### The Violent Forces on Coastal Structures due to Storm Waves

**Submitting Institution**

University of East Anglia**Unit of Assessment**

Mathematical Sciences**Summary Impact Type**

Technological**Research Subject Area(s)**

Earth Sciences: Oceanography

Engineering: Maritime Engineering, Interdisciplinary Engineering

**Download original**

PDF**Summary of the impact**

Mathematical models of violent flows developed by Dr Mark Cooker at UEA have been adopted by industry. The work enhances the capabilities of coastal engineers to design and repair seawalls and coastal structures, and enhances their interpretation of damage inflicted by storm waves. The research has direct industrial application, and is used to contain, interpret and lessen sea-wave damage to structures. Commercial software has proved inadequate in this field, compared with Cooker's mathematical modelling, because computations alone cannot resolve the brief time- scales and short length-scales over which there are large changes in pressure, and sudden excursions of the liquid as splashes. An example of this impact is the design of an observation gantry exposed to storm waves.

**Underpinning research**

This study concerns the work of **Dr Mark Cooker**, appointed 1992.
The research was undertaken at UEA from 1993 up to the present.

In wave impact research Cooker has made significant applications of pressure-impulse theory (which he co-developed) to practical situations [1-4]. In particular the idea of pressure-impulse [2,4] is now widely used (for example [5]) by coastal engineers for dynamic forces on seawalls, as it is an efficient way of predicting loads on a structure during breaking-wave impact and therefore has underpinned direct industrial application [6].

The underlying mathematics presented in [2] was started while Cooker was employed at Bristol University, but the paper required substantial further work to satisfy reviewers. This additional theoretical work was carried out by Cooker at UEA, and included a critical point of contention: the occurrence of a singularity in some solutions where the boundary conditions are discontinuous at a right angle in the boundary. This revealed extreme violence in the corner of the fluid domain, and the need for an inner solution to describe the splash-jet root. The resolution of the primary importance of the outer solution was a crucial part of the research, and its subsequent scientific development.

One of the underlying mathematical ideas that Cooker developed in [2],
and subsequently for example in [4], involves calculating the
pressure-impulse distribution in the water during impact. At each
geometric point the pressure-impulse is the time-integral of the large
transient pressure over the short duration of an impact. The pressure can
rise from ambient value to a peak of several atmospheres and decline
again, all within a few milliseconds. The time-integral of the pressure is
a mathematically flexible quantity with which to model significant changes
in the impacting wave flow. This idea is useful for design, because
simplified model equations and easily specified initial data predict the
sudden change in fluid velocity, the splash, the total impulse, and the
overturning moment on the structure that is hit. The theory [2,4] explains
the movement of debris along the seabed *away* from a seawall. The
impulses contribute to a wave-excavation of bed material that is then
pushed away from the foot of the wall by succeeding impacts. On a seawall,
the theory also predicts the forces made by the penetration of wave water
into confined spaces, such as cracks. From this the associated impulsive
forces on the interior of the structure can be estimated [6].

Experimental results have shown that high pressure coincides with the
start of a splash made by a wave impact. At a vertical wall, the forward
face of the wave is an accelerating and converging concave surface. From
the bottom of the surface, the splash jet emerges and climbs the wall,
accelerating as it ascends, ahead of the rest of the advancing wave face.
This ultra-violent flow is known as *flip-through*. Flip-through
coincides with the conditions for the highest impact pressures. Cooker's
analysis of this important phenomenon, modelled in [3], explains how and
where such large and damaging pressures occur.

**References to the research**

(UEA authors in bold)

[1] **Cooker, M.J.** (2009) Theories of wave impact pressures on
coastal structures. *Proceedings of the 31st International Conference
on Coastal Engineering*, Hamburg 2008. World Scientific for ASCE,
3212-3223 ISBN: 9789814277402

[2] **Cooker, M.J.** and Peregrine, D.H. (1995) Pressure impulse
theory for liquid impact problems*. Journal of Fluid Mechanics,* **297**,
193-214 DOI: 10.1017/S0022112095003053

[3] **Cooker, M.J.** (2010) The flip-through of a plane inviscid jet
with a free surface. *Journal of Engineering Mathematics*, **67**
(1-2), 137-152 DOI:10.1007/s10665-009-9302-2

[4] **Cox, S.J.** and **M.J. Cooker** (1999) The motion of a
rigid body impelled by sea-wave impact. *Applied Ocean Research*, **21**,
113-125 DOI: 10.1016/S0141-1187(99)00005-X

