Camputer-simulated deformation af meandering river patterns Beek, Stuart Murray, Ph.D.

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Camputer-simulated deformation af meandering river patterns
Beek, Stuart Murray, Ph.D.
University r:Á MinDe80~~ 1988
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Cornputer-simulated deÎormatioD oi meandering river pattt!rns
Beek, Stuart Murray, Ph.D.
University cL Minlleaota., 1988
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1S. ether
U·MI
COHPUTER-SIMULAïED OEFORHATION or
MEANOERING RIVER PATTERNS
A THESIS
SUBMITTED TO THE FACULTY OF THE G?~OUATE SCHOOL
OF THE UHIVERSITY OF MINHESOTA
Sy
Stuart Murray Beek
IH PARTlAL FULFILLMEHT OF THE REQUIREMEHTS
FOR !HE OEGREE OF
DOCTOR OF PHILOSOPHY
June, 1988
Stuart Murray Beek
All RightS ~eserved
CONTENTS
1. INTRODUCTION..... . •• •••••••••. . . . . . . . . •.••••••••••• l
2. DESCRrPTrON OF P~YSICAL PROCESSES.................. 27
2.1 Flow Fiel d. .. . .•. .•. •. . . . . . . . . . . . . .. . ••••••••• Z7
2.2 Channel Oeforrnation........................... 39
3. THEORY ~............••..•.•.• 4-Z
3.1 Ge~eral Solution............... ........•..•... ~Z
3.2 Sine·Generated Meander Patterns.. ....••....... 87
3.3 Linear Stability Analysis...... ......•........ 91
3.4 Dimensional Considerations .......'.........••.. 94
3.S Proposed Oeformation Model.................... 98
4. NUMERrCAL HETHOOS .....•.................•.....•...• 106
4.1 Coordinate Transformation ............•.•.••.•• 106
4.2 Depth-Averaqed Velocities ...........•.•....••. 114
4.3 Cha.nnelOeformation 131
5. RESULTS OF NUMERICAL EXPERrMEHTS .......•••...•...•• 134
5.1 [ledTopography.................... ..••••.•.••. 134-
5.2 Oepth·Averaged lJelocity Field........•........ 147
5.3 Channel Deformation. 16~
6. CONCLUSIONS .......•..•••...............•.•••••••••• 196
7. RCFERENCES ........•................-.......••..•__•.. 198
. i .
LIST OF FIGURES
Figure 1.1. Klaralven River, Sweden.................. 4
Figure 1.2. Development of a meandering
channe1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
~
Figure 1.3. Typical f~ow patterns in a meandering
channe1. . . . . . . . . . . . . . . . . . •. . •. . . . . . . . . . . . 7
Figur~ 1.4. Sine-generated meander pattern........... 10
Figure 1.5. Hickin's bank erosion model.............. 12
Figure 1.6. Ikeda-Parker-Sawai bank erosion
mode1. . . . . • . . . . . . . . . • • . • . • • . • . •• • •• • . . . . . 13
Figure 1.7. Genesee River near Mount Morr;s Dam, New
'(ark,1938-1954.................... IS
F~gure 1.8. Deveiopment of a neek cutoff............. 17
Figure 1.9. Reid's self-stabilization model.......... 18
Figure 1.10. Initial conditions....................... 19
Figure 1.11. Example of self-stabilization 21
Figure 1.12. Example of neek cutoff development....... 22
Figure 1.13. Three different types of behavior........ 23
Figure 1.14. Tendeney of the Ikeda-Parker-Sawai
mode 1. . . . . . • • . . . . . . • . . . • . . • • . . . . • • • • . . • • • 24
Figcre 2.1. Superelevation........................... 28
Figure 2.2. Seeondary flow and bed topography........ 30
Figure 2.3. Secondary flow and bed topography in a
large amplitude meander pattern.......... 32
Figure 2.4. Secondary flow and bed topography in a
sma11 amplitude meander pattern.......... 33
Figure 2.S. Forces aeting on a sediment
particle 3S
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Figure 2.6. Depth-averaged velocity pattern in a
large amplitude meander pattern_......... 37
Figure 2.7. Depth-averaged velocity pattern in a
small amplitude meander pattern.......... 38
Figure Z.S. Rohrer's bank erosion mC)ce1..•.~..•...... 40
0............
Figure 3.1. Coordinate system........••. 43
~
Figure 1.2. Near-bed veTocity vector................. 47
Figure l.3. Transverse bed slope, Zimmerman and
Kennedy (1978) ..........•••• ~............ 51
Figure 3.~. Pembina River cross sections.•.........~. 52
Figure 3.5. Transverse bed sloge parameter........... 54
Figure 3.6. Transverse bed slope 55
Figure 3.7. Cross sectional shape....••.............. 57
Figure 3.8. Proposed cross sectional shape.... 59
Figure 3.9. Transverse bed slope lag................. 63
Figure 3.11. Dimensionless wavelength.. ••. 97
Figure 3.12. Half-width to depth ratiQ................ 99
Figure 3.13. Wavelength to half-width ratio....••••••• 100
Figure 3.14. Cnannel deformation phase lag.••••••••••• lal
Figure 3.15. The transverse bed slope parameter .•••••. 104
Figure 3.16. Sediment transportatian exponent••••••••• 105
Figure 4.1. Determinatien of 8...............•.•••... 107
s ~....
Figure 4.2. Determinatien of III
Figure 4.3. Curvilinear coordinates .••••.••••••.•.••• 113
Figure 4.4. Control volume for th~ S:.direction
momentum equation ........•.••••.•.••••.•. 117
Figure 4.5. Control volume for the ~.directjon
momentum equation .......••••.••••...•.... 118
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