ABSTRACT

Glejin, J.; Sanil Kumar, V., and Sheela Nair, L., 2020. Occurrence of gravity and infra gravity waves in the nearshore region at Ratnagiri, west coast of India. In: Sheela Nair, L.; Prakash, T.N.; Padmalal, D., and Kumar Seelam, J. (eds.), Oceanic and Coastal Processes of the Indian Seas. Journal of Coastal Research, Special Issue No. 89, pp. 92-96. Coconut Creek (Florida), ISSN 0749-0208.

This study analyses the sea level data measured simultaneously using S4DW and directional Wave Rider Buoy (WRB) off Ratnagiri, eastern Arabian Sea, located along the west coast of the Indian sub-continent. The objective of the study is to investigate the presence of infra-gravity waves as well as the source of infra-gravity waves that reach the near-shore regions of eastern Arabian Sea. Based on FFT analysis of the wave data, the estimated mean infragravity wave height is 0.04 m with a peak value of 0.08 m whereas the mean wave period of the infra-gravity waves is 60 s with a standard deviation of 8.9 s. Detailed analysis of the WRB data (wave period in the range of 0-30 s) provide reliable evidence indicating the presence of infra-gravity waves in the eastern Arabian Sea. The source of infra-gravity waves that propagate into the nearshore region could be either remotely or locally generated waves. However, it is observed that the presence of long-period gravity waves in the region has a direct influence on the infra-gravity waves. The amplitude of the infra-gravity is found to increase with the arrival of long period swell waves and vice-versa.

INTRODUCTION

Ocean surface waves even though ubiquitous, are subjected to spatial and temporal variations depending on the environmental conditions. As these waves play a major role in the offshore and coastal dynamics of a region, their studies have gained importance both in the scientific and engineering field. The ocean surface waves primarily comprise of gravity waves with dominant periods typically varying between 2 and 30 s and they are mostly generated by winds. The gravity waves can be further classified into wind seas and swell waves depending on their source of generation, growth and propagation. There is also another type of surface wave called, the Infra-Gravity (IG) waves, which are much smaller in magnitude and have periods ranging from 30 s to 5 min. (Munk, 1949). Despite being small, these IG waves can induce deformations on the seabed which can alter the seismometer measurements of the seafloor (Webb and Hildebrand, 1988).

The study of ocean surface waves is important, as it is mandatory to have site specific wave data for different offshore and coastal related applications viz. design of marine structures and other offshore systems; coastal erosion, pollutant dispersion and sediment transport studies (Aagaard and Greenwood, 2008), wave run-up (van Gent, 2001), dune erosion (De Vries et al., 2008; Roelvink et al., 2009), over wash (McCall et al., 2010), and the generation of the Earth's seismic ‘hum’ (Rhie and Romanowicz, 2006; Webb, 2007, 2008).

Earlier, it was known that the the non linear interactions between high frequency waves can only generate IG motions (Herbers et al., 1995; Longuet-Higgins and Srewart, 1962). Recent studies conducted by Harmon et al. (2012) based on the data from seismometers and differential pressure gauges revealed the presence of remotely generated free IG waves along coastlines. These IG waves can be either free (Herbers et al., 1994) or “bound” (Herbers et al., 1995). The IG waves in coastal areas are of higher amplitudes but shorter wavelengths compared to that of the offshore. Hence detailed investigation of the IG waves is needed to understand their influence along the coast.

IG waves induced low-frequency motions can alter large scale sedimentary features of natural beaches (Bowen and Inman, 1971). Beach and Sternberg (1991) and Aagaard and Greenwood (2008) carried out studies on sediment re-suspension in the surf-zone due to IG waves and its dominance over the incident wind/swell waves. In general, the influence of IG waves in the outer surf-zone area, particularly the sediment re-suspension process is not so prominent compared to the inner surf-zone, because of relatively small amplitude whereas in shallow depths the IG waves acquire enough orbital velocity to mobilize the bottom sediments (Aagaard and Greenwood, 2008).