[5] Müller, G., Hull, P., Allsop N.W.H., Bruce, T., Cooker, M.J. and
Franco, L. (2002) Wave effects on blockwork structures: model tests. *Journal
of Hydraulic Research,* **40** (2), 117-124 DOI:
10.1080/00221680209499854

[6] Müller, G., Wölters, G. and **Cooker, M.J.** (2003)
Characteristics of pressure pulses propagating through water-filled
cracks. *Coastal Engineering*, **49** (1), 83-98 DOI:
10.1016/S0378-3839(03)00048-6

**Details of the impact**

When a sea wave hits a structure such as a seawall, a series of violent fluid flows occur, as vividly illustrated at any harbour during high winds. These impacts may damage the structure and cause hazardous splashes and overtopping. These flows are complex, and demand sophisticated mathematical tools to analyse and predict their movements, forces and outcomes. Better understanding of violent flows leads to improved design, engineering and repair of such coastal structures, and also allows time-dependent safety advice for users of harbour walls to be provided with greater confidence.

Engineers need to interpret the damage made by waves. For example, how do
storm waves *withdraw* blocks from a seawall? Violent flows due to
breaking-wave impacts can damage a structure by over-straining materials,
fragmenting components and undermining foundations. Violent flows are
inherently difficult to compute, particularly in domains with complicated
shapes of boundary. The International Conference on Coastal Engineering
(see [1] above) is a forum of industrial research, at which there is
recurring impetus from the designers to the theorists to improve design
methods, by developing accurate and efficient mathematical models that
predict wave impact forces. The work ultimately has many benefits. For
example, wave splashes are hazardous to persons and vehicles on top of a
harbour wall, and the harbour master's safety advice may depend on a
confident knowledge of the risks from the waves in that setting.

Below we provide three specific examples of the use of Cooker's models of the effects of wave impact in this REF period:

**Charles Scott and Partners**: In 2006, Cooker began a collaboration
with *Charles Scott and Partners*, Glasgow (consulting engineers,
providing services in civil engineering) who wanted to understand how and
why a gantry had been knocked down by storm-waves in Shetland in November
2005. The gantry was a 5.5 metre high free-standing steel structure with
angled struts, designed to allow a person to work safely at an elevated
viewpoint, on a beach with high wave exposure. The unexpected failure of
the original design presented a safety problem. The company was at a loss
to explain the failure, and needed to design a safe replacement. The
company had no method to predict the forces on the gantry, so they
approached Cooker on the strength of his publications and expertise in
predicting wave forces. Drawing on his research, ([2], [4]) Cooker
described how and why the gantry was knocked down onto the beach. He
showed that the failure was due to the sudden huge loads (and moments
about the base) that were exerted on the cylindrical support when struck
by waves. The model was crucial to the company's understanding and their
subsequent design-work on the new gantry, to obtain the right number of
struts and their angles of inclination. Cooker was also able to dispel a
false notion that the two front struts of the structure could in some way
shelter the two rear struts from wave impact. Using these ideas, a
replacement gantry was built to a new design and successfully installed.

*Charles Scott and Partners*with a successful predictive method to model, and hence design, all future structures exposed to wave impact.

**HRWallingford Ltd**: In the coastal wave-impact context, Cooker was a
partner in the EPSRC-funded ViFSNet group (2001-2004). This network
identified critical research problems that needed to be addressed post-2004,
as judged by professional engineers involved in the design and construction
of seawalls and harbours. This led to several collaborations, including with
*HR Wallingford Ltd.*, who are a leading centre for (i)
coastal-engineering consultancy advice around the world, and (ii) the
modelling and computation of waves in the presence of coastal structures
(corroborating source [B]). This on-going commercial link ensures that
Cooker's research on wave impacts is used by industry.

**Atkins UK**: In addition, Cooker's expertise on wave impacts is
widely sought. For example, his expertise on offshore structures and
violent wave-structure interactions, has been applied to estimate the wave
impact forces on wave energy extraction devices. He has provided outcomes
of his research on wave impacts on several occasions in the past five
years to *Atkins*, global engineering and design consultants. The
interest by *Atkins* is in the need to account for the potentially
damaging and destructive wave forces, as well as the useful energy
available for extraction from steep and breaking waves, using devices of
novel design (corroborating source [C]).

**Sources to corroborate the impact **

[A] Personal letter of thanks to Cooker from *Charles Scott and
Partners*, Glasgow. Held on file at UEA.

[B] Corroboration from *HR Wallingford Ltd.*

[C] Corroboration from *Atkins UK*.