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Shoreline instability under low-angle wave incidence

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Shoreline instability under low-angle wave incidence
  Shoreline instability under low-angle wave incidence 1 D. IdierBRGM, 3 Avenue C. Guillemin, BP 6009, 45060 Orl´eans Cedex 2, France 2 A. Falqu´esUPC, C/ Jordi Girona 1-3, Modul B4/B5, despatx 103 - E-08034, Barcelona, 3 Catalonia, Spain 4 B.G. RuessinkUtrecht University, Institute for Marine and Atmospheric Research Utrecht, 5 Faculty of Geosciences, Department of Physical Geography, P.O. box 80115, 6 3508 TC Utrecht, The Netherlands 7 R. GarnierInstituto de Hidr´aulica Ambiental IH Cantabria, Universidad de Cantabria, 8 ETSI Caminos Canales y Puertos, Avda. los Castros s/n, 39005 Santander, 9 Cantabria, Spain 10 D. Idier, BRGM, 3 Avenue C. Guillemin, BP 6009, 45060 Orl´eans Cedex 2, France.( Falqu´es, UPC, C/ Jordi Girona 1-3, Modul B4/B5, despatx 103 - E-08034, Barcelona,Catalonia, Spain. ( D R A F T September 27, 2011, 5:50pm D R A F T    h  a   l  -   0   0   6   3   5   2   1   1 ,  v  e  r  s   i  o  n   1  -   2   4   O  c   t   2   0   1   1 Author manuscript, published in "Journal of Geophysical Research Earth Surface (2011) 45 p." DOI : 10.1029/2010JF001894  Abstract. 11 The growth of megacusps as shoreline instabilities is investigated by ex- 12 amining the coupling between wave transformation in the shoaling zone, long- 13 shore transport in the surf zone, cross-shore transport, and morphological 14 evolution. This coupling is known to drive a potential positive feedback in 15 case of very oblique wave incidence, leading to an unstable shoreline and the 16 consequent formation of shoreline sandwaves. Here, using a linear stability 17 model based on the one-line concept, we demonstrate that such instabilities 18 can also develop in case of low-angle or shore-normal incidence, under cer- 19 tain conditions (small enough wave height and/or large enough beach slope). 20 The wavelength and growth time scales are much smaller than those of high- 21 angle wave instabilities and are nearly in the range of those of surf zone rhyth- 22 mic bars, O(10 2 −  10 3 m) and O(1  −  10 days), respectively. The feedback 23 mechanism is based on: (1) wave refraction by a shoal (defined as a cross- 24 shore extension of the shoreline perturbation) leading to wave convergence 25 shoreward of it, (2) longshore sediment flux convergence between the shoal 26 and the shoreline, resulting in megacusp formation, and (3) cross-shore sed- 27 B.G. Ruessink, Utrecht University, Institute for Marine and Atmospheric Research Utrecht,Faculty of Geosciences, Department of Physical Geography, P.O. box 80115, 3508 TC Utrecht,The Netherlands. ( Garnier, IH Cantabria, Universidad de Cantabria, Avda. los Castros s/n, 39005 Santander,Cantabria, Spain. ( D R A F T September 27, 2011, 5:50pm D R A F T    h  a   l  -   0   0   6   3   5   2   1   1 ,  v  e  r  s   i  o  n   1  -   2   4   O  c   t   2   0   1   1  iment flux from the surf to the shoaling zone, feeding the shoal. Even though 28 the present model is based on a crude representation of nearshore dynam- 29 ics, a comparison of model results with existing 2DH model output and lab- 30 oratory experiments suggests that the instability mechanism is plausible. Ad- 31 ditional work is required to fully assess whether and under which conditions 32 this mechanism exists in nature. 33 D R A F T September 27, 2011, 5:50pm D R A F T    h  a   l  -   0   0   6   3   5   2   1   1 ,  v  e  r  s   i  o  n   1  -   2   4   O  c   t   2   0   1   1  1. Introduction Rhythmic shorelines featuring planview undulations with a relatively regular spacing or 34 wavelength are quite common on sandy coasts. In the present study, we focus on undu- 35 lations that are linked to submerged bars or shoals and are generally known as shoreline 36 sandwaves [ Komar  , 1998;  Bruun  , 1954]. These sandwaves can be classified according to 37 their length scale as short and long sandwaves (see, e.g.,  Stewart and Davidson-Arnott  38 [1988]). 