Supplemental Figures

Transcription

1 Supplemental Figures Main paper: Morphodynamics of Tidal Inlet Systems Annu. Rev. Fluid. Mech : doi: /annurev.fluid H. E. de Swart (1), J.T.F. Zimmerman (2,1) (1) Institute for Marine and Atmospheric research, Utrecht University, P.O. Box , 3508 TA Utrecht, the Netherlands (2) Royal Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Den Burg, the Netherlands 1

2 Figure 1: Landsat satellite image of the Wadden Sea, situated between the North Sea and the mainlands of Denmark, Germany and the Netherlands. Figure reproduced by the kind permission of the Common Wadden Sea Secretariat in Wilhelmshaven ( 2

3 initial bathymetry bathymetry after 300 years depth (m) bathymetry after 100 years bathymetry after 400 years bathymetry after 200 years bathymetry after 500 years Figure 2: Bathymetry of the Frisian Inlet system during a period of 500 years. The initial state at t = 0 is a constant depth of 2 m in the tidal basin and a depth in the sea that increases linearly with increasing distance from the coast. Scale of the domain is about 20 by 20 km. From Van Leeuwen et al. (2003), Estuarine Coastal and Shelf Science 22, Reproduced with the permission of Elsevier. 3

4 0.5 0 Canale S. Lorenzo Canale S. Felice η 0.5 η η X 0.5 Canale dei Bari X η X 0.5 Canale Riga X Figure 3: Comparison between the equilibrium bottom profile, calculated with the model of Lanzoni & Seminara (Journal of Geophysical Research 107 (C1), DOI: /2006JC000468), and field data of four channels in Venice Lagoon, which have lengths of 5375 m (S. Lorenzo), 9872 m (S. Felice), 9826 m (dei Bari) and 2668 m (Riga). Depths are scaled with the depth at the seaward boundary, which are 4 m, except for dei Bari, which has a depth of 5 m at that location. Figure reproduced with the permission of the American Geophysical Union. 4

5 a ( x 10-6 ) 1 0 r=0.12 r=0.14 r= l n b y=b y x=0 x y=0 x=l Figure 4: (a) Dimensionless growth rate Γ (scaled by tidal frequency) of bottom perturbations versus transverse wave number l n = nπ/w, where W is the width of the embayment, for the first longitudinal mode and for different values of the dimensionless linear bottom friction coefficient r. Situation close to critical conditions. For a fixed value of W the parameter l n attains only discrete values. (b) Contour plot of the bottom perturbation that has the fastest growth rate in case r = The arrows indicate the magnitude and direction of the net sediment transport. Adapted from Schuttelaars & de Swart (1999, Journal of Fluid Mechanics 386, 15-42), reproduced with the permission of Cambridge University Press. 5

6 a b A2 0.2 A ~ ~ 0.14 r r + c - sea side - + land side + - Figure 5: (a) Dependence of dimensionless amplitude (scaled with water depth H at the seaward boundary) of the symmetric bottom mode (n = 1, m = 2) on the dimensionless bottom friction parameter r = r/(ωh). Dashed and solid lines represent different types of equilibrium states. (b) As in panel a, but for the antisymmetric bottom mode (n = 1, m = 3). (c) Contour plot of the perturbed bottom for r = In this experiment the embayment has a length L = 20 km and a width of 2.1 km. In the spectral expansions 3 longitudinal modes and 14 transverse modes were used. The + and - symbols indicate shoals and pools, respectively. Figures adapted from Schuttelaars, H.M., 1997, Evolution and stability analysis of bottom patterns in tidal embayments, PhD Thesis, Utrecht University. 6

7 1 bar y/b Π Π k x pool Figure 6: Bottom pattern of the fastest growing mode in the case of a channel with width W (U/ω), as is investigated in Schramkowski (2002, Continental Shelf Research 22, ) and Hibma et al. (2004, Continental Shelf Research 24, ). 7

8 a b Figure 7: (a) Bottom shear stress in Venice Lagoon by currents only (Nm 2 ), computed with the numerical model discussed in Umgiesser et al. (2004, Journal of Marine Systems 51, ). (b) As in panel a, but for wind waves only. Reproduced with the permission of Elsevier. 8

9 U b Figure 8: Dimensionless orbital velocity amplitude U b = u b /(σh 0 ) on a flat tidalflat as a function of dimensionless tidal-mean water depth ˆd = k 0 (d 0 ) d 0 for a position near the channel-flat boundary (green dashed curve) and near the far end of the flat (blue curve), as well as the curve for the same parameter averaged over the total length of the flat (red curve); all curves for λ w = λ d = 1. d^ 9

10 Figure A1 General structure of morphodynamic models.

11 Figure A2 Example of the geometry of a simple inlet-basin system. Such systems are considered in Section 2 of the main text

12 Figure A3 The geometry of the tidal embayments that are discussed in Section 4 of the main text.

13 Figure B1 (a) Dimensionless tidal velocity u/u 2 versus dimensonless time t for = Other parameter values are u 0 = u 6 = 0, (u 4 /u 2 ) = (b) As in panel a, but for = /2.

14 Figure B2 (a) Net sediment transport < q > / qˆ versus relative phase for u c = 0 (blue curve) and u c = u 2 /2 (red curve).

15 Figure C1 Situation sketch of tidal water level intersecting with the bottom profile of a tidal flat.

16 Figure C2 Maximum current U max (red curves) versus X. The solid and dashed curves correspond to two different bottom profiles Z(X), which are indicated by the green solid and green dashed curve, respectively.

17 Figure C3 Dimensionless wave height (red), dimensionless wave orbital velocity amplitude (green), and sea-level variation (arbitrary scale, blue curve) as a function of dimensionless time tˆ = t/(2 ) for three positions on a flat tidal flat: near channel/flat boundary (solid curves), on the middle of the flat (small dashed curves) and at the far end of the flat (large dashed curves); all curves for * w = * d =1.