# 8.4.4: Shoreline perturbation

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This section discusses the evolution of a single perturbation (a ‘bump’) in the shoreline. Such a bump in the shoreline can have various origins, for instance a nourishment scheme or a significant supply of sediment by rivers, leading to delta formation (see Sect. 8.4.6). In Example 8.4.4.1, we consider an initial disturbance of the system by a nourishment (or any other perturbation of the coastline for that matter).

Assume a beach nourishment has recently been executed on an initially straight stretch of coast. Some time after the nourishment, the sediment has been redistributed in the cross-shore and the shoreline is given by the dotted line in Fig. 8.25. As a result of the nourishment the shoreline has advanced, after cross-shore redistribution, over an alongshore distance of 1000 m. The maximum shoreline advance is 50 m. The angle between the original and nourished coastline is everywhere smaller than \(10^{\circ}\).

**Questions**

- The waves are normally incident to the original shoreline. Sketch how the coastline will qualitatively develop in time. In order to substantiate your answer, draw the initial longshore transport rates as a function of the distance along the coast (as in the middle panel of Fig. 8.19) and indicate, based on the longshore transport gradients, where erosion and accretion take place. What are the locations with the largest shoreline change?
- As 1. but now the waves have an angle of incidence in deep water of \(20^{\circ}\) with respect to the original shoreline;
- As 1. but now the waves have a deep water angle of incidence of \(70^{\circ}\) with respect to the original shoreline.

Figure 8.26, based upon concepts by Ashton and Murray (2006), contains some of the answers to the questions in Example 8.4.4.1. Figure 8.26b shows the transport as a function of the deep water wave angle relative to the shore (denoted \(\varphi_0\) in these lecture notes). It can be seen that for low-angle waves the transport increases with larger relative angles (from 1 to 2 to 3 in Fig. 8.26b). By contrast, for high-angle waves the transport decreases with increasing angle (from 4 to 5 to 6 in Fig. 8.26b).

Figure 8.26c shows the shoreline response to low-angle waves. At the ‘horizontal’ parts of the shoreline the transport magnitude is equal and given by point 2 in Fig. 8.26. However, at the ‘left’ and the ‘right’ flank of the ‘bump’ the relative wave angles and thus the transport magnitudes are smaller (point 1) and larger (point 3) respectively. The crest of the bump erodes, since there the transport increases (diverges) in the transport direction (positive transport gradient). A decreasing (converging) transport in the transport direction (negative transport gradient) causes deposition. The end result is a flattening of the shape towards a straight coastline for which no further changes occur. For high-angle waves (greater than \(45^{\circ}\)) the pattern of erosion and deposition is reversed, leading to growth of the bump (Fig. 8.26d).

The shoreline response to low-angle waves is a clear example in which negative feedbacks stabilise the shoreline by eroding the perturbations (see Sect. 1.5.2). For high-angle waves, positive feedbacks promote the growth of perturbations, leading to self-organised patterns (see also Intermezzo 7.2).