## 1998 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, 1998 through February 2, 1999

**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 is being achieved by analyzing recent laboratory dispersion data and developing an improved gravity current model for the lofting plume spread. The second is to enhance a hybrid Lagrangian dispersion model for predicting concentrations in buoyant plumes by including the improved gravity current model. 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:

During year 1 of the program, we focused on the first objective. Experiments on plume dispersion in a laboratory convection tank were recently conducted under another project to simulate full-scale dispersion in the CBL. The plume dispersion parameters or spreads in the lateral and vertical directions were analyzed for their dependence on downstream distance and source buoyancy. The focus here is on the lateral dispersion, which agreed well field observations. We briefly summarize: 1) new findings on the entrainment velocity for lofting plumes, and 2) new results on the lateral plume spread from an improved gravity current model.The experimental data has changed our conceptual picture and model of the lofting plume. In the new model, the elevated plume is assumed to be embedded vertically within the CBL entrainment layer and to spread laterally as a gravity current. The plume is assumed to lose buoyancy and pollutant mass due to entrainment by the CBL turbulence. Empirical estimates of the entrainment velocity were deduced from the variation of the mean entrapment---the fraction of the plume mass lying above the CBL top?with downstream distance. From the data, we found that the entrainment velocity decreased systematically and in inverse proportion to the source buoyancy flux, which is consistent with our intuition.

In addition, the above results led to an empirical relationship for the entrainment velocity, which was found to be inversely proportional to a Richardson number based on the entrainment layer thickness. The entrainment relationship was in good agreement with previous laboratory experiments on heat entrainment at the CBL top. This is encouraging since the earlier experiments dealt with an ``infinite" plane source at the CBL top instead of the finite, laterally-expanding plume source. Thus, the entrainment is observed to be independent of the source geometry.

A gravity current model was adopted for the lateral spread of the lofting plume. This predicts the flow or advancement of one fluid into another as a result of the density difference between them, where the advancing flow is the less dense fluid in the lofting plume. We derived a simple equation for the lateral spreading rate, which depends on the local buoyancy flux. For a plume with a conserved buoyancy flux, the spread equation can be integrated to give a simple power law dependence of spread on distance. However, for a lofting plume that is slowly eroded by the CBL turbulence, one must account for the buoyancy loss. Based on energy or buoyancy conservation, an expression for the time rate of change of the buoyancy flux was derived. The lateral spread was found by simultaneously solving the equations for the lateral spread and buoyancy using the empirical entrainment relationship.

Comparisons between the modeled lateral dispersion and the laboratory data were made with the buoyancy loss included and without it (for reference). For short distances, the results for the two cases were essentially identical and only at greater distances did they differ. For the constant buoyancy case, the lateral spread varied as the two-thirds power of distance. With the buoyancy loss included, the spread approached a short regime of the ``two-thirds" dependence but then fell below this curve at larger distances. The spread for the buoyancy loss model followed the laboratory data trends quite well for all cases and indeed better than the results for the constant buoyancy reference model. This lends credibility to the concept of buoyancy and mass loss of the lofting plume through CBL entrainment.

### Future Activities:

Our plans for year 2 are to extend a hybrid Lagrangian dispersion model by including the new gravity current model and a delayed source of pollutants at the CBL top. The Lagrangian model will be completed first for the calculation of the mean concentration field and then extended for the calculation of the concentration variance (i.e., concentration fluctuations).We also will consider a new treatment of particle and plume interaction with the stable layer above the CBL. In addition, we plan to submit a paper for journal publication on the gravity current model and the hybrid Lagrangian model.

### 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