Shoreface profile

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Definition of Shoreface profile:
The shoreface profile, often called beach profile, is the cross-shore coastal depth profile extending from the low-water line to the closure depth.
This is the common definition for Shoreface profile, other definitions can be discussed in the article


Introduction

Figure 1. Schematic representation of a shoreface profile. The vertical/horizontal scale ratio is greatly exaggerated.


Figure 2. The barred coast of North Holland, The Netherlands. https://beeldbank.rws.nl, Rijkswaterstaat / Rens Jacobs

The shoreface is the zone where offshore generated waves interact with the upward sloping seabed, in front of the shoreline. The width of sandy shorefaces typically ranges between a few hundred meters and a few kilometers and the average slope between 1/20 and 1/200. Incident waves are transformed and dissipate most of their energy on the shoreface, whereby large amounts of sediment are suspended and transported. Most energy is dissipated in the upper part of the shoreface, the surf zone (or breaker zone), where waves overturn and break. The lower part of the shoreface extends to the so-called closure depth; beyond this depth the seabed is hardly influenced by waves and wave-induced sediment transport is insignificant (see also Active coastal zone). The lower part of the shoreface is also called shoaling zone; wave shoaling is the process of wave amplification when waves travel from deep to shallow water before breaking (see Shallow-water wave theory). The division between upper and lower shoreface profiles is often marked by an inflexion point, a bar or a terrace, indicating transition of morphodynamics [1] (Fig. 1). Another transition exists at the shoreline where waves collapse and run up the beach; this so-called swash zone is dealt with in the article Swash zone dynamics. The surf zone profile is often undulated due to the presence of one or several bars. These bars have mainly a shore parallel orientation, but more complex three-dimensional patterns are ubiquitous (see Rhythmic shoreline features and Fig. 2).


Morphodynamic feedback

Sediment transport on the shoreface depends on the local wave climate. By 'wave climate' is meant the description of incoming waves in terms of a statistical distribution of incident wave directions, wave heights and wave periods (see Statistical description of wave parameters). Sediment transport also depends on the characteristics of bed sediments and on the seabed bathymetry. For small wave incidence angles (close to the shore-normal direction) the relevant seabed bathymetry is the cross-shore shoreface profile.

The shoreface profile influences cross-shore sediment transport, but the inverse is also true: changes of the shoreface profile result from gradients in the cross-shore sediment transport. This is called morphodynamic feedback: for a given incident wave field the shoreface profile determines the transformation of the wave field on the shoreface and therefore the resulting sediment transport, whereas the resulting sediment transport determines the shoreface profile. As a result of this morphodynamic feedback, the shoreface profile tends to an equilibrium shape for a given stable wave climate. A dynamic equilibrium is reached when onshore directed sediment transport and offshore directed transport are equal on average over a period exceeding the morphodynamic adaptation time. This holds for alongshore uniform coasts; the equilibrium requirement for non-uniform coasts is a vanishing divergence of the long-term average total sediment transport vector (cross-shore and alongshore). It was realised already long ago that the shoreface of a sedimentary coast should not be regarded as a geologically inherited feature, but as the result of natural adaptation to modern hydrodynamic conditions [2] [3].

Knowing how to determine the equilibrium shoreface profile has great practical interest. It provides quantitative insight in the response of the shoreface to changes in the local wave climate by human and natural causes; such insight is important for testing and improving the effectiveness of measures to combat coastal erosion and shoreline retreat.


Bedforms and sediment sorting

Morphodynamic feedback involves not only shoreface profile development, but also sediment grainsize and bed roughness. Grainsize and bed roughness strongly influence sediment transport [4]. Inversely, sediment transport strongly influences the grainsize distribution of bed sediments. Bed roughness depends on the presence of bedforms (ripples, dunes), which in turn depend on sediment transport and sediment grainsize. Consequently, shoreface profile development, wave transformation on the shoreface, sediment transport, grainsize sorting and bedform emergence are all dynamically coupled processes.

