Journal
Journalof
ofCoastal
CoastalResearch
Research
SI 64
pg -- pg
572
575
ICS2011
ICS2011 (Proceedings)
Poland
ISSN 0749-0208
Shallow Water Wave Characteristics in Persian Gulf
S. Mazaheri† and Z. Ghaderi‡
†Maritime Engineering &
Technology Research Center
National Institute for
Oceanography, Tehran
141554781, Iran
[email protected]
‡ Maritime Engineering &
Technology Research Center
National Institute for
Oceanography, Tehran
141554781, Iran
[email protected]
ABSTRACT
Mazaheri, S. and Ghaderi, Z., 2011. Shallow water wave charecteristics in Persian Gulf. Journal of Coastal
Research, SI 64 (Proceedings of the 11th International Coastal Symposium),. Szczecin, Poland, ISSN
0749-0208
The Persian Gulf is a large semi-enclosed bay located at the North west-end of the Indian Ocean. The spectrum
of wind-waves which are very important for the design of marine structures is affected by the relatively shallow
water basin and also by the surrounding topographies. Wave spectra and wave parameters at a given location are
necessary for every engineering activity such as design of harbors, coastal and offshore structures. Several
spectra such as Bretschneider, Scott and JONSWAP were used in the region by various authors and
organizations. This study aimed to investigate the shallow water wave characteristics of the north part of the
Persian Gulf by analyzing the measured data obtained from 6 stations for a period of 6 months. PUV and AST
methods were used for processing the data. The analysis showed that the ranges of the peak and mean wave
periods in respect to significant wave height are different from those ranges recommended by ISSC and Kumar.
Furthermore, the measured spectra from those stations were compared with The Pierson-Moskowitz, JONSWAP,
Bretschneider, Ochi and TMA spectra. The comparisons showed that none of the mentioned spectra can
adequately describe the water waves of the Persian Gulf area. Meanwhile, the study showed that the JONSWAP
spectrum can be modified to fit closely with those spectra obtained from the measurements. In order to extend
the results and outcomes of this study to the whole area of the Persian Gulf, more data should be collected and
analyzed.
ADDITIONAL INDEX WORDS: Wave spectrum ,Significant wave height,
INTRODUCTION
The Persian Gulf (Figure 1) is a large semi-enclosed bay located
at the North west-end of the Indian Ocean. The spectrum of windwaves which are very important for the design of marine
structures is affected by the relatively shallow water basin and also
by the surrounding topographies. Knowledge of wave spectra and
wave parameters at a given location is necessary for every
engineering activity such as design of harbors, coastal and
offshore structures. In addition, the study of coastal morphology,
littoral drift and marine environment is highly dependent on the
wave spectrum and its characteristics. These characteristics
include significant wave height, zero crossing period, spectral
peakedness, spectral width, maximum spectral energy, spectral
peak period and spectral narrowness. It is generally believed that
defining a unique spectral wave model, which can be applied in all
parts of the world, is difficult and sometime impossible. For
different locations and climate conditions a number of semi
empirical spectral models were proposed which some of them are
summarized by Chakrabarti (2005). For a fully arisen sea
condition the Pierson Moskowitz spectrum can be used to describe
the spectral characteristics (Pierson and Moskowitz, 1964). For a
growing sea state, Joint North Sea Wave Project (JONSWAP)
spectrum can be used (Hasselman, 1973). Ochi and Hubble (1976)
found that JONSWAP spectrum provided a good approximation to
the data for uni-model spectra with mean JONSWAP parameters
of γ (peak enhancement parameter) equal to 2.2 and α (Philips
constant) equal to 0.023. Ochi (1993) and Young (1998) have
shown that the spectra recorded during storm conditions were unimodel and appeared similar to typical fetch limited data and were
represented by JONSWAP form. The Bretschneider spectrum is
also accepted by ISSC (1967) and ITTC (1969) as a standard
spectrum (Journee, 2001). The Scott spectrum (1965) was