39 The spacing of short sandwaves ranges from several tens to several hundreds of meters 40 and their seaward perturbations are known as megacusps. Observations show that these 41 megacusps can develop shoreward of crescentic bar systems during the typical “Rhythmic 42 Bar and Beach” morphological beach state or can develop from the shore attachment 43 of transverse bars that characterise the “Transverse Bar and Beach” state [ Wright and  44 Short  , 1984]. These transverse bars can appear where the horns of a previous crescentic 45 bar approach the shoreline [ Wright and Short  , 1984;  Sonu  , 1973;  Ranasinghe et al. , 2004; 46 Lafon et al. , 2004;  Castelle et al. , 2007]. On the other hand, transverse bars can also 47 develop freely, independently of any offshore rhythmic system (e.g. the “transverse finger 48 bars” [ Sonu  , 1968, 1973;  Ribas and Kroon  , 2007]). The formation of rhythmic surf zone 49 bars and associated megacusps is believed to be due primarily to an instability of the 50 coupling between the evolving bathymetry and the distribution of wave breaking (bed- 51 surf coupling) [ Falqu´es et al. , 2000]. The developing shoals and channels cause changes in 52 wave breaking, which in turn cause gradients in radiation stresses and thereby horizontal 53 circulation with rip currents. If the sediment fluxes carried by this circulation converge 54 D R A F T September 27, 2011, 5:50pm D R A F T    h  a   l  -   0   0   6   3   5   2   1   1 ,  v  e  r  s   i  o  n   1  -   2   4   O  c   t   2   0   1   1  over the shoals and diverge over the channels, a positive feedback arises and the coupled 55 system self-organizes to produce certain patterns, both morphological and hydrodynamic 56 (see, e.g.,  Reniers et al.  [2004];  Garnier et al.  [2008]). In the case of oblique wave inci- 57 dence, a meandering of the longshore current is also essential to the instability process 58 [ Garnier et al. , 2006]. Two important characteristics of all available models of the self- 59 organized formation of rhythmic surf zone bars are that they (1) are essentially based 60 on sediment transport driven by the longshore current and rip currents only, i.e. ignore 61 cross-shore transport induced by undertow and wave non-linearity and (2) do not consider 62 morphological changes beyond the offshore reach of the rip-current circulation. 63 Rhythmic shorelines can also develop as a result of an instability not related to bed- 64 surf coupling.  Ashton et al.  [2001] and  Ashton and Murray   [2006a, b] have shown that 65 sandy shorelines are unstable for wave angles (angle between wave fronts and the local 66 shoreline orientation) larger than about 42 ◦ in deep water, leading to the formation of  67 shoreline sandwaves, cuspate features and spits.  Falqu´es and Calvete   [2005] have found 68 that the initial characteristic wavelength of the emerging sandwaves is in the range of 3 to 69 15 km, i.e., much larger than that of surf zone rhythmic bars. This instability caused by 70 high-angle waves will henceforth be referred to as HAWI (High-Angle Wave Instability). 71 The physical mechanism can be explained as follows. For oblique wave incidence, there 72 are essentially two counteracting effects. On one hand, the angle relative to the local 73 shoreline is larger on the lee of a cuspate feature than on the updrift side. This tends to 74 cause larger alongshore sediment flux at the lee and thereby divergence of sediment flux 75 along the bump, which therefore tends to erode. On the other hand, since the refractive 76 wave ray turning is stronger at the lee than at the updrift flank, there is more wave energy 77 D R A F T September 27, 2011, 5:50pm D R A F T    h  a   l  -   0   0   6   3   5   2   1   1 ,  v  e  r  s   i  o  n   1  -   2   4   O  c   t   2   0   1   1
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