A free boundary problem arising in a kinematic wave model of channel flow with infiltration
Author:
B. Sherman
Journal:
Quart. Appl. Math. 39 (1981), 87-96
MSC:
Primary 76S05
DOI:
https://doi.org/10.1090/qam/613953
MathSciNet review:
613953
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Abstract: Water flowing down a dry channel and infiltrating into the channel bed constitutes a free boundary problem. The free boundary is the time history of the water edge or front. In this paper we discuss a kinematic wave model of the problem. The problem is formulated in Sec. 1 and the results summarized in Sec. 2. In Secs. 3 and 4 the mathematical details are carried out, and in Sec. 5 a model using the continuity and momentum equations of hydraulics is discussed.
C. L. Chen, Surface irrigation using kinematic wave method, J. Irrig. Drain, Div. Amer. Soc. Civil Eng. 96(IR1), 39–46 (1970)
R. Courant and D. Hilbert, Methods of mathematical physics, vol. 2, Interscience, New York, 1962
J. A. Cunge and D. A. Woolhiser, Irrigation systems, in Unsteady flow in open channels, edited by K. Mahmood and V. Yevjevich, chapter 13, 522–537, Water Resources Publications, Fort Collins, Colorado, 1975
P. S. Eagleson, Dynamic hydrology, McGraw-Hill, 1970
F. M. Henderson, Flood waves in prismatic channels, J. Irrig. Drain. Div. Amer. Soc. Civil Eng. 89, 39–67 (1963)
F. M. Henderson, Open channel flow, Macmillan, New York, 1966
B. Sherman and V. P. Singh, A kinematic model for surface irrigation, Water Resources Res. 14, 357–364 (1978)
B. Sherman and V. P. Singh, A kinematic model for irrigation II (submitted to Water Resources Research)
R. E. Smith, Border irrigation advance and ephemeral flood waves, J. Irrig. Drain, Div. Amer. Soc. Civ. Eng. 98(IR2), 289–307 (1972)
J. J. Stoker, Water waves, Interscience, New York, 1957
D. A. Woolhiser, Discussion of: Surface irrigation using kinematic wave method by C. Chen, J. Irrig. Div. Amer. Soc. Civil Eng. 96, 498–500 (1970)
C. L. Chen, Surface irrigation using kinematic wave method, J. Irrig. Drain, Div. Amer. Soc. Civil Eng. 96(IR1), 39–46 (1970)
R. Courant and D. Hilbert, Methods of mathematical physics, vol. 2, Interscience, New York, 1962
J. A. Cunge and D. A. Woolhiser, Irrigation systems, in Unsteady flow in open channels, edited by K. Mahmood and V. Yevjevich, chapter 13, 522–537, Water Resources Publications, Fort Collins, Colorado, 1975
P. S. Eagleson, Dynamic hydrology, McGraw-Hill, 1970
F. M. Henderson, Flood waves in prismatic channels, J. Irrig. Drain. Div. Amer. Soc. Civil Eng. 89, 39–67 (1963)
F. M. Henderson, Open channel flow, Macmillan, New York, 1966
B. Sherman and V. P. Singh, A kinematic model for surface irrigation, Water Resources Res. 14, 357–364 (1978)
B. Sherman and V. P. Singh, A kinematic model for irrigation II (submitted to Water Resources Research)
R. E. Smith, Border irrigation advance and ephemeral flood waves, J. Irrig. Drain, Div. Amer. Soc. Civ. Eng. 98(IR2), 289–307 (1972)
J. J. Stoker, Water waves, Interscience, New York, 1957
D. A. Woolhiser, Discussion of: Surface irrigation using kinematic wave method by C. Chen, J. Irrig. Div. Amer. Soc. Civil Eng. 96, 498–500 (1970)
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Article copyright:
© Copyright 1981
American Mathematical Society