Gravimeter measurements of vertical displacements of ice islands indicate presence of waves with periods more than 30 s in the Arctic Ocean (Crary, Cotell, and Oliver, 1952). Eventhough energetic pressure fluctuations caused by freely propagating IG surface waves are observed both at the Pacific and the Atlantic Oceans (Webb, Zhang, and Crawford, 1991), the higher energetic waves are in the Pacific ocean. There are also evidence of the presence of IG waves in the Indian Ocean. Hermon et al. (2012), who studied the infragravity waves from cross correlations between 5 ocean bottom differential pressure gauges located off the coast of Sumatra using back projection method and found that infragravity waves were arriving from all directions.

Many of the earlier studies on ocean waves carried out on the Indian coast were based on the data recorded by the surface-following Datawell WRB. The major limitation of these investigations is that the studies were mostly restricted to gravity waves, as the WRB is designed to record waves with periods ranging from 1.6 to 30 s. Since the data pertaining to IG waves were not available, there is hardly any study related to IG waves in the North Indian ocean. Ardhuin et al. (2014) used numerical simulation and found that the IG wave field has strong temporal variability in coastal areas which result in bursts of free IG energy. The measurements of infragravity waves can be conducted using pressure data (Aucan and Ardhuin, 2013; Elgar et al., 1992; Nose et al., 2017; Tatavarti et al., 1999; Webb, Zhang, and Crawford, 1991), GPS directional wave rider buoy measures up to 100 s (De Vries et al., 2003), and doppler sonar techniques and ambient seismic noise (Dolenc et al., 2008; Webb, 2007). In this context the present study was taken up to investigate the role of IG waves along the Indian coast. For this the pressure data recorded using S4DW has been used along with the WRB data off Ratnagiri coast (west coast of India) in the North Indian Ocean.

BACKGROUND

Study Area

The study area is the coast off Ratnagiri, a major fish landing centre, located along the west coast of India bordering the Eastern Arabian Sea (Figure 1). The shelf width off the Ratnagiri coast varies between 100 and 128 km with a corresponding depth ranging from 100 to 130 m. The inner shelf slopes varies 2:1250 up 50 m depth and outer shelf in 1.5:1000 up to 200 m depth to the west. The inner shelf is marked by an even and gentle topography with a slope of 1:700 to 1:3300 (Wagle and Veerayya, 1996).

Figure 1

Study area showing the wave measurement location. The depth contours are in meter.

Figure 1

Study area showing the wave measurement location. The depth contours are in meter.

The gravity waves generated in the Arabian Sea not only depend on the wind conditions that prevail over the area, but also on southwesterly (SW) long period swells that are propagated from the Southern Ocean (Glejin et al., 2013). The wave climate of the Arabian sea, in general, is dominated by energetic summer monsoon swell waves (Glejin et al., 2012). Rest of the season, calm waves with long periods (Tp > 13 s) are observed. Diurnal cycle of the coastal wave climate is influenced by the sea-breeze/land breeze during the pre- and post-monsoon seasons (Glejin et al., 2013).

MATERIALS AND METHODS

All the measured data used in this study are from a bottom moored pressure sensor (S4DW wave and current meter) and a moored Datawell Directional Wave Rider buoy DWR-MK III (Barstow and Kollstad, 1991) deployed off Ratnagiri (16°58′ 48.3″N, 73°15′ 30.3″E). The bottom pressure data have been collected for a period of 78 days (15 October 2012 to 31 December 2012) at a depth of 5 m off Ratnagiri. The S4DW measures sea surface elevation at a rate of 2 Hz (0.5 s) for 18 minutes during an hour and at 14 m water depth during the same period.

Wave Measurement using Wave Rider Buoy

Wave spectrum from the measured buoy data is obtained by applying the Fast Fourier transform (FFT) technique. FFT of 8 series, each consisting of 256 measured vertical displacements of the buoy data, are added to obtain the spectra. The high frequency cut-off is at 0.58 Hz and the resolution is 0.005 Hz. The significant wave height (Hm0) and mean wave period (Tm02) are estimated from the spectral moments as given below.

 
formula
 
formula

where mn is the nth order spectral moment given by

 
formula

n = 0 and 2, S(f) is the spectral energy density at frequency f and fmin = 0, fmax = ∞ The period corresponding to the maximum spectral energy, i.e., spectral peak period (Tp) is estimated from the wave spectrum.

