Numerical Study Of The Effect Of Spectral Shape On Wave Breaking

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Numerical Study Of The Effect Of Spectral Shape On Wave Breaking

Presented by: Dayang Dania Dayana Binti Azlan (17009173) Supervised by: Dr. Mohamed Latheef


Introduction &

Problem Statement

01 Contents

Objective & Scope of study


Literature Review


Results &





Conclusion &




Background of Study

• Oil and gas is a major source of energy and exports in Malaysia.

• Apart from holding some of the largest reserves in Southern Asia, most of the explorations are concentrated in the South China Sea.

• As developments for explorations move into deeper waters, introduction of

floating structures like spars and FPSOs are needed.

• An important factor that are going to affect these structures are extreme waves including breaking waves.


Breaking Wave

Large offshore structures and coastal structures are exposed to breaking waves which lead to very high peak pressures and wave loads.

Breaking waves are also accompanied by:

Many bubbles

Intense water turbulence

Therefore, water quality related to organic matter seems to change under the effect of breaking waves.


Wave whose amplitude reaches a critical level at which some process can suddenly start to occur that causes large amounts of wave energy to be

transformed into turbulent kinetic energy.

What is breaking wave?


Problem Statement


Lack of research on which spectrum can lead to more

energetic breaking


Lack of research that focused on JONSWAP spectrum and how it affect



Lack of research on how large wave can get before

and after breaking


Objectives & Scope of Study

01 02 01 02

Scope of Study Objective

Research spectrum limited to JONSWAP

spectrum Numerical study

limited to 2 - dimensional waves To quantify the effect

of spectral shape on the onset of breaking

To quantify crest height changes post



Literature Review

Category 1

Predicting the criteria of wave



Category 2

Predicting how large wave can get before it

breaks and its behavior before/after


2 Category 3

The type of sea states in which the

wave can break



Wave breaking criteria may be divided in a broad sense into two types:

Dynamic Geometric

Category 1: Criteria for Wave Breaking


Geometric Dynamic

Use a limiting steepness parameter to determine wave breaking onset (Seiffert, Ducrozet and Bonnefoy 20 17)

Very steep permanent progressive deep- water waves (wave slope ak close to the limiting value of ≈ 0 .443) subjected to normal mode perturbation may rapidly overturn and break due to superharmonic instability (Longuet- Hinggins and

Dommermuth 1997).

More convenient to work in regular waves.

Barthelemy et al, 20 18 introduced energy flux parameter, B = 𝑢𝑢𝑐𝑐 where Uis the component of liquid velocity at the wave crest in the direction of the propagation and C is the phase speed.

𝑢𝑢𝑐𝑐 shows that it can be seen physically that the wave particles move faster to the surface.

More convenient to work in irregular waves.


Category 2: Wave Behaviour Before & After Breaking

Numerous studies has been done on this topic and the examples include:

• D. Drazen, W. Melville, and L. Lenain, 2018 discussed energy dissipation in due to wave breaking but focuses on simple Top - Hat spectra.

• L. Deike, N. Pizzo, and W. Melville focused on enhanced transport of suspended particles due to wave breaking.

• N. Pizzoand W. K. Melville study relates to turbulent vortexes post - breaking


Category 3: Sea States

- Waves propagating over the surface of a homogenous fluid over a flat impermeable bed without change of form.

- Comprise of a single frequency, f of period, T=1𝑓𝑓

- Commonly observed in the ocean, is most conveniently treated as a

summation of regular waves of varying frequency.

- Figure below demonstrate random phase shifts in irregular waves.

Regular Sea States Irregular Sea States



● Model can be utilize to simulate fully nonlinear wave

● Highly accurate

● Efficient

Simulation of the effect of spectral shape on the onset of breaking.

Using a model referring to Bateman, Swan &

Taylor (2001, 2003)


For analysis, establish breaking lim it

Generate breaking groups for each γ Generate wave groups for

different γ

Establish relation between γand 𝜼𝜼𝑚𝑚𝑚𝑚𝑚𝑚, 𝜼𝜼𝑑𝑑

Establish relation between 𝜼𝜼𝑚𝑚𝑚𝑚𝑚𝑚post breaking for

different γ Run Katsardi’s 2D to

validate current im plem entation of Batem an, Swan & Taylor

(2001, 2003) m odel

Stage 1

Stage 2

Stage 3




Two wave groups consists of wave with gamma 1 and gamma 7 were analysed.