Grainsize sorting is primarily due to differences in transport modes of different grainsize fractions. The finer fractions are more easily brought and maintained in suspension than the coarser fractions. They are transported further away from their initial location and tend to settle on the lower shoreface zone where wave-induced bed shear stresses are lower than on the upper shoreface. The coarse fraction is transported partly as suspended load and partly as bedload in the wave boundary layer. Wave transformation in shallow water leading to wave skewness (stronger onshore than offshore wave orbital velocity) and wave asymmetry (stronger onshore than offshore wave orbital acceleration) favour net onshore transport in the wave boundary layer. Fine sediments are resuspended from the upper shoreface due to undertow currents and turbulent shear stresses generated by breaking waves. Sediments on the upper shoreface are therefore coarser than on the lower shoreface. Fine sediment particles can still be present on the upper shoreface if they are 'hidden' by overlying coarser sediment particles – a phenomenon called 'bed armouring'.

The largest bedforms on the shoreface, such as shoreface-connected ridges (scale of several kilometers) and shore-oblique bars (scale of the order of hundred meters) are mainly related to morfodynamic feedback processes that interact with longshore transport, see the articles Sand ridges in shelf seas and Rhythmic shoreline features. Other large bedforms, the so-called breaker bars (scale also of the order of 100 meters) arise from morphodynamic coupling with the wave breaking process, through the resulting flow structure at the breaker bar and interaction with cross-shore and longshore transport [5][6]. Bedforms at much smaller scales – ripples with wavelengths of the order of 1 m – are formed in the less exposed parts of the shoreface under low to moderate wave conditions. Morphodynamic feedback processes, leading to regular ripple patterns, involve ripple-induced near-bed flow circulation [7], vortex shedding at ripple crests [8] and non-linear ripple-ripple interactions [9]. For a more detailed discussion, see the articles Wave ripples and Wave ripple formation. The time lag of sediment suspension and settling related to vortex shedding at the ripple crests strongly influences the direction of residual cross-shore sediment transport on the shoreface, see section #Onshore wave-induced sediment transport.


Beach classification

The beach profile in the upper shoreface zone can be highly variable. The profile tends to steepen in periods of low-energy waves (especially long-period swell waves) and to flatten under high-energy storm waves (see Active coastal zone). Sediment characteristics also play an important role. Coarse-grained beaches, typical for high-energy coasts, have steeper slopes than fine-grained beaches, typical for moderate-to-low-energy coasts [10]. Gently sloping beaches dissipate almost completely the energy of incident waves, whereas steep-sloping beaches tend to reflect (partly) incident waves. For distinguishing between reflective and dissipative beaches the Dean-parameter [math]\Omega[/math] is often used [11][12]:

[math]\Omega = \Large \frac{H}{wT} \normalsize , \qquad(1)[/math]

where [math]H[/math] is the offshore wave height before breaking, [math]T[/math] is the peak spectral wave period and [math]w[/math] is the mean sediment fall velocity. By analysing beach profiles in Australia, Wright and Short (1984) [13] found that beach types could be characterised by the parameter [math]\Omega[/math]:

  • reflective beaches correspond to [math]\Omega \lt 1 [/math];
  • intermediate beaches correspond to [math]1\lt \Omega \lt 6 [/math];
  • dissipative beaches correspond to [math]\Omega \gt 6 [/math].

The tidal range also influences the beach profile, because the surf zone is shifted across the shoreface with tidal level. For large tides (tidal range much larger than wave height) the surf zone covers during the tidal cycle a much larger area than for small tides. Beaches with large tides therefore have smaller upper shoreface slopes compared to beaches with the same [math]\Omega[/math] and small tides.


Cross-shore sediment transport

Sediment transport on the shoreface depends on many processes. We focus on processes relevant for cross-shore transport. It should be realised, however, that longshore transport processes can also play an important role. Shifts in the cross-shore position of the shoreface profile and the generation of bars on the shoreface are strongly influenced by longshore transport processes. See for example the articles: Natural causes of coastal erosion, Littoral drift and shoreline modelling and Rhythmic shoreline features. In the following we consider sandy beaches, with grain sizes typically between 0.2 and 0.5 mm (fine to medium sand). Coarse sedimentary beaches are dealt with in the article Gravel Beaches.

