\documentstyle[12pt]{article} \textheight 24 cm \textwidth 16 cm \setlength{\parsep}{0.5ex plus0.2ex minus0.1ex} \newcommand{\singlespacing}{\let\CS=\@currsize\renewcommand{\baselinestretch} {1.0}\tiny\CS} \newcommand{\doublespacing}{\let\CS=\@currsize\renewcommand{\baselinestretch} {1.5}\tiny\CS} \doublespacing \begin{document} \begin{center} {\large{\bf A numerical study of dispersion from a time-dependent source}} \end{center} \vspace{0.5cm} {\singlespacing \begin{center} \begin{tabular}{ccc} D. C. Dalal & and & B. S. Mazumder \\ Department of Mathematics & & Physics and Applied Mathematics Unit\\ Indian Institute of Technology & & Indian Statistical Institute\\ Guwahati 781 001, India & & Calcutta 700 035, India \end{tabular} \end{center}} \vspace{0.5cm} \singlespacing \noindent {\bf Abstract - } The dispersion of contaminants from a time dependent release is an important problem in controlling pollution. The aim of this work is to explore the dispersion of passive contaminants in a turbulent flow due to the combined effect of logarithmic velocity and eddy diffusivities, when the distribution of concentration across the flow is prescribed as a harmonic function of time. The transport equations have been solved numerically for a better understanding the dispersion process of contaminant in the flow influenced by the frequency of oscillatory release. Calculations have been made over a gravel bed and compared with the experimental findings. A combined finite difference implicit scheme of central and 4-point upwind differences has been used to solve the unsteady convective diffusion equations. It is shown how the mixing of concentration of solute is influenced by the logarithmic velocity, the eddy diffusivities and the frequency of oscillatory release. The problem has been studied for time periodic continuous line as well as point sources. The concentration profiles for the steady elevated sources agree well with the existing experimental data. It has been observed that for low-frequency, the iso-concentration lines become elongated without any oscillation in concentration in the longitudinal direction whereas, for higher frequency, the contours show a decaying oscillatory nature in concentration distribution along the downstream direction. It is worth mentioning that the effect of the gravel bed is not significant in the main flow except for a small effect near the boundary. Injection of materials with low frequency does not effect much the nature of steady release whereas, with an increase of frequency, the oscillatory nature of injection gets reflected in the concentration distribution along the downstream distance. Along the lateral direction there is an oscillation in concentration which is directly related to the injection frequency and fluctuations gradually decay downstream. As the contaminant moves faster for a higher elevated source than for a lower one, there is a tendency to develop an asymmetry in dispersion of materials when it is injected near the bottom wall. This perhaps due to the eddies formation near the wall which increase the mixing processes. \end{document} 