Figure 1: Maximum Surface Elevation, 𝜂𝜂𝑚𝑚𝑚𝑚𝑚𝑚 plotted against Amplitude

• Gamma 1 and gamma 7 gradually increases in term of surface elevation as the amplitude increases.

• Wave group with higher gamma tends to have higher surface elevation

compared to lower gamma .



Gamma, 𝛄𝛄 Amplitude, A Maximum Surface Elevation, 𝜂𝜂𝑚𝑚𝑚𝑚𝑚𝑚 Increment (%)

1 4 0.044 25%

5 0.055 22%

8 0.107 22%

9 0.118 10%

7 4 0.046 28%

5 0.059 25%

8 0.112 14%

9 0.121 8%

Table 1: Comparison between percentage of increment of maximum surface elevation for both cases

• Gamma 7 has higher increment compared to gamma 1.

• Waves with higher gamma will produce larger maximum surface elevation.

• Proves that waves with higher gamma values has more energy compared to lower gamma values.



Figure 2: Maximum Energy Flux Density,

𝐵𝐵𝐵𝐵𝑚𝑚𝑚𝑚𝑚𝑚 plotted against Amplitude

• Black line indicates the breaking point at Bx = 0 .65.

• Gamma 1 breaks earlier than gamma 7 where gamma 1 breaks at A = 6.35 and gamma 7 breaks at A = 7.86.

• This can be further explained by analysing the U/C ratio and how it changes at the threshold of breaking.


Figure 3: 𝜂𝜂𝑚𝑚𝑚𝑚𝑚𝑚 vs. time for gamma 1


Figure 4: 𝜂𝜂𝑚𝑚𝑚𝑚𝑚𝑚 vs. time for gamma 7

• Maximum surface elevation of gamma 1 is 0.07m at time 100.18s while maximum surface elevation of gamma 7 is 0.097m at time 88.73s.

• Proving that wave group with a higher gamma values will have a higher maximum surface elevation before breaking and it breaks later.


Figure 5: Crest speed vs. time Figure 6: Fluid velocity vs. time U/C Crest analysis for Gamma 1

• Crest speed, C for gamma 1 is decreasing while the fluid velocity, U is increasing at breaking threshold.

• Hence, a breaking wave is produced when the fluid velocity is increasing and crest speed is decreasing.


Figure 7: Crest speed vs. time Figure 8: Fluid velocity vs. time U/C Crest analysis for Gamma 7

• Wave group with larger gamma takes a larger and more significant step to increase or decrease instead of gradual changes.

• Larger frequency wave contains more energy to move faster.



Waves with higher values of gamma would break later than waves with lower gamma and will have a higher maximum surface elevation at

breaking threshold

The energy that comes with the wave is later dissipated into air injection and formed the bubbles post breaking.

Waves are susceptible to breaking when the fluid particle velocity is increasing meanwhile the crest speed is decreasing.

This study successfully achieved its objective which are:

• To quantify the effect of

spectral shape on the onset of breaking

• To quantify crest height changes post breaking



More spectrums can be used to observe variations in the outcomes .

Study on the effect of spectral shape on wave breaking for 3- dimensional waves.

Study looking into the directionality which could have different effects on the amplification of the waves.



Seiffert , B. and Ducrozet , G., 2017. Simulation of breaking waves using the high- order spectral method with laboratory experiments: wave - breaking energy dissipation. Ocean Dynamics, 68(1), pp.65- 89.

N. Pizzo, E. Murray, D. L. Smith, and L. Lenain, “The role of bandwidth in setting the breaking slope threshold of deep - water focusing wave packets,” Physics of Fluids, vol. 33, no. 11, p. 111706, 2021.

D. Drazen, W. Melville, and L. Lenain, “Inertial scaling of dissipation in unsteady breaking waves,” J. Fluid Mech. 611, 307 – 332 (2008).

L. Romero, W. K. Melville, and J. M. Kleiss, “Spectral energy dissipation due to surface wave breaking,” J. Phys.

Oceanogr . 42, 1421–1444 (2012).



L. Deike, N. Pizzo, and W. Melville, “Lagrangian transport by breaking surface waves,” J. Fluid Mech. 829, 364 –391 (2017).

L. Deike, W. K. Melville, and S. Popinet , “Air entrainment and bubble statistics in breaking waves,” J. Fluid Mech. 801, 91–129 (2016).

Seiffert , B., Ducrozet , G. and Bonnefoy , F., 2017. Simulation of breaking waves using the high- order spectral method with laboratory experiments: Wave - breaking onset. Ocean Modelling, 119, pp.94- 104.


Thank you




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