Maths and coastal defence.

As a result of ongoing coastal erosion and storms, coastal land-based infrastructure is in constant danger of both large-scale damage and flooding. Existing coastal defences, predominantly vertical and/or planar walls, although providing some protection, are frequently breached in severe conditions, which breach necessitates costly repair and/or rescue operations. Such walls are particularly ineffectual in deflecting the high-amplitude waves that occur during storms and/or high tides. The video below illustrates this problem, in which water can be seen breaching the wall and inundating the area behind it.

For videos of coast ripped up by waves, see, e.g., https://www.youtube.com/watch?v=mFrRXlulVFU

For videos of coast ripped up by waves, see, e.g., this link.

Applied mathematical modelling can play a crucial role in dealing with this problem. It enables one to determine the shape of the sea wall that is optimal on two fronts: first, which prevents breaching by water; second, which minmises the load applied by the incoming waves on the wall.
Usual vertical wall, as shown in the first movie.

Usual vertical wall, used in the first movie.

New shape, defined as optimal using mathematical methods.

Optimal shape, defined using mathematical methods.

Using mathematical and computational optimisation methods, a new barrier shape has been designed that dramatically changes the behaviour of the wave impacting upon the wall: mathematics has played a key role in protecting the land-based infrastructure from the waves! The next video illustrates the results of this new design by demonstrating how the breaching has been minimised (by comparison with the first video).

blog_coast2

Note: the shape has been designed by students William Booker, Thomas Goodfellow and Jacob van Alwon.

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