Understanding breaking waves

Lead Research Organisation: Imperial College London
Department Name: Civil & Environmental Engineering

Abstract

From an engineering perspective, wave breaking is of particular interest in the design and re-assessment of offshore and coastal structures. As this is an area of active research, the process of wave breaking is probably one of the least understood topics in wave mechanics. Although it has significant effects on the magnitude of wave loads, the understanding of the process itself is rendered difficult due to the complexity given by the different length scales of turbulent eddies forming and the interaction between two fluid phases, amongst others.

The overarching aim of this research project is to further the understanding of wave breaking. The objectives of the project include:
- Examining whether a geometric criterion be successfully applied to detect wave breaking if more advanced transforms are employed to accurately calculate the wave number.
- Investigate the coupled effects of changes in crest speed and increase in particle kinematics in describing the formation of breaking waves and the role of nonlinearity, spectral type and bandwidth.
- Develop a new wave breaking identification method that only uses a single time history of the surface elevation, as typically recorded in field measurements.
- Develop a new numerical model that is capable of accurately incorporating nonlinearity, directional-spreading and wave breaking. This model should be computationally efficient such that it can run hundreds of simulations of random irregular waves to provide key statistics such as distributions for the wave height, crest elevation and underlying kinematics.

In order to achieve these objectives, the project will examine existing experimental investigations of breaking waves to determine the best breaking criteria, test the breaking detection methodology and quantify the energy dissipation caused by breaking waves. Computational fluid dynamics simulations will be run to complement the experimental measurements. A high-order spectral method will also be improved to include the effect of wave breaking.

The novel part of this research includes improving our understanding of wave breaking, providing an accurate method to detect breaking waves in the ocean from single-point time histories, quantifying the degree of energy dissipation that breaking causes in realistic sea states and providing a computationally-efficient numerical model that can accurately simulate random sea states that incorporates nonlinearities, directional spreading and wave breaking. This project is relevant to the "Fluid dynamics and aerodynamics" EPSRC research area.

Publications

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Craciunescu C (2019) The effect of wave crest speed in breaking waves in IOP Conference Series: Materials Science and Engineering

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Craciunescu C (2020) On the calculation of wavenumber from measured time traces in Applied Ocean Research

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509486/1 01/10/2016 31/03/2022
1855727 Studentship EP/N509486/1 01/10/2016 31/03/2020 Constantin Cosmin Craciunescu
 
Description This award has funded work into understanding waves breaking in the ocean, which are very complex
and there are many open research questions. Several findings have resulted from this project,
which has focused on studying the initiation, detection and experimental modelling of realistic
breaking waves and ultimately on their inclusion within efficient numerical models.

Historically, breaking thresholds have been quantified using geometric parameters, such as the wave
steepness that depends on the wavelength, which therefore needs to be accurately estimated. The
majority of field measurements record a time history of the water surface at a single location in
the ocean. This directly provides the wave periods, but the user needs to assume a relationship
between the wave period and wavelength: this is referred to as the dispersion equation. The present
work has demonstrated that the linear dispersion equation, which is commonly used in design
calculations, can be up to 30\% inaccurate; the nonlinear version of the dispersion equation
performs only slightly better. An alternative proposed within the literature uses the Hilbert
Transform, however, the present work found that this incorrectly estimates the wavelength by up to
20\% for broad-banded sea states. This project demonstrated that the best estimate of the wavelength
(within 2\%) is provided by a highly-nonlinear numerical model, however it is computationally
expensive requiring several hours to run. Therefore, the present work also provided simple empirical
corrections to the linear dispersion equation for the largest waves in the ocean, which can easily
be employed in design calculations.

Given that field measurements only provide a time history of the water surface, it is not possible
to directly ascertain whether waves are breaking; this requires a profile in space rather than in
time. Therefore, this project developed a novel methodology using a numerical model to detect wave
breaking within measured time-histories. The numerical model was shown to be in excellent agreement
with experimental measurements and successfully identified breaking events.

With respect to physical understanding, results show that increased water particle velocity coupled
with reduced wave crest speed explains the formation of deep water breaking waves. The present study
has provided new physical insight that explains why large waves see a reduction in their crest
speeds. The results also confirm the validity of a recently proposed kinematic wave breaking
criteria, which the present study has employed to include the effects of wave breaking into a
numerical model. Futhermore, the present work involved new experimental investigations that
quantified the energy dissipated by realistic breaking waves. These experiments demonstrated that a
wave breaking dissipation coefficient needs to be increased by 85\% for realistic sea states.

Finally, all these findings were implemented into an efficient numerical model allowing it to
successfully incorporate breaking waves. Using this new numerical model, the present work was the
first to replicate experimental measurements of wave crest elevations including nonlinear
amplification and wave breaking in realistic sea states. The numerical model was compared with three
large experimental datasets and it demonstrated excellent agreement across all cases.
Exploitation Route There are several ways that the outcomes can be taken forward in academia and industry. First, the
empirical corrections to the linear dispersion equation can be used to accurately calculate the
wavelength from experimental investigations and field measurements, both of which typically only
measure time-histories. This will improve academic research and is easily applicable within industry
for design calculations.

Second, the novel wave breaking detection methodology can be employed to determine the occurrence of
wave breaking within measured time traces, whether recorded in the laboratory or in the field. This
will aid with the quality control of field measurements, as well as enabling the frequency of
wave breaking to be ascertained.

Third, the new numerical model that includes wave breaking can be used in both academia and industry
to determine wave statistics of realistic sea states. This could previously only be achieved by
running expensive model test campaigns, the cost of which limits both the range as well as the
duration of sea states that can be examined.

Finally, the recommendations proposed within the present work can be put to use towards better and
safer design practices and methodologies in the marine and offshore industries.
Sectors Aerospace, Defence and Marine,Construction,Energy,Environment,Transport