Wind seas and swells from the measured data are separated following Portilla, Ocampo-Torres, and Monbaliu (2009) using a 1-D separation algorithm based on the assumption that the energy at peak frequency of a swell system cannot be higher than the value of a PM spectrum (Pierson and Moskowitz, 1964) with the same peak frequency. The algorithm calculates the ratio (γ*) between the peak energy of a wave system and the energy of a PM spectrum at the same frequency. If γ* is above a threshold value of 1, the system is considered to represent wind sea, else it is taken to be swell and a cut off frequency fc is estimated (Portilla, Ocampo-Torres, and Monbaliu, 2009). Swell parameters are computed by integrating frequencies ranging from 0.025 Hz to fc and the wind sea parameters by integrating frequencies ranging from fc to 0.58 Hz.

Wave Measurement using S4DW

Bottom mounted S4DW is used to measure the wave and tide by sensing the wave orbital current components and the 0-70 m high-resolution depth sensor with 4 mm depth resolution. Data collection started on 15 October 2012 and continued till retrieval of the instrument on 31 December 2012 at a depth of 5 m off Ratnagiri. The S4DW samples sea surface elevation at a rate of 2 Hz (0.5 s) for 18 minutes during an hour. The recorded sea surface elevation acquired from S4DW is detrended to remove the tidal effects, tapered and Fourier transformed to produce elevation spectra (Elgar et al., 1992). This is followed by the computation of wave parameters such as significant wave height and mean wave period that are related to the surface elevation by partially integrating the spectrum for wind sea (0 - fc), swell (fc - 30 s) and IG waves (30 s - 5 min.) using Equations (1) and (2).

RESULTS AND DISCUSSION

Infra-Gravity Waves

Spectral energy associated with the sea surface elevations measured from the study area is parted into three classes; (i) swell, (ii) wind sea and (iii) infra-gravity waves (Figure 2). The energy levels of the measured IG waves and swells are well correlated which indicates that IG waves are driven by swells (Munk, 1949; Tucker, 1950). The correlation between IG wave and wind sea is very poor (Table 1). Based on the analysis the estimated mean IG wave height off the Ratnagiri coast is 0.04 m with a maximum of 0.08 m.

Figure 2

Temporal variation of significant wave height of swell, wind sea, infra-gravity waves during the post monsoon season of 2012 off Ratnagiri. C1 and C2 represents the time period of cyclonic storm Murjan and Deep depression over the western Arabian Sea respectively. The boxes show the correlation between wind sea, swell and IG waves.

Figure 2

Temporal variation of significant wave height of swell, wind sea, infra-gravity waves during the post monsoon season of 2012 off Ratnagiri. C1 and C2 represents the time period of cyclonic storm Murjan and Deep depression over the western Arabian Sea respectively. The boxes show the correlation between wind sea, swell and IG waves.

Table 1

Corelation analysis between IG waves and Gravity waves.

Corelation analysis between IG waves and Gravity waves.
Corelation analysis between IG waves and Gravity waves.

The study indicates that the influence of IG waves along the eastern the eastern Arabian Sea is less energetic compared to the Atlantic and Pacific Ocean during the winter season (Aucan and Ardhuin, 2013; Webb, Zhang, and Crawford, 1991). The mean wave period corresponding to IG waves off Ratnagiri, is 60 s with a standard deviation of 8.9 s. The study reveals that the measured IG wave height is ∼1/10 of swell wave height measured using both directional wave rider buoy and S4DW (Munk, 1949). Another interesting observation is that the energy spectrum of wind sea, swell and IG waves were mostly in phase througout the study period (boxes) except during 2 events which witnessed the passage of a cyclonic storm (C1) and a deep depression (C2) over the region. During these periods the increase (decrease) in IG waves are correlated with increase (decrease) in swell and wind sea height. This clearly indicates that the locally generated IG waves were generated by the interaction between the sea waves (or wind stress) and swells over the region. It is also observed that the ephemeral dominance of sea over swells diminish the effect of IG waves over the region. This can be attributed to the dissipation of swells and energy dissipation from turbulence generated by the short period waves. The study also shows that waves with period higher than 8 s (swells) are responsible for the locally generated IG waves.

