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On the nature of bend instability Stefano Lanzoni University of Padua, Italy Bianca Federici and...
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![Page 1: On the nature of bend instability Stefano Lanzoni University of Padua, Italy Bianca Federici and Giovanni Seminara University of Genua, Italy.](https://reader035.fdocuments.us/reader035/viewer/2022070605/5a4d1aeb7f8b9ab05997b01c/html5/thumbnails/1.jpg)
On the nature of bend instabilityStefano Lanzoni
University of Padua, Italy
Bianca Federici and Giovanni SeminaraUniversity of Genua, Italy
![Page 2: On the nature of bend instability Stefano Lanzoni University of Padua, Italy Bianca Federici and Giovanni Seminara University of Genua, Italy.](https://reader035.fdocuments.us/reader035/viewer/2022070605/5a4d1aeb7f8b9ab05997b01c/html5/thumbnails/2.jpg)
Meanders wandering in a flat valley
(Alaska -USA)
Meanders evolving in a rocky environment
(Utah- USA)
Tidal meanders within the lagoon of Venice
(Italy)
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Field examples of meander featuresFlow direction
Beaver River
Upstream skewed
meanders
Downstream skewed
meandersFlow direction
Fly River
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Coexistence of upstream and downstream
skewed meanders
Multiple loops
White River
Flow direction
Flow direction
Pembina River
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Scope of the work
• Under which conditions is the planimetric development of meandering rivers downstream/upstream controlled?
• How is downstream/upstream influence related to the nature of bend instability?
• Which are the implications for the boundary conditions to be applied when simulating the planimetric development of natural rivers?
![Page 6: On the nature of bend instability Stefano Lanzoni University of Padua, Italy Bianca Federici and Giovanni Seminara University of Genua, Italy.](https://reader035.fdocuments.us/reader035/viewer/2022070605/5a4d1aeb7f8b9ab05997b01c/html5/thumbnails/6.jpg)
Notations
Planform view Sez. A-A
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Formulation of the problem
•Dimensionless planimetric evolution equation (Seminara et al., Jfm 2001)
• Erosion law (Ikeda, Parker & Sawai, Jfm 1981)
semilarghezza velocità media
lateral migration speed
long term erosion coefficient
time longitudinal coordinate
depth averaged longitudinal
velocity
lateral coordinate
![Page 8: On the nature of bend instability Stefano Lanzoni University of Padua, Italy Bianca Federici and Giovanni Seminara University of Genua, Italy.](https://reader035.fdocuments.us/reader035/viewer/2022070605/5a4d1aeb7f8b9ab05997b01c/html5/thumbnails/8.jpg)
•Flow field (Zolezzi and Seminara, Jfm 2001)
Characteristic exponents
integration constants
channel axis curvature
um= um(, Cf0, * )
aspectratio
frictioncoefficient
Shieldsparameter
![Page 9: On the nature of bend instability Stefano Lanzoni University of Padua, Italy Bianca Federici and Giovanni Seminara University of Genua, Italy.](https://reader035.fdocuments.us/reader035/viewer/2022070605/5a4d1aeb7f8b9ab05997b01c/html5/thumbnails/9.jpg)
• Dispersion relationship for bend instability (Seminara et al., Jfm 2001)
• Perturbation
Planimetric stability analysis
: complex angular frequency
: complex phase velocity
: complex group velocity
= (, Cf0, * )
![Page 10: On the nature of bend instability Stefano Lanzoni University of Padua, Italy Bianca Federici and Giovanni Seminara University of Genua, Italy.](https://reader035.fdocuments.us/reader035/viewer/2022070605/5a4d1aeb7f8b9ab05997b01c/html5/thumbnails/10.jpg)
Characteristic of bend instability
growth rate
dune covered bedplane bed
phase speed
r
r
r
•
• response excited at resonance
• super-resonance: bend migrate upstream
• sub-resonance: bend migrate downstream
![Page 11: On the nature of bend instability Stefano Lanzoni University of Padua, Italy Bianca Federici and Giovanni Seminara University of Genua, Italy.](https://reader035.fdocuments.us/reader035/viewer/2022070605/5a4d1aeb7f8b9ab05997b01c/html5/thumbnails/11.jpg)
Instability classification
Absoluteinstability
Convectiveinstability
initial impulse perturbation
initial impulse perturbation
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Linear analysis of bend instability(Briggs' criterion, 1964)
Absoluteinstability
Convectiveinstability
branch point singularities = 0
