ANALYSING THE WAVE SPECTRUM FOR THE PERSIAN GULF IN ...

چهاردهمين كنفرانس ژئوفيزيك ايران،‏ تهران،‏ 23-21 ارديبهشت 89، موسسه ژئوفيزيك،‏ مقالات پوستري،‏ فيزيك فضا،‏ صفحه 177-174.
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ANALYSING THE WAVE SPECTRUM FOR THE PERSIAN GULF
IN BUSHEHR PROVINCE
ABSTRACT
The Persian Gulf wave spectrum might not necessarily be defined by known spectrums such as
Bretschneider, Pierson-Moskowitz, JONSWAP and others. In this paper it is attempted to compare
the measured wave spectrums with some of the well-known spectrums i.e. Bretschneider, Pierson-
Moskowitz, JONSWAP (Hasselmann), JONSWAP (edited by Ochi), Scott and TMA. Furthermore,
it is tried to express a formula which can describe the wave spectrum in Persian Gulf. As part of
monitoring research project in Persian Gulf accomplished by the Iranian Ports and Maritime
Organization, some shallow and deep water wave stations were installed close to the Iranian
coastlines. One year continues wave parameters were measured and collected from those stations.
The collected data was processed and analyzed. Then, for each hour of the measured data the wave
spectrum was obtained. Each wave spectrums which got the significant wave height more than 1.0
m was selected. The selected wave spectrums were compared with six known spectrums named
above. This procedure was done for both shallow and deep water wave stations. Comparisons
showed that the measured wave spectrums were not exactly in line with the above mentioned
spectrums. In addition, there are rare signs of swell waves in the trends. Meanwhile, effects of local
wind waves always can be seen in higher band frequency of the wave spectrum. Based on the
results it is attempted to find the best fitted standard spectrum by some modifications to determine
the wave spectrum in the Persian Gulf.
1. INTRODUCTION
Wave spectra and wave parameters at a given location are necessary for every engineering activity.
In addition, the study of coastal morphology, littoral drift and marine environment is highly
dependent on wave spectrum.
In this paper, it is attempted to describe the study area, locations of the stations, type of data
collected and their specifications. Then the time series of converted to wave spectrums and wave
parameters like significant wave height, mean zerocrossing period, peak wave period have been
extracted. Subsequently, the bad data have been detected and removed. Consequently, the
distribution of above mentioned wave parameters related to each other has been shown and the
limitations were illustrated in each station. Then wave spectra from the most severe sea state storms
have been carried out, and data series, specially the highest waves were compared with the standard
spectrums such as Bretschneider, pierson-Moskowitz, Scott, JONSWAP proposed by Hasselmann
and edited by Ochi and TMA. Finally, the best fitted one is determined in this region. The results
show that the measured wave spectrums are not exactly similar to the mentioned spectrums.

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2. STUDY AREA
Data set used in this study comprises of wave data parameters gathered in six stations in Naiband
Gulf, Nakhle-Taghi port, Parak region, Taheri and Kangan port locations, during six months field
measurements from August 23 rd 2008 to February 23 rd 2009. The Plan view of the measurement
stations locations is plotted in figure #1.
Figure 1. Study area in Persian Gulf
3. METHODOLOGY AND DATA PROCESSING
3.1. DATA
The data available for this research are obtained by ADCP (Acoustic Doppler Current Profiler) and
ADV (Acoustic Doppler Velocimeters) wave and current measurement instruments which are
manufactured by the NORTEK (Norwegian) Company and their work mechanism is by sending and
receiving under water transmission acoustic signals.
The present data collected is driven directly from the installed instrument applied in the six
locations during six months and measure waves in 17 minute intervals and the wave parameters are
sampled every hour. Some severe storms occurred during the study and all wave parameters are
recorded and stored from these events.
The time series and power spectrums, derived through Fast Fourier Transform (FFT) became
available. Next step was finding bad data or errors that could be detected by means of empirical
observations. The pressure signal is utilized to estimate the non-directional, energy spectrum. The
total energy distribution in this spectrum is then used to estimate wave height and period. The
cross-correlation of the U and V velocity measurements (of the waves’ orbital velocities) provided
us with a means to estimate the wave direction at specified frequencies. Time series estimates
utilize the “zero-crossing” technique to identify individual waves in a time record.
Table 1. Location, water depth and data recording specifications of the marine measurement instruments.
If smoothing was not used than values would appear extremely noisy. The smoothing used specified
by the number of FFT bins used in processing. A value of 64 is encouraged; however the most
suitable of course is dependent on the number of samples recorded for each burst.