Infra-Gravity Waves and Long Period Waves

Long period waves persist throughout the year in the eastern Arabian Sea (Glejin et al., 2013) and they dominate during the pre and post-monsoon seasons. The occurrences of long period waves and their interaction with IG peak events along the nearshore regions of the eastern Arabian Sea have been analysed (Figure 3). It is observed that there is a direct correlation between the occurrence of peak values of significant wave height and the peak wave period. A cut-off peak period of 16 s was used to relate the IG waves and wave buoy measurement. Even though the study indicated a positive correlation between the peak wave period of the spectrum and the significant wave height of the IG waves during the passage of cyclonic storms over the Arabian Sea (Table 1), the same trend was not observed during the remaining period. Contardo and Symonds (2013) observed a stronger relation between IG waves and long period swells compared to short period waves. Peak wave period is directly correlated with the maximum wave height, while during the rest of the study period, we could not find any direct relationship between these two variables (IG wave height and peak wave period).

Figure 3

Co-occurrence of peak wave height of swells (Tp > 16 s) associated with the temporal variation of infra-gravity wave height during the post monsoon season of 2012 off Ratnagiri.

Figure 3

Co-occurrence of peak wave height of swells (Tp > 16 s) associated with the temporal variation of infra-gravity wave height during the post monsoon season of 2012 off Ratnagiri.

Table 2

Storm and cyclonic activity over the Arabian Sea during 2012.

Storm and cyclonic activity over the Arabian Sea during 2012.
Storm and cyclonic activity over the Arabian Sea during 2012.

Cyclones and Infra-Gravity Waves

Infra-gravity waves present at a particular location may be due to remotely generated or locally generated waves. Cyclones are associated with strong winds and can generate long period waves capable of travelling long distances across the ocean (Glejin et al., 2013; Snodgrass et al., 1966). Unlike the Bay of Bengal, the Arabian Sea is less prone to storms. The two major systems that developed over the south Arabian Sea during the study period are the Cyclonic storm, Murjan (C1) and a Deep Depression (C2) (Table 1). From Figure 3 it can be seen most energetic IG events are observed along the eastern Arabian Sea during C1 and C2 (Figure 2). During these events both swell and IG waves showed good correlation. The IG wave periods also showed a similar trend as is evident from the rise in peak wave period during the events C1 and C2. On the contrary, wind sea showed an opposite trend with a decrease in wave height, as they are primarily influenced by the local winds which also includes the sea-breeze/land-breeze system (Aparna et al., 2005; Glejin et al., 2013; Neetu, Shetye, and Chandramohan, 2006).

CONCLUSIONS

Wave data measured for a period of 3 months at a depth of 5 m off Ratnagiri, located along the west coast of India is used to analyse the infra-gravity waves over the near-shore regions of eastern Arabian Sea. Infra-gravity waves observed over the eastern Arabian Sea are due to both locally (wind sea - swell interaction) and remotely (cyclonic winds) generated waves. The presence of remotely generated infra-gravity waves in the nearshore regions can be identified by examining the directional wave rider buoy data as the waves are associated with a peak period of more than 16 s and have an inverse correlation with wind sea over the region.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial support given by the Earth System Science Organization, Ministry of Earth Sciences, Government of India to conduct this research. Director, CSIR-NIO, Goa and Director, INCOIS, Hyderabad and Science and Engineering Research Board (SERB) provided encouragement to carry out the study. We thank Mr. Jai Singh, Technical Assistant, CSIR-NIO, Dr. T.M. Balakrishnan Nair and Mr. Arun Nherakkol, Scientist, INCOIS for the help during data collection. This is NIO contribution no. 6402.

