Form Approved
REPORT DOCUMENTATION PAGE
OMB No. 0704-0188
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1. AGENCY USE ONLY (Leave blank)
2. REPORT DATE
3. REPORT TYPE AND DATES COVERED
January 1998
4. TITLE AND SUBTITLE
5. FUNDING NUMBERS
Analysis of Linear and Monoclinal River Wave Solutions
DA Project DT08
CWIS Project 7VC103
6. AUTHORS
Michael G. Ferrick and Nicholas J. Goodman
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
8. PERFORMING ORGANIZATION
REPORT NUMBER
U.S. Army Cold Regions Research and Engineering Laboratory
72 Lyme Road
CRREL Report 98-1
Hanover, New Hampshire 03755-1290
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
10. SPONSORING/MONITORING
AGENCY REPORT NUMBER
Office of the Chief of Engineers
Washington, D.C. 20314-1000
For conversion of SI units to non-SI units of measurement consult Standard Practice for Use of the
11. SUPPLEMENTARY NOTES
International System of Units (SI), ASTM Standard E380-93, published by the American Society for Testing and Materials,
1916 Race St., Philadelphia, Pa. 19103.
12a. DISTRIBUTION/AVAILABILITY STATEMENT
12b. DISTRIBUTION CODE
Approved for public release; distribution is unlimited.
Available from NTIS, Springfield, Virginia 22161.
13. ABSTRACT (Maximum 200 words)
Linear dynamic wave and diffusion wave analytical solutions are obtained for a small, abrupt flow increase from
an initial to a higher steady flow. Equations for the celerities of points along the wave profiles are developed from
the solutions and related to the kinematic wave and dynamic wave celerities. The linear solutions are compared
systematically in a series of case studies to evaluate the differences caused by inertia. These comparisons use the
celerities of selected profile points, the paths of these points on the x-t plane, and complete profiles at selected
times, indicating general agreement between the solutions. Initial diffusion wave inaccuracies persist over rela-
tively short time and distance scales that increase with both the wave diffusion coefficient and Froude number.
The nonlinear monoclinal wave solution parallels that of the linear dynamic wave but is applicable to arbitrarily
large flow increases. As wave amplitude increases the monoclinal rating curve diverges from that for a linear
wave, and the maximum Froude number and energy gradient along the profile increase and move toward the
leading edge. A monoclinaldiffusion solution is developed for the diffusion wave equations, and dynamic wave
diffusion wave comparisons are made over a range of amplitudes with the same case studies used for linear
waves. General dimensionless monoclinaldiffusion profiles exist for each depth ratio across the wave, while cor-
responding monoclinal wave profiles exhibit minor, case-specific Froude number dependence. Inertial effects on
the monoclinal profiles occur near the leading edge, increase with the wave amplitude and Froude number, and
are responsible for the differences between the dimensionless profiles.
14. SUBJECT TERMS
15. NUMBER OF PAGES
30
Analytical solutions
Flood routing
River waves
Diffusion wave
Linear waves
Unsteady flow
16. PRICE CODE
Dynamic wave
Monoclinal waves
17. SECURITY CLASSIFICATION
18. SECURITY CLASSIFICATION
19. SECURITY CLASSIFICATION
20. LIMITATION OF ABSTRACT
OF REPORT
OF THIS PAGE
OF ABSTRACT
UNCLASSIFIED
UNCLASSIFIED
UNCLASSIFIED
UL
Standard Form 298 (Rev. 2-89)
NSN 7540-01-280-5500
Prescribed by ANSI Std. Z39-18
298-102
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