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چهاردهمين كنفرانس ژئوفيزيك ايران
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3.2. DISTRIBUTION AND RANGES
The range and average value of wave parameters of the data considered in the study is shown in
figure #3 to #5.
Figure 2. Variation of mean wave period with
significant wave height
Figure 3. Variation of peak wave period with
significant wave height
Figure 4- Variation of peak wave period with
mean wave period.
4. RESULTS, DISCUSSIONS AND CONCLUSIONS
4.1. DATA DISTRIBUTION AND RANGE
Sea state is generally defined using few parameters derived from the wave spectrum. Significant
wave height (H s ) and peak period (T p ) are the most commonly used parameters. Mean wave period
associated with high wave is usually obtained by assuming a significant wave steepness. In the
present case, waves with H s higher than 0.5m are only considered. It was found that T m02 varies
0.5
0.5
between 2.5H s
and 7H
s
(figure #3). While ISSC (1979) recommendation shows T m02 is in a range
0.5
0.5
of 2.6H s
and 3.9H
s
.The present study shows that T m02 beyond ISSC range. T p was found to be
0.5
0.5
between 3.2H s
and 12.5H
s
(figure #4). T p was found to be varying between the values estimated
using the equations given below (figure #5):
T
p
4.5T
m02
4.8,
T 9.15 3.95 0.55
2
p
T
m02 T
m02
.
And also it was obviated that the relation between peak wave period and mean wave period is:
T p 1.51 Tm
02
(2)
4.2. COMPARISONS BETWEEN MEASURED WAVE SPECTRUMS AND STANDARD
SPECTRUMS RESULTS
The measured wave spectrum has been compared with the aforementioned well-known spectrums.
The spectral peak period estimated by the Scott and JONSWAP (Hasselmann) was higher than the
measured peak value (sometimes they deviate too much). It was found that the Pierson-Moskowitz
spectrum can sometimes estimate the spectral peak value but in prediction of peak wave period and
frequency band it is not reliable due to independency of T p in their formulas. It was found that
although most of the spectra were with predominant single peak, lots of them have local maximums
in higher frequencies as well. Another phenomenon which can be seen in comparisons is that TMA
spectrum fits better in deeper stations than the shallow waters although, the whole trend is not
acceptable.
Generally, the comparisons showed that the measured wave spectrum is more close to JONSWAP
spectrum modified by Ochi than the other spectrums. Then it was attempted to justify the modified
JONSWAP spectrum formula mentioned in equation #3.
4
2
g
5 f
S( f ) exp
4 5 (2 ) f 4
f
p
0.07, f

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چهاردهمين كنفرانس ژئوفيزيك ايران
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0.34
9.5Hs
f
4.5H f
2 4
s p
It has been found that by modifying the peak enhancement factor, γ, in Ochi formula as mentioned
in equation #4 the measured spectrum will fit better with the modified JONSWAP wave spectrum.
0.34
7.5H
s
f p
(4)
Figure #6 shows the measured and parameterized wave spectrums for one of the stations during the
most severe storms in 2008 -2009.
p
Figure 5- Comparison of Standard Spectral
Formulations with the Measured Spectra in the AQ1
station
.
Figure6 - Measured and parameterized wave spectra
for the most severe sea state measured at the shallow
water location, AQ1. Date 30.11.2008, Hs =0.97 m,
Tp=4.75 s, HsDir=172.69°
In this study six measured wave stations were considered to study the wave spectrum in Persian
Gulf. Based on In order to find a general formula which can describe the wave spectrum in Persian
Gulf, more measured wave data from other locations in Persian Gulf will be required. The outcomes
of this study should be checked by other measured wave data in order to verify the suggested wave
spectrum in Persian Gulf.
Therefore, further studies and investigations will be required.
5. REFERENCES
1. V. Sanil Kumar, K.A.K., Spectral characteristic of high shallow water waves. Ocean Engineering, 2008. 35.
2. Chakrabarti, S.K., Handbook of Offshore Engineering. Ocean Engineering Series. Vol. 1. 2005, Amsterdam:
Elsevier.
3. Hasselmann, Measurment of wind wave growth and swell decay during the Joint North Sea Wave Project
(JONSWAP). Deutsche Hydrographische Zeitschrift, 1973. A 12: p. 95.
4. Ochi, M.K., Hubble, E.N. One six parameter wave spectra. in Proceeding of the 15th Coastal Engineering
Conference. 1976. New York: ASCE.
5. Ochi, M.K. On hurricane-generated seas. in Proceeding of the Second International Symposium on Ocean Wave
Measuremnet and Analysis 1993. New Orleans: ASCE.
6. Young, I.R., Observation of the spectra of hurricane generated waves. Ocean Engineering, 1998. 25: p. 261-276.
7. J.M.J. Journee, W.W.M., Offshore Hydrodynamics. first ed. 2001: Delft University of Technology.
8. Sorensen, R.M., Basic Coastal Engineering. Third ed. 2006: Springer.
9. Holthuijsen, L.H., Waves in Oceanic and Coastal Waters. 2007, New York: Cambridge university press.