Onshore wave-induced sediment transport

Wave transformation in shallow water (see Shallow-water wave theory) is a major factor for onshore sediment transport [14]. Waves become skewed and asymmetric, producing near-bed shear stresses which are stronger in onshore direction than in offshore direction [15] [16][17]. Phase lags between bed shear stress and sediment suspension determine to which degree wave skewness induces onshore transport; in some situations (rippled bed, sheet flow) a large phase lag can reverse the net sediment transport direction. A large time lag implies that sediment particles that are stirred up by turbulent eddies during onshore orbital motion are transported offshore after reversal of the wave orbital velocity [18][19][15][20]. Onshore transport is stimulated by wave breaking that generates turbulent fluid motions and sediment resuspension under the wave crest [21]. The development of forward streaming at the top of the wave boundary layer also contributes to onshore transport [22], but this only holds for smooth beds and not in cases where the seabed is rippled, in cases of strongly skewed waves or for sheet flow conditions [23][24] (see also Sediment transport formulas for the coastal environment). Another, but generally lesser contribution to onshore sediment transport is further due to net mass transport in the upper layer between wave trough and wave crest.

Offshore wave-induced sediment transport

Offshore transport is due to so-called undertow: the compensating return current for the net onshore mass transport in the layer between wave trough and wave crest [25][26][27]. The undertow current is particularly strong just in front of the location where waves are breaking and where much sediment is brought into suspension[28]. Bound infragravity waves may also contribute to net offshore sediment transport, as discussed in the article Infragravity waves.

Downslope sediment transport

Downslope transport occurs when sediment particles roll down the shoreface slope. However, this is not the primary cause of downslope sediment transport for fine to medium sandy beaches [29]. Gravity-induced sediment transport is a minor effect for two reasons: (1) the shoreface slope is small and (2) sediment particles are mainly transported in suspension, more than as bedload, especially on the upper shoreface. When a sediment particle is lifted from the bed to a certain level [math]z[/math] into the fluid, it moves with the wave orbital flow over a net distance [math]l[/math] until it settles again onto the bed. The net distance [math]l[/math] travelled by the sediment particle depends on the settling time; the longer the settling time, the greater the distance. The settling time is inversely proportional to the sediment fall velocity [math]w[/math]. Because the shoreface has a seaward dipping slope, the net travelled distance by an offshore moving sediment particle is larger than for a flat bottom; the inverse holds for an onshore moving sediment particle. The slope effect thus requires a correction to the net sediment transport over a flat bottom, which depends on the slope [math]S[/math] and the fall velocity [math]w[/math]. Formulas for suspended sediment transport assume in general that the slope effect can be represented by a correction factor to the wave-induced transport components of the form [30]

[math](1- S \, \gamma \Large \frac{u }{w} \normalsize ) , \qquad(2)[/math]

where [math]S[/math] is the bed slope, [math]u[/math] the instantaneous wave orbital velocity, [math]w[/math] the sediment fall velocity and [math]\gamma[/math] an efficiency parameter. Although not proven, it is often assumed that the slope effect is a major factor compensating for net wave-induced onshore transport (sum of wave-induced onshore and offshore transport components) in situations close to equilibrium. This implies that the equilibrium shoreface slope [math]S[/math] will be steeper (larger [math]S[/math]) for a coarser seabed (large fall velocity [math]w[/math]) than for a finer sediment bed (small fall velocity [math]w[/math], smaller [math]S[/math]). This is expressed by the correction factor (2) and is in general agreement with field observations. When averaging over the wave period (or, more precisely, the wave climate), the bed-slope effect on the total net sediment transport can be related to the equilibrium bed slope [math]S_{eq}[/math] by the correction factor [math](1 – S / S_{eq})[/math] [31].

Sediment transport modelling

The processes involved in sediment transport on the shoreface, as described above, are complicated and not yet fully understood. Even the most sophisticated process-based mathematical models, like XBEACH [32], make use of approximate empirical formulations for several processes contributing to sediment transport and involve parameters that need to be tuned. Empirical formulas for wave-induced sediment transport on the shoreface that are often used in practice are given in the articles Sediment transport formulas for the coastal environment and Sand transport. These formulas are based on laboratory and field measurements for a large range of conditions. Rough estimates can be obtained with the empirical default parameters given in these articles. For better estimates it is necessary to tune these parameters to field data.


