The solutions of the equations that describe the distribution of biochemical oxygen demand (BOD) and dissolved oxygen deficit (DOD) in an idealized natural stream with a time varying velocity can be obtained intuitively from an extension of the well known solutions, which apply for a constant stream velocity. By introducing the concept of the release time, i.e., the time τ(χ, t) at which the particle of water being observed at point χ at time t was released at point χ = 0, the solution for the time varying flow and velocity follows. The formal solution can also be obtained using the LaPlace transform with respect to the space variable χ. An application of this analysis to the effect of a random component of velocity on the BOD and DOD distributions indicates that the standard deviations of the resulting BOD and DOD distributions are approximately equal to the coefficient of variation of the velocity times the BOD and DOD distributions calculated using the mean velocity.
Water Resources Research – Wiley
Published: Jun 1, 1968
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