Nat Hazards (2016) 80:1369–1380
DOI 10.1007/s11069-015-2027-9
ORIGINAL PAPER
Neap—spring variability of internal waves over the shelfslope along western Bay of Bengal associated with local
stratification
Himansu K. Pradhan1
•
A. D. Rao1 • Madhu Joshi1,2
Received: 29 August 2014 / Accepted: 10 October 2015 / Published online: 22 October 2015
Ó Springer Science+Business Media Dordrecht 2015
Abstract Interaction of barotropic tide with the continental shelf break region is studied
in the presence of local stratification. To achieve this, MITgcm is developed for the
western part of Bay of Bengal to simulate the internal tide that manifests itself as internal
wave (IW) of predominant M2 tidal frequency. The QuikSCAT daily winds and real-time
tides along with monthly climatology of density are used as initial forcing fields to drive
the model. From the energy spectra analysis, variability of dominant semi-diurnal IWs is
addressed on both spatial and temporal scales. Computed spectral estimates of temperature
and density fields off Visakhapatnam using the time series data are in good agreement with
observations during 23–25 February 2007 and 18–20 October 2006. Isopycnal displacement of about 15 m is computed which compared well with observations for February
2007, confirming the presence of internal tides. Spectral energy peak is higher for spring
than for neap as the associated astronomical forcing is maximum. The IW peak is simulated at 75 m depth which falls within the pycnocline depth. Two vertical cross sections
bearing different stratifications along the Bay of Bengal coast are studied to delineate IW
energy propagation over the shelf-slope region. The spatial model results show that the
location of peak energy shifted a few kilometres onto the shelf towards the coast during
October. Our simulation results during February and October demonstrate that IW energy
varies across the shelf break with energy peaks at the shelf break, and their dissipation
range is affected by the degree of stratification.
Keywords Barotropic tide Shelf break Stratification MITgcm Energy spectra Neap—spring
& Himansu K. Pradhan
[email protected]
1
Centre for Atmospheric Sciences, Indian Institute of Technology Delhi, New Delhi 110016, India
2
Present Address: Amity Centre for Ocean-Atmosphere Science and Technology, Amity University,
Gurgaon 122413, India
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1 Introduction
Internal waves in the shelf region of western Bay of Bengal (BoB) are unique due to
barotropic tidal flow over (steeply varying) continental shelves combined with intricate
stratification conditions. It has been pointed out that an abrupt or fairly sharp density
gradient interface within the fluid is not essential for the existence of waves that owe their
restoring force to gravity; any hydrostatically stable density stratification can support IWs
(Garrett and Munk 1979). Huge IWs can augment surface waves through coupling (Gargettt and Hughes 1972), and when such a coupling occurs during storm surges and high
tides, there could be an increasing risk near the coastal regions.
Although IW activity depends mainly on the degree of stratification of the medium and
strength of tidal forcing (Rao et al. 2010), the variation of slope at the shelf break is also critical
for barotropic to baroclinic energy conversion (Baines 1974; Carter et al. 2005). Energy from
tides is utilized for the displacement of density surfaces which then radiates away as IWs. The
shelf edge which separates the shelf seas from the open ocean remains as the most important
region for internal wave generation. An oscillating barotropic tidal flux approaching the shelfslope region from deep ocean leads to wave excitement, thereby increasing the height and
steepness of the bottom topography (Vlasenko et al. 2005). The shelf-slope front acts as a semipermeable barrier in which exchange of mass and momentum is considerably significant,
enhancing the mixing processes in the region (Sharples et al. 2007).
Earlier observational and modelling studies for BoB confirm that the peak energy is
associated with the semi-diurnal frequency (Rao et al. 2010; Babu and Rao 2011).
