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{\large{\bf
A numerical study of dispersion from a time-dependent source}}
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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
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\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.

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