LITERATURE CITED

LITERATURE CITED
Aagaard,
T.
and
Greenwood,
B.
,
2008
.
Infragravity wave contribution to surf zone sediment transport - the role of advection.
Marine Geology
,
251
(
1-2
),
1
14
.
Aparna,
M.
;
Shetye,
S.R.
;
Shankar,
D.
;
Shenoi,
S.S.C.
;
Mahra,
P.
, and
Desai,
R.G.P.
,
2005
.
Estimating the seaward extent of seabreeze from Quik SCAT scatterometry.
Geophysical Research Letters
,
32
(
13
),
1
4
.
doi:10.1029/2005GL023107
Aucan,
J.
and
Ardhuin,
F.
,
2013
.
Infragravity waves in the deep ocean: an upward revision.
Geophysical Research Letters
,
40
(
13
),
3435
3439
.
doi:10.1002/grl.50321
Barstow,
S.F.
and
Kollstad,
T.
,
1991
.
Field trials of the directional wave rider.
Proceedings of the First International Offshore and Polar Engineering Conference (Edinburgh, United Kingdom)
, pp.
55
63
.
Bowen,
A.J.
and
Inman
D.L.
,
1971
.
Edge waves and crescentic bars.
Geophysical Research Letters
,
76
(
36
),
8662
8671
.
Crary,
A.P.
;
Cotell
R.D.
, and
Oliver,
J.
,
1952
.
Geophysical studies in the Beaufort Sea.
Eos, Transactions American Geophysical Union
,
33
(
2
),
211
216
.
De Vries,
J.V.T.
;
Van Gent,
M.R.A.
;
Reniers,
A.J.H.M.
, and
Walstra,
D.J.R.
,
2008
.
Analysis of dune erosion processes in large scale flume experiments.
Coastal Engineering
,
55
(
12
),
1028
1040
.
doi:10.1016/j.coastaleng.2008.04.004
Dolenc,
D.
;
Romanowicz,
B.
;
McGill,
P.
, and
Wilcock,
W.
,
2008
.
Observations of infragravity waves at the ocean-bottom broadband seismic stations Endeavour (KEBB) and Explorer (KXBB).
Geochemistry, Geophysics, Geosystems
,
9
(
5
),
1
18
.
Elgar,
S.
;
Herbers,
T.H.C.
;
Okihiro,
M.
;
Oltman-Shay,
J.
, and
Guza,
R.T.
,
1992
.
Observations of infragravity waves.
Journal of Geophysical Research: Oceans
,
97
(
C10
),
15573
15577
.
doi:10.1029/92JC01316
Glejin,
J.
;
Kumar,
V.S.
;
Nair,
T.B.M.
, and
Singh,
J.
,
2013
.
Influence of winds on temporally varying short and long period gravity waves in the near shore regions of the eastern Arabian Sea.
Ocean Science
,
9
,
343
353
.
doi:10.5194/os-9-343-2013
Glejin,
J.
;
Kumar,
V.S.
;
Sajiv
P.C.
;
Singh,
J.
;
Pednekar,
P.
;
Ashok,
K.K.
;
Udhaba,
D.G.
, and
Gowthaman,
R.
,
2012
.
Variations in swells along eastern Arabian Sea during the summer monsoon.
Open Journal of Marine Science
,
2
(
2
),
43
50
.
Harmon,
N.
;
Henstock,
T.
;
Srokosz,
M.
;
Tilmann,
F.
;
Rietbrock,
A.
, and
Barton,
P.
,
2012
.
Infragravity wave source regions determined from ambient noise correlation.
Geophysical Research Letters
,
39
(
L04604
),
1
5
.
doi:10.1029/2011GL050414
Herbers,
T.H.C.
;
Elgar,
S.
, and
Guza,
R.T.
,
1994
.
Infragravity-frequency (0.005-0.05 Hz) motions on the shelf. Part I: Forced waves.
Journal of Physical Oceanography
,
24
,
917
927
.
Herbers,
T.H.C.
;
Elgar,
S.
, and
Guza
R.T.
,
1995
.
Infragravity-frequency (0.005-0.05 Hz) motions on the shelf. Part II: Free waves
,
Journal of Physical Oceanography
,
25
,
1063
1079
.
Longuet-Higgins,
M.S.
, and
Stewart,
R.W.
,
1962
.
Radiation stress and mass transport in surface gravity waves with application to ‘surf beats'.
