The Distribution of Dissolved Oxygen in a Stream with Time Varying Velocity

The Distribution of Dissolved Oxygen in a Stream with Time Varying Velocity 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Water Resources Research Wiley

The Distribution of Dissolved Oxygen in a Stream with Time Varying Velocity

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Publisher
Wiley
Copyright
Copyright © 1968 by the American Geophysical Union.
ISSN
0043-1397
eISSN
1944-7973
DOI
10.1029/WR004i003p00639
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Water Resources ResearchWiley

Published: Jun 1, 1968

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