recommended for the west coast of India by Dattatri et al. (1977),
Narasimhan and Deo (1979), Baba et al. (1989) and Kumar et al.
(1994). Meanwhile, Kumar et al. (2008) modified γ and α
parameters of JONSWAP spectrum for shallow water waves of
Indian Ocean. Some researchers tried to predict the significant
wave heights and weather conditions in Persian Gulf by different
approaches. Parvaresh et al. (2005) used statistical analysis on
measured wind and wave data in Boushehr water area, located in
the northern part of Persian Gulf. The WAM model was used by
Rakha et al. (2007) to present a wave atlas for Persian Gulf. Glenn
et al. (1993) used the Bretschneider Spectrum to describe wave
phenomena in South Pars region of the Persian Gulf. The Scott
spectrum is suggested by ASCE based on observations (Task
Committee on Forces on Inclined and Vertical Wall Structures,
1995). In view of the above, it can be concluded that it is still
difficult to choose a spectrum which can express the wave
behavior generated in the Persian Gulf and therefore, more
research is required to determine an appropriate spectrum for the
region.
Journal of Coastal Research, Special Issue 64, 2011
572
Shallow Water Wave Characteristics in Persian Gulf.
Table 1: The details of stations (AQ stands for Aquadopp,
AW stands for AWAC and VE stands for Vector devices)
Station
Name
Location
Start Time
AQ1
Kangan
AQ2
Nakhle Taghi
AW1
Kangan
2008/8/22
17:00
2008/8/23
13:00
2008/8/23
13:00
2008/8/23
13:00
2008/8/22
17:00
2008/8/23
13:00
AW2
Taheri
VE1
Parak
VE2
Nayband
Position
Depth
(m)
X
4
602987
3079323
4
655836
3041707
22
601525
3075411
Parameter
AQ1
AQ2
VE1
VE2
Hs (m)
(Ave.)
0.5-1.19
(0.631)
0.5-2.04
(0.91)
0.5-1.67
(0.67)
0.5-1.86
(0.8)
0.5-1.31
(0.67)
0.5-1.38
(0.75)
Tm02 (s)
(Ave.)
2.58-5.74
(3.39)
2.6-5.64
(3.61)
2.05-4.52
(3.04)
2.5-4.83
(3.51)
2.25-4.7
(3.33)
2.18-5.28
(3.56)
Tp (s)
(Ave.)
3.13-9.2
(4.76)
2.93-8.47
(5.36)
2.47-8.48
(4.23)
3.03-8.47
(4.89)
2.33-9
(5.43)
2.19-8.82
(5.9)
Maximum
Spectral
Energy
(m2/Hz)
1.91
3.128
2.074
2.78
1.043
1.28
Y
25
634509
3057863
2.5
637946
3058900
2.5
664773
3036935
In this regard, as a way towards the determination of an
appropriate spectrum, it is tried to study the shallow water wave
characteristics of the northern part of Persian Gulf (Figure 1) by
analysing the measured wave data at 6 stations (Gulf of Naiband,
Nakhle-Taghi, Parak, Taheri and Kangan) (Figure 2). The wave
data was measured for six months between August 23rd 2008 and
February 23rd 2009. The nomenclature used in the following
context is as follows:
S(ω), S(f)
γ
α
Hs
Tm02
Tp
ωp
g
DATA AND METHODOLOGY
Table 1 shows the details of each station including the water
depth. In each station, the data was measured for 17 minutes per
hour.
Wave Spectrum based on ω,f
Peak Enhancement Factor
Philips Constant
Significant Wave Height
Mean Zerocrossing Period
Peak Wave Period
Angular Peak Wave Frequency
Gravity Acceleration
Constant Coefficient
Table 2: The range of wave parameters at each station.
Wave
Stations
AW1
AW2
PUV process method was applied for the data collected by Vector
and Aquadopp devices. For processing the data measured by
AWAC devices, Acoustic Surface Tracking (AST) method was
used. Only the time series of waves with at least 0.5 m significant
wave hieght were considered for further analysis. The range of
wave parameters values considered for this study are shown in
Table 2.
The wave spectrum for each station was obtained from the
collected and filtered data by Fast Fourier Transform (FFT)
approach. Then, the obtained spectrum was compared with six
other known spectra.
σ
AQ1 (4m)
fp
f
H1/3
W
Φ
d
Peak Wave Frequency
Frequency
Specific Wave Height
Wind Speed
TMA Spectrum Frequency Dependant Factor
Water Depth
AW1(22.5
VE1
AW2
AQ2 (4m)
VE2
Naiband gulf and Kangan
Figure 2. The locations and water depth of the measuring
stations inside the study area of the Persian Gulf.
The Pierson-Moskowitz spectrum can be written as:
S (f ) =
αg 2
exp {−1.25(f p / f ) 4 }
(2π ) 4 f 5
(1)
The JONSWAP spectrum was obtained by doing some
modifactions on Equation (1) and enhancing the peak of the
spectrum by including the γ factor. So it can be expressed as:
Figure 1. The study area.
 5 f
αg 2

S (f ) =
exp
 − 
4 5
(2π ) f
4 f
  p
Journal of Coastal Research, Special Issue 64, 2011
573
−4




 exp[ − ( f −f p )2 / 2σ 2f p 2 ]
γ

(2)
Mazaheri and Ghaderi
0.07,
 0.09,
σ =
f<f p ,
which is between
f ≥ fp
(2.6H )
0 .5
s
and
(3.9H )and found by
0 .5
s
Kumar and Kumar (Kumar and Kumar, 2008) for the Indian
Bretschneider spectrum which is especially suited for open sea
areas can be written as:

1/ 2 



(ω − ω p ) 2
 



2
 0214 H s exp  − 
 , -0.26<( ω -ω p ) < 1.65

S (ω ) = 
0.065(
026)
−
+
ω
ω
 

p


 


Otherw ise
0,

Ocean waves which is between
(3.2H ) and (5.5H ).
0 .5
s
0.5
s
(3)
Ochi (1993) fitted JONSWAP spectral form to the hurricane data
and represented JONSWAP parameters as:
γ = 9.5H s0.34f p
(4)
α = 4.5H s2f p4
Scott also expressed the wave spectrum as:

1/ 2 



(ω − ω p ) 2
 


 0214 H 2 exp  − 
 , -0.26<( ω -ω p ) < 1.65


s
S (ω ) = 
  0.065(ω − ω p + 026) 







Otherw ise
0,

(5)
Figure 4. The relationship between significant wave height and
peak wave period.
The TMA spectrum which is also a modified JONSWAP spectrum
by water depth
(d ) and wave frequency ( f ) can be written as:
S (f )TMA = S (f )JONSW A P Φ (f , d )
Φ=
2
2π f d
g
for
Φ = 1 − 0.5[2 − 2π f (d / g )0.5 ]2
f <(
(6)
2π d ( −0.5)
)
g
for
f >(
2π d (−0.5)
)
g
RESULTS AND ANALYSIS
Significant wave hieght, peak wave period and mean wave periods
are the most common parameters of wave characteristics in every
region. The relation between significant wave hieght and mean
wave period is shown in Figure 3. Figure 4 illustrates the relation
between the significant wave hieght and peak wave period.
Finally, the relation between the peak and mean wave periods is
plotted in Figure 5.
Figure 5. The relation between peak wave period and mean
wave period.
With refer to Figure 4, the variation of the peak wave period
(T ) was found to be between (3.2H ) and (12.5H ). In
0 .5
s
p
0.5
s
addition from Figure 5, the following equations can be derived to
represent the variation of the peak wave period in respect to the
mean wave period.
T p = 4.5T m 02 + 4.8,
T p = 9.15 − 3.95T m 02 + 0.55T m2 02 .
Figure 3. The relation between significant wave height and mean
wave period.
The data presented in Figure 3 shows that the mean wave period
(Tm 02 )
varies between
(2.5H )
0.5
s
and
(7 H )
0.5
s
(7)
Meanwhile, the relation between the peak wave period and the
mean wave period can expressed approximately by the following
formula.
T p ≈ 1.51 T m 02
(8)
which is
different from those values recommended by ISSC (ISSC, 1979)
Journal of Coastal Research, Special Issue 64, 2011
574
Shallow Water Wave Characteristics in Persian Gulf.
γ = 7.5H s0.34 f p
α = 4.5H s2 f p4
(9)
ACKNOWLEDGMENT
This study was carried out as a part of main project named
“Determination of water wave spectrum in Persian Gulf” at
National Institute of Oceanography, Tehran. So, the financial
support to carry out this study and present the paper is appreciated.
In addition, the authors would like to thank Port and Maritime
Organisation (PMO) for letting them to use the data for this study.
LITERATURE CITED
Figure 6. Comparison between measured and other wave
spectra in AW1 station.
Figure 2. Comparison between measured and other wave
spectra in AW2 station.
DISCUSSION AND CONCLUSION
The measurement carried out in the mentioned 6 stations located
in the northern section of Persian Gulf showed that the wave
characteristics of the region are different from other sea water
regions. In this regard, the measured wave spectra were compared
with well-known spectra for every station. Figures 6 and 7
illustrate the comparisons between the measured and other wave
spectra in stations AW1 and AW2 respectively. It can be seen that
none of the known spectra can fully express the wave behavior of
the measured area in the Persian Gulf. The same result can be also
expected from other parts of Persian Gulf, however, more data is
required from those areas to prove this idea. In addition, the
present study showed that the JONSWAP spectrum can be fitted
closely to those measured spectra at AW1 and AW2 stations if the
parameters indicated in equation (9) are applied to the JONSWAP
spectrum.
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