Journal of Fluid Mechanics
,
13
,
481
504
.
McCall,
R.T.
;
De Vries,
J.V.T.
;
Plant,
N.G.
;
Van Dongeren,
A.R.
;
Roelvink,
J.A.
;
Thompson,
D.M.
, and
Reniers,
A.J.H.M.
,
2010
.
Two-dimensional time dependent hurricane overwash and erosion modeling at Santa Rosa Island.
Coastal Engineering
,
57
(
7
),
668
683
.
Munk,
W.H.
,
1949
.
Surf beats.
EOS, Transactions American Geophysical Union
,
30
(
6
),
849
854
.
Neetu,
S.
;
Shetye,
S.
, and
Chandramohan,
P.
,
2006
.
Impact of sea breeze on wind-seas off Goa, west coast of India
.
Journal of Earth System Science
,
115
(
2
),
2031
2038
.
Pierson,
W.J.
and
Moskowitz,
L.
,
1964
.
A proposed spectral form for fully developed wind seas based on the similarity theory of S.A. Kitaigoirodskii.
Journal of Geophysical Research
,
5181
5190
.
Portilla,
J.
;
Ocampo-Torres,
F.J.
, and
Monbaliu,
J.
,
2009
.
Spectral partitioning and identification of wind sea and swell.
Journal of Atmospheric and Oceanic Technology
,
26
,
117
122
.
Rhie,
J.
and
Romanowicz,
B.
,
2006
.
A study of the relation between ocean storms and the Earth's hum.
Geochemistry, Geophysics, Geosystems
,
7
(
10
),
1
23
.
Roelvink,
J.A.
;
Reniers,
A.J.H.M.
;
Van
D.A.R.
;
Van Thiel de Vries,
J.S.M.
;
McCall,
R.T.
, and
Lescinski,
J.
,
2009
.
Modelling storm impacts on beaches, dunes and barrier islands.
Coastal Engineering
,
56
(
11-12
),
1133
1152
.
Snodgrass,
F.E.
;
Groves,
G.W.
;
Hasselmann
K.
;
Miller,
G.R.
;
Munk,
W.H.
; and
Powers,
W.H.
,
1966
.
Propagation of ocean swells across the Pacific.
Philosophical Transactions of the Royal Society of London
,
A249
,
431
497
.
Tatavarti,
R.
;
Narayana,
A.C.
;
Kumar,
P.M.
, and
Chand,
S.
,
1999
.
Mudbank regime off the Kerala coast during monsoon and non-monsoon seasons.
Proceedings of the Indian Academy of Sciences-Earth and Planetary Sciences (New Delhi, India)
,
108
(
1
), pp.
57
68
.
Tucker,
M.J.
,
1950
.
Surfboats: sea waves of 1 to 5 minutes' period.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
,
202
(
1071
),
565
573
.
Van Gent,
M.R.A.
,
2001
.
Wave runup on dikes with shallow foreshores.
Journal of Waterway, Port, Coastal, and Ocean Engineering
,
127
(
5
),
254
262
.
Wagle,
B.G.
and
Veerayya,
M.
,
1996
.
Submerged sand ridges on the western continental shelf off Bombay, India: evidence for Late Pleistocene-Holocene sea-level changes.
Marine Geology
,
136
(
1-2
), pp.
79
95
.
Webb,
S.C.
,
2007
.
The Earth's ‘hum’ is driven by ocean waves over the continental shelves.
Nature
,
445
(
7129
),
754
756
.
Webb,
S.C.
,
2008
.
The Earth's hum: The excitation of Earth normal modes by ocean waves.
Geophysical Journal International
,
174
(
2
),
542
566
.
doi:10.1111/j.1365-246X.2008.03801.X
Webb,
S.C.
and
Hildebrand,
J.A.
,
1988
.
Constraints on crustal structure beneath axial volcano derived from long period acceleration and pressure measurements.
EOS
,
69
,
1484
.
Webb,
S.C.
;
Zhang,
X.
, and
Crawford,
W.
,
1991
.
Infragravity waves in the deep ocean.
Journal of Geophysical Research: Oceans
,
96
,
2723
2736
.