> 0•• the spatial branches of dispersion relationship (igiven, rvarying) lie in distinct half -planes for large enough values of the temporal growth rate i
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Results of linear theory: First scenario=8, =0.3, d=0.005, dune covered bed
a) i=[i], b) i=1.5[i], c) i=2[i]
Convective instability
![Page 14: On the nature of bend instability Stefano Lanzoni University of Padua, Italy Bianca Federici and Giovanni Seminara University of Genua, Italy.](https://reader035.fdocuments.us/reader035/viewer/2022070605/5a4d1aeb7f8b9ab05997b01c/html5/thumbnails/14.jpg)
=25, =0.7, d=0.005, dune covered bedResults of linear theory: Second scenario
a) i=[i]
b) i=2[i]
c) i=5[i]
Absolute instability
![Page 15: On the nature of bend instability Stefano Lanzoni University of Padua, Italy Bianca Federici and Giovanni Seminara University of Genua, Italy.](https://reader035.fdocuments.us/reader035/viewer/2022070605/5a4d1aeb7f8b9ab05997b01c/html5/thumbnails/15.jpg)
Linear theory
Bend instability is generally convective, but a transition to absolute instability occursfor large values of , dune covered bed and
large values of *
The group velocity ∂r/∂ associated to thewavenumber max characterized by the
maximum growth rate changes sign as resonance is crossed
moreover,
r
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Numerical simulations of nonlinear planimetric development
i
= t/E
pi
Boundary Conditions:
i = E (Ui|n=1-Ui|n=-1)
Ui=Ui(*,ds,cmj )
Free B.C.Periodic B.C. cmj j=1,4Forced B.C.
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Numerical results: Free boundary conditions
=8, =0.3, d=0.005 dune covered bed
=25, =0.7, d=0.005 dune covered bed
Sub-resonant conditions, Convective instabilitywavegroup migrate downstream
Super-resonant conditions, Convective instabilitywavegroup migrate upstream
Super-resonant conditions, Convective instabilitywavegroup migrate upstream
=15, =0.3, d=0.005 dune covered bed
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Numerical results: Periodic boundary conditions
Sub-resonant conditions, Convective instabilitywavegroup migrate downstream
Super-resonant conditions, Convective instabilitywavegroup migrate upstream
=8, =0.3, d=0.005 dune covered bed
=15, =0.3, d=0.005 dune covered bed
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Numerical results: Forced boundary conditions
=30, =0.1, d=0.01, dune covered bedsuper-resonant conditions
periodic B.C.
free B.C.
forced B.C.
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Numerical results: Free boundary conditions incipient cut off configuration
=15, =0.3, d=0.005 dune covered bed
incipient cut off configuration
planform configurations after several neck cut offs
The length of straight upstream/downstream reaches continues to increase
Cutoff spreads in the direction of morphodynamic influence
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Conclusions
• Bend instability is invariably convective• Meanders are typically upstream skewed• Wave groups travel downstream• The upstream reach tends to a straight configuration in absence of a persisting forcing
• The choice of boundary conditions strongly affects numerical simulations of the planimetric development of alluvial rivers
• Sub-resonant conditions ( < r)
• Bend instability may be absolute for a dune covered bed and high enough values of the Shields parameter• Meanders are typically downstream skewed• Wave groups travel downstream• The downstream reach tends to a straight configuration in absence of a persisting forcing
• Super-resonant conditions ( > r)
![Page 22: On the nature of bend instability Stefano Lanzoni University of Padua, Italy Bianca Federici and Giovanni Seminara University of Genua, Italy.](https://reader035.fdocuments.us/reader035/viewer/2022070605/5a4d1aeb7f8b9ab05997b01c/html5/thumbnails/22.jpg)
Open issues
• Systematic field observations are needed to further substantiate the morphodynamic upstream influence exhibited by bend instability under super-resonant conditions
• The role of geological constraints possibly present in nature and their relationships with the features typical of bend instability has to be investigated.
• Which boundary conditions have to be applied when simulating the planimetric development of alluvial rivers?
• Further analyses are required to clarify the effects of chute and neck cut off on river meandering.