For oral exam June 27 2005
The excel

Journal Review: Alongshore Variation in Beach Cusp Morphology in A Coastal Embayment

Earth Surface Processes and Landforms Journal. Vol 24. Page 335-347.1999.


Gerhard Masselink


What is his research type?
His research is to examine the beach cusp characteristic in 1 km embayment beach (Pearl Beach, New South Wales)


Is he in "Edge-Wave-Theory" or "Self-organization theory"?
He said: Edge wave mechanism of beach cusp formation COULD NOT account for the observed trend in cusp spacing.


Why?
Because, there is NO RELATIONSHIP could established between the spacing of the cusp and the gradient of the beachface.
It said that beach cusp develop and are maintained by 3D swash flow circulation pattern characterized by wave uprush.


History of Research
Standing Edge Waves Theory
According to this theory, swash superimposed on the motion of standing edge waves and produce a systematic alongshore variation in swash height. This variation will result in regular erosional perturbation. The swash cirsulation will enhance topographic perturbation.
Two edge wave type that generally implicated are:
a. Mode Zero, subharmonic edge waves
b. Synchronous edge waves

In edge wave theory, can predict a cusp spacing as a function of incident wave period and beach gradient.


The self-organization theory
This theory said that:
Beach cusp formation consider beach cusp to be the result of feedback processes between morphologic and swash flow.
Positive feedback : Enhances RANDOM MORPHOLOGIC IRREGULARITIES
Negative feedback : Inhibits EROSION AND ACCRETION on well develop cusps.
In this theory, dimension of rythmic morphology is a function of horizontal swash excursion.

How to validate those theories?
There are two avenues of investigation:
1.Monitoring of the water motion in the swash and surf-zones during beach cusp formation.
2.Comparing the equation of cusp spacing in both theories.


Please think this phenomena!
In coastal area,
Wave height, beach gradient, sediment size, cusp spacing, and swash excursion are VARY ALONG ITS SHORELINE.
in contrast the wave period remain UNIFORM
This clue is an ideal opportunity to investigate the two models of beach cusp formation.
So, if egde wave is valid,
The alongshore variation in cusp spacing should be explained in terms of the beach gradient.
However, if the self-organization theory valid,
The alongshore variation in cusp spacing should be accounted for by the alongshore variation in the horizontal swash excursion.


Field Experiment on Pearl Beach
There are 45 beach cusp appear on Pearl Beach with cusp spacing of 22-23 m.
In each profile, were surveyed:
1. Berm Crest
2. Mid-beach face position
3. Down rush limit (the lowest point on the beachface that falls dry during swash action).


Four Parameters were derived from data set:
1. Cusp spacing
2. Beach face gradient
3. Cusp prominence (a function of beach slope at beach cusp horn and bay)
4. Horizontal Swash excursion


How to determined?
1. Cusp Spacing :
From alongshore distance between 2 cusp horn
2. Beachface gradient :
Computed for each mini-profile from the berm crest to the downrush limit.
It obtained by averaging the gradient of the cusp horn and embayment.
3. Cusp Prominence, by computation
4. Horizontal swash excursion, by statistical parameter.
Swash motion monitored at least 30 minute before the swash length parameter can be computed. (Parameter : Mean, max and significant swash excursion)

Result
1. Beach cusp have formed at the preceding day and/or night
2. Edge wave model can only be made to fit the morphological data by invoking several episodes of beach cusp formation.
3. Does the mean of the cusp horn and embayment gradient represent the beachface gradient during cusp formation?
Cusp horn result from a local steepening of the formation of cusp embayment. Mean of the horn and embayment gradient is characteristic of pre-cusp brachface gradient.


S U M M A R Y
There is a strong relationship between cusp spacing and swash excursion.

Self Organization in Beach Cusp Formation

What is Beach cusp?
Beach cusps are cuspate patterns with concave seaward, are usually formed at the shoreline, and have longshore wavelengths varying from less than 1 m until 700 m. They enumerate some traditional names given cuspate features on ocean shorelines. The classification are Typical Beach Cusps which wavelength 8-25 m, Storms Cusps which wavelength 70-120 m and Giant Cusps which wavelength 700-1500 m (Guza et al 1975).

Why beach cusp appears?
Many studies have been conducted in case to know how beach cusp formed. Early studies said that beach cusp formed by the action of nearshore current system. The generation mechanisms are classified into two types: those due to a longshore variation in the external force and those due to hydrodynamic instability (Tanikawa et al, 2004). The former one includes theories in which the wave field loses its uniformity due because of external causes. Such as edge waves and cross wave (Guza 1973) and the other one means that rhythmic formation is because fluid dynamic instability breaks the uniformity of radiation stress even without an external cause (Hino 1973).

How to explain their formation?
Beach cusp research has been studied to approach their formation in several ways
1. Field Experiment (Gerhard Masselink, 2003)
2. Laboratory (Guza,1973)
3. Numerical Program (Coco, et al, 2003)
4. Mathematic Analysis (Hino, 1975; Izumi, 2004)

Which one is the most powerful to approach beach cusp formation?
Not clear though. When doing any research, we didn’t know which one is the most powerful. In my case, I want to show their formation by mathematic analysis.

Why use mathematic analysis?
Beach cusp is more like a perturbation on linear shoreline. Their pattern can reminder us to sinusoidal function. They have a constant wavelength in each formation. In mathematic analysis, we would find any solution to represent the case. This solution would be real and/or unreal. If the solution real, the base state in linear stability analysis become stable, it means beach cusp don’t occur on linear shoreline. Otherwise, we would find beach cusp when we have unreal solution.
Numerical analysis can’t solve the unreal solution. There will be error or we can not continue our programming.
Therefore, we need mathematic analysis.


What is perturbation equation?
An equation which perturbated the linear base state. We can assume anything in this equation.
For example, we assume that:
a) Beach cusp is a function of beach slope
b) Function of grain size sediment
c) Function of wave height
d) Swash action
e) Breaking zone width
f) Radiation stress
g) etc

From this assumption, we can make any equation which have a function of those. In mathematic analysis, if we have a complex function, we solve one by one. Then, we make a graphic. From this graphic, later on, we could know, which one of those functions, which closely approach the formation of beach cusp. When there is a function which have less contribution to beach cusp, then this function will be denied and become an error.


What is Base State?
Base state is initial condition in linear stability analysis. A system equation which have some function like in the perturbation equation, but we make the linear function.

Conclusion?
So, with mathematic analysis, there will be many ways to develop the early model since numeric analysis can not solve this.
This analysis will provide the scientist to explore all his hipotesa to base state and perturbation equation.
More simple and free.

Some mathematic tricks
Non-dimensional analysis needed to get simpler.
Often, the equations we want to solve in fluid problems can not solved with all the terms present. By using this analysis, we often gain an insight into what physical processes.

Still need to study though !!!

Summary Beach Cusp

For presentation at February 1st 2005

SEDIMENTATION PROCESS STUDY AT ENTRANCE CHANNEL,CASE STUDY: PULAU BAAI PORT

ABSTRACT
Dynamical process in tidal inlet or entrance channel is affected by littoral transport due to wave action and onshore-offshore transport due to tidal action. The equation to formulate the relationship between depth and other parameters such as tide velocity, sediment discharge due to tide, and littoral drift in tidal inlet. The equation in this thesis is defined by applying continuity equation of sediment. It can then be used to predict variation of depth in time as the function of sediment discharge out of the inlet and sediment discharge into the inlet and also to predict equilibrium depth at entrance channel.

keywords : sediment, tidal inlet, equilibrium