1. WHAT CONTROLS BAR MIGRATION IN TIDAL CHANNELS?
Valeria Garotta
Michele Bolla Pittaluga
Giovanni Seminara
UNIVERSITY OF GENOA
ITALY
DEPARTMENT OF ENVIRONMENTAL ENGINEERING

2. A 2-D MODEL FOR THE FORMATION OF TIDAL BARS
Main goals:
Verify the adoptability of a 2-D model.
Investigate the mechanism whereby tidal bars may experience a net migration.
Basic assumptions:
Hydrodynamics modeled by means of the shallow water equations;
Suspended sediment flux modeled by means of the analytical relationship proposed by Bolla Pittaluga e Seminara (2003).
Mathematical approach:
Linear stability analysis of flow and bed topography.

3. ALTERNATE BARS IN STRAIGHT TIDAL CHANNELS
x(m)
Y(m)
z (m)
A sketch of tidal bars observed in the experiments of Tambroni et. al. (2005)
Scours and depositions alternating from one bank to the other one
Sediment transport in tidal environments is dominantly suspended. In order to account for the 3-D nature of suspended load, a 3-D model is required.
How to model suspended load using a 2-D model?
The analytical relationship of Bolla Pittaluga and Seminara (WRR, 2003) for the concentration field in slowly varying flows, allows the usage of a depth-averaged model.
Why use a 2-D model?
In order to tackle more complex problems, such as the non linear development of tidal bars, with a lower computational effort than a 3D formulation.

4. DIMENSIONLESS PARAMETERS
STATEMENT OF THE MODEL
SCALING
HYDRODYNAMICS
aspect ratio;
ratio between the time required for the average flow to travel along a reach B and the tidal period.
DIMENSIONLESS PARAMETERS
ratio between the scales of bed load flux and suspended flux;
BOTTOM EVOLUTION
BED LOAD FLUX
U, V: depth-averaged longitudinal and transversal flow velocity;
H, D: water surface elevation and flow depth;
Qb, Qs: bed load and suspend load fluxes.

5. SUSPENDED SEDIMENT FLUX
Dimensionless form of the advection - diffusion equation:
Asymptotic expansion:
Rouse solution
Closed formula for suspended sediment transport

6. BASIC FLOW AND PERTURBATIONS
Normal mode analysis
Alternate bars: m = 0
Solution

7. MARGINAL STABILITY CONDITIONS
2-D MODEL VALIDATION: COMPARISON WITH THE 3-D MODEL (Seminara e Tubino, 2001). 2D
O(xd) 3D
THE EFFECT OF THE SPATIAL AND TEMPORAL VARIATIONS OF THE CONCENTRATION FIELD: THE O(d) CORRECTION

8. THE ROLE OF OVERTIDES ON MARGINAL STABILITY CONDITIONS
The presence of overtides (curve b) modifies the marginal stability conditions with respect to the case of a monochromatic tidal wave (curve a), being destabilizing for low values of the bar wavenumber l and stabilizing for high values of l.
Curve a) 
Curve b) 
Overtides of increasing amplitude give rise to a decrease of both the critical value bcr for the bar type instability and the critical bar wavenumber lcr.

9. TIDAL BAR MIGRATION
MONOCHROMATIC TIDE
NO NET MIGRATION

10. TIDAL BAR MIGRATION EFFECT OF AN OVERTIDE
AFTER 10 TIDAL CYCLES THE BAR HAS MOVED LANDWARD FOR A DISTANCE OF 10% OF WAVELENGTH.

11. WHY DO TIDAL BARS MIGRATE? Flow asymmetry parameter
The flow asymmetry, due to the presence of overtides, gives rise to an asymmetric forward-backward movement of bars throughout the tidal cycle. The direction of the migration process depends on the phase lag between the overtide and the dominant harmonic.
bar net displacement
Flow asymmetry parameter
flow asymmetry parameter
phase lag

12. THE EFFECT OF THE FLOW ASYMMETRY: O(x)
AMPLITUDES OF SEDIMENT TRANSPORT PERTURBATIONS
PHASE LAGS BETWEEN SEDIMENT TRANSPORT PERTURBATIONS AND BOTTOM PROFILE

13. CONCLUSIONS AND FUTURE DEVELOPMENTS
A 2-D model is proper to describe the formation of free bars in tidal channels;
the flow asymmetry due to the presence of overtides is one of the possible mechanisms responsible for bar migration.
study more complex problems dealing with tidal bars;
experimental study on physical model of the interaction of free bars and curvature forced bars in tidal channels.

14. THANK YOU FOR YOUR ATTENTION!