Equilibrium shoreface profile (sandy beach)

For a given stable wave climate the shoreface profile tends after a long period to an equilibrium profile. This equilibrium profile can be computed by applying sediment transport formulas to an initial profile for a period comprising all wave conditions according to local wave climate statistics. This requires heavy calculations that are moreover subject to large uncertainty margins. Therefore, equilibrium profiles derived from field observations are generally used. From analysis of a large number of beach profiles of the Californian and Danish coasts [33][34] and the US Atlantic and Gulf coasts [35] Bruun (1954) and Dean (1977) derived an equilibrium profile (often called the Dean/Bruun profile) of the form (Fig. 3)

Figure 3. The Bruun/Dean profile (Eq. 3) and the equivalent Bodge profile (Eq. 4).

[math]h(x)=A \; x^{2/3}, \qquad(3)[/math]

where [math]h[/math] is the water depth [m], [math]x[/math] the cross-shore distance [m] ([math]x=0[/math] at the shoreline) and [math]A [/math] a coefficient depending on the sediment fall velocity [math]w[/math] [m/s], [math] \quad A \approx 0.5 \; w^{0.44} [m^{1/3}][/math].

Dean [35] showed that the exponent 2/3 is consistent with the assumption of constant wave energy dissipation per unit volume throughout the surf zone.

Because the Bruun/Dean profile has an infinite slope at the shoreline, an alternative form was proposed by Bodge (1992) [36],

[math]h(x)=B \; (1 – e^{-kx}) , \qquad(4)[/math]

where [math]k[/math] is an empirical coefficient in the range [math]3 \; 10^{-5} - 1.16 \; 10^{-3} \; [m^{-1}][/math].

From an analysis of terrace-shaped shoreface profiles in northern Spain, Bernabeu et al. (2003) [37] found that the Bruun/Dean profile was adequate only for the upper shoreface; for the lower shoreface they proposed the form

[math]h(x)=A' \; (x-x_0)^{2/3} , \qquad(5)[/math]

where [math]x_0[/math] is determined such that the two profiles (3) and (5) match at the inflexion point between the upper and lower shoreface.

Inman et al. (1993) [38] used a similar procedure for the analysis of beach profiles for the coasts of south California, North Carolina and the Nile delta. They found best fits with exponents ranging between 0.3 and 0.45 instead of 2/3.


The cross-shore profile of gravel beaches is not the same as for sandy beaches, see: Gravel Beaches.


Analytical equilibrium models

Because of the earlier mentioned difficulties to derive model estimates of the equilibrium shoreface profile, taking into account the full wave climate, analytical models have been developed in which the wave climate is replaced by a single representative monochromatic incident wave. An alongshore uniform shoreface is assumed with perpendicular wave incidence. In these models a simple wave transformation model is used based on depth saturation of broken waves (wave height limited by depth) and shallow-water wave theory. An analytical expression for the equilibrium shoreface slope can be derived by requiring that the total wave-integrated cross-shore sediment flux equals zero throughout the shoreface zone [39] [29] [40]. Although these models reproduce certain properties also observed in the field, such as increasing profile steepness with increasing grain size and with increasing wave period, a more detailed comparison of computed profiles with observations exhibits large discrepancies. The computed concavity of the upper shoreface profile is much stronger than generally observed in the field and much stronger than for the Bruun/Dean profile. This is perhaps not surprising in view of the simplicity of the model for wave-induced sediment transport, which ignores many of the processes described in the previous paragraphs. These analytical models also ignore the influence of extreme storms, which can flatten the profile out to great depths within a few days. The profile adaptation time scale for the entire shoreface being quite long (order of centuries [29]), it is plausible that observed shoreface profiles generally correspond to transient profiles [40].


Related articles

Bruun rule
Active coastal zone
Coastal Hydrodynamics And Transport Processes
Coastal and marine sediments
Gravel Beaches


Further reading

Komar, P.D. 1998. Beach processes and sedimentation. Prentice Hall, London, pp. 544.