Observational evidence from SAR imageries over western BoB reveals that the IWs
particularly over the continental shelf propagate from the shelf edge towards the coast
during calm sea conditions (Prasad and Rajasekhar 2011). The BoB is known for seasonally reversing monsoon winds and is situated over the tropics, which results in the
varying stratification conditions throughout the year. Hence, it is argued that the behaviour
of IWs changes in the shelf/slope topography region round the year. In addition, spatially
organized temperature inversions (TIs) that occur in coastal waters along the western and
north-eastern BoB during winter (November–February) can also alter the stratification
conditions (Thadathil et al. 2002). Observational study by Rao and Ram (2005) indicated
that the inter-annual variability of freshwater flux and surface winter cooling in the
northern BoB causes high inter-annual variability of temperature inversions. In the
southern BoB, deep mixed layer is found in winter and summer monsoons, whereas
shallow mixed layer forms during spring and autumn seasons (Keerthi et al. 2013).
Internal tides are IWs at a tidal frequency and are generated when barotropic
tides/surface tides interact with a shallow bottom. Tides in the BoB are dominated by semidiurnal in most places except in the south-western sector, where mixed tides are also
reported (Murty and Henry 1983). Among all the tidal components, the semi-diurnal
constituents M2 (12.4 h) and S2 (12 h), and diurnal constituents K1 (23.93 h) and O1
(25.82 h) are considered in this study. In general, the amplitude of each tidal constituent in
the BoB increases from south-west to north or north-east.
The first modelling efforts to the best of our knowledge were reported by Rao et al.
(2010, 2011), Babu and Rao (2011) using a 3D Princeton Ocean Model. They studied the
generation of IWs off the east coast of India by prescribing the tidal elevations in the model
along the open boundaries. The study includes model validation with observations and
SAR imageries. It reveals the presence of low-frequency IWs that are semi-diurnal and
diurnal in nature. The model uses smoothened topography and the simulation analysis was
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limited to validation with the available observations only. However, the study does not
include anything about neap—spring variability of IWs and spatial distribution of spectral
estimates of IWs.
Studies were also carried out using Massachusetts Institute of Technology general
circulation model (MITgcm) (Marshall et al. 1997a, b) for modelling the internal waves.
The study includes higher resolution model both spatially and temporally over canyons,
sills, straits, continental shelf and fjords (Holloway 2001; Lien and Gregg 2001; Holloway
et al. 2001; Lueck and Mudge 1997; Toole et al. 1997). Vlasenko and Stashchuk (2007)
analysed large amplitude IWs in the Andaman Sea of BoB with MITgcm arising from
topographical effects. Since very few efforts are made for the western shelf of BoB, the
present study attempts to understand the internal wave variability using MITgcm during
neap—spring tide and spatial distribution of IW activity in terms of spectral energy for two
specific months bearing different stratifications in the region.
2 Model set-up
A three-dimensional primitive equation model, MITgcm is an open source code available
to the community, (refer to http://mitgcm.org/). It is designed for both oceanic and
atmospheric phenomena, utilizing a hydrostatic/non-hydrostatic, z-coordinate finite volume
model that solves the incompressible Navier–Stokes equations with Boussinesq approximation on an Arakawa-C grid. Topographical variations are represented by lopped cells
(partial steps) (Adcroft et al. 1997) which are essential for accurate representation of the
interaction of barotropic tides with the topography and hence the wave generation process.
Fig. 1 Bathymetry of the model domain. The black solid lines denote cross sections off Visakhapatnam and
Paradeep
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Horizontal sub-grid-scale mixing is parameterized using a constant eddy viscosity
approach. In the current set of numerical experiments, the model uses the polynomial
equation of state (McDougall et al. 2003) for the computation of density field.
The model domain and associated bathymetry for the western BoB is depicted in Fig. 1.
Cross-shore width of the model domain is 400 km and the along-shore length is 1200 km
extending from 12°N to 21.5°N (zoomed area from 15°N to 21.5°N is only shown).
Bathymetry of the model is derived from the modified ETOPO2 (Sindhu et al. 2007).
Width of the continental shelf in the western BoB is narrower along the south and wider in
the north. An orthogonal curvilinear grid is used that essentