravity current approach for lofting plumes. We also plan to prepare several 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