Woodroffe, C.D. 2002. Coasts, form, processes and evolution. Cambridge Univ.Press, 623 pp.

Dronkers, J. 2017. Dynamics of Coastal Systems. World Scientific Publ. Co. 753 pp.


References

  1. ↑ Wright, L.D., Chappel, J., Thom, B.G., Bradshow, M.P. and Cowell, P. 1979. Morphodynamics of reflective and dissipative beach and inshore systems: south-eastern Australia. Mar.Geol. 32: 105-140
  2. ↑ Cornaglia, P. 1889. Delle Spiaggie. Accademia Nazionale dei Lincei, Atti.Cl.Sci.Fis., Mat.e Nat.Mem. 5: 284-304
  3. ↑ Johnson, D.W. 1919. Shore processes and shoreline development. Prentice Hall, N-Y, 584 pp.
  4. ↑ Van Rijn, L.C. 1998. Principles of Coastal Morphology. Aqua Publications, The Netherlands (aqua publications.nl.
  5. ↑ Reniers, A.J.H.M., Thornton, E.B., Stanton, T.P. and Roelvink, J.A. 2004. Vertical flow structure during Sandy Duck: observations and modelling. Coast.Eng. 51: 237-260
  6. ↑ Jacobsen, N.G. and Fredsoe, J. 2014. Formation and development of a breaker bar under regular waves. Part 2: Sediment transport and morphology. Coastal Eng. 88: 55-68
  7. ↑ Sleath, J.F.A. 1984. Sea bed mechanics. Wiley, New York.
  8. ↑ Fredsøe, J., Andersen, K.H. and Sumer, M.B. 1999. Wave plus current over a ripple-covered bed. Coastal Eng. 38: 177-221
  9. ↑ Marieu, V., Bonneton, P., Foster, D.L. and Ardhuin, F. 2008. Modeling of vortex ripple morphodynamics. J. Geophys. Res. 113, C09007, doi:10.1029/2007JC004659
  10. ↑ Bujan, N., Cox, R. and Masselink, R. 2019. From fine sand to boulders: Examining the relationship between beach-face slope and sediment size. Marine Geology 417, 106012
  11. ↑ Gourlay, M. R. 1968. Beach and dune erosion tests. Rep. m935/m936, Delft Hydraul. Lab., Delft
  12. ↑ Dean, R.G. 1973. Heuristic models of sand transport in the surf zone. Proc. Conf. Eng. Dynamics in the Surf Zone, Sydney: 208-214.
  13. ↑ Wright, L.D. and Short, A.D. 1984. Morphodynamic variability of surf zones and beaches: a synthesis. Mar.Geol. 56: 93-118
  14. ↑ Elgar, S., Gallagher, E.L. and Guza, R.T. 2001.Nearshore sandbar migration. J.Geophys.Res. 106: 11,623-11,727
  15. ↑ 15.0 15.1 Nielsen, P. 1992. Coastal bottom boundary layers and sediment transport. In: Advanced Series on Ocean Engineering, IV. World Scientific.
  16. ↑ Abreu, T., Silva, P.A., Sancho, F. and Temperville, A. 2010. Analytical approximate wave form for asymmetric waves. Coastal Eng. 57: 656-667
  17. ↑ Van der A, D.A., O’Donoghue, T., Davies, A.G. and Ribberink, J.S. 2011. Experimental study of the turbulent boundary layer in acceleration-skewed oscillatory flow. J. of Fluid Mech. 684: 251-283
  18. ↑ Vincent, C.E. and Green. M.O. 1990. Field measurements of the suspended sand concentration profiles and fluxes and of the resuspensionm coefficient over a rippled bed. J.Geophys.Res. 95: 11591-11601
  19. ↑ Ribberink, J.S. and Al-Salem, A.A. 1995. Sheet flow and suspension of sand in oscillatory boundary layer. Coastal Eng. 25: 205-225
  20. ↑ Ruessink, B.G., Michallet, H., Abreu, T., Sancho, F., van der A, D.A., van der Werf, J.J. and Silva, P.A., 2011. Observations of velocities, sand concentrations, and fluxes under velocity-asymmetric oscillatory flows. J. Geophys. Res. 116, C03004, doi:10.1029/2010JC006443
  21. ↑ Christensen, D.F., Brinkkemper, J., Ruessink, G. and Aagaard, T. 2019. Field observations of intra-wave sediment suspension and transport in the intertidal and shallow subtidal zones. Marine Geology 413: 10–26
  22. ↑ Longuet-Higgins, M.S. 1953. Mass transport in water waves. Royal Soc. London, Phil.Trans. 245A: 535-581
  23. ↑ Trowbridge, J.H. and Madsen, O.S. 1984. Turbulent wave boundary layers: 2. Second-order theory and mass transport. J.Geophys.Res. 89: 7999-8007
  24. ↑ Kranenburg, W. M., Ribberink, J. S., Uittenbogaard, R. E. and Hulscher, S. J. M. H. 2012. Net currents in the wave bottom boundary layer: on wave shape streaming and progressive wave streaming. J. Geophys. Res. 117(F03005), doi:10.1029/2011JF002070
  25. ↑ Stive, M.J.F. and Wind, H.G. 1986. Cross-shore mean flow in the surf zone. Coastal Eng. 10: 325-340
  26. ↑ Cox, D.T. and Kobayashi, N. 1998. Application of an undertow model to irregular waves on plane and barred beaches. J.Coast.Res. 14: 1314-1324
  27. ↑ Gallagher, E.L., Elgar, S. and Guza, R.T. 1998. Observations of sand bar evolution on a natural beach. J. Geophys. Res. 103: 3203–3215
  28. ↑ Reniers, A.J.H.M., Thornton, E.B., Stanton, T.P. and Roelvink, J.A. 2004. Vertical flow structure during Sandy Duck: observations and modelling. Coast.Eng. 51: 237-260
  29. ↑ 29.0 29.1 29.2 Stive, M. J. F. and de Vriend, H. J. 1995. Modelling shoreface profile evolution. Marine Geology 126: 235–248
  30. ↑ Bagnold, R.A. 1963. Mechanics of marine sedimentation. In: The sea, vol.3. Ed. M.N.Hill, Wiley-Interscience: 507-528
  31. ↑ Patterson, D.C. and Nielsen, P. 2016. Depth, bed slope and wave climate dependence of long term average sand transport across the lower shoreface. Coastal Engineering 117: 113–125
  32. ↑ https://oss.deltares.nl/web/xbeach/home
  33. ↑ Bruun, P. 1954. Coast erosion and the development of beach profiles. Beach Erosion Board, US Army Corps of Eng., Tech.Mem. 44: 1-79
  34. ↑ Dean, R.G. 1977. Equilibrium beach profiles: US Atlantic coast and Gulf coasts. Ocean Eng.Tech.Rep. 12, Univ. of Delaware, Newark, 45 pp .
  35. ↑ 35.0 35.1 Dean, R.G. 1977. Equilibrium beach profiles: US Atlantic coast and Gulf coasts. Ocean Eng.Tech.Rep. 12, Univ. of Delaware, Newark, 45 pp.
  36. ↑ Bodge, K.R. 1992. Representing equilibrium beach profiles with an exponential expression. J. Coastal Research 8: 47-55.
  37. ↑ Bernabeu, A.M., Medina, R. and Vidal, C. 2003. A morphological model of the beach profile integrating wave and tidal influences. Mar.Geol. 197: 95-116
  38. ↑ Inman, D.L., Elwany, M.H. and Jenkins, S.A. 1993. Shorerise and bar-berm profiles on ocean beaches. J.Geophy.Res. 98: 18181-18199
  39. ↑ Bowen, A.J. 1980. Simple models of nearshore sedimentation; beach profiles and longshore bars. In: The coastline of Canada, Ed. by S.B. McCann, Geological Survey of Canada, Ottawa, pp. 1-11
  40. ↑ 40.0 40.1 Ortiz, A.C. and Ashton, A.D. 2016. Exploring shoreface dynamics and a mechanistic explanation for a morphodynamic depth of closure. J. Geophys. Res. Earth Surf 121: 442–464 doi:10.1002/2015JF003699


The main author of this article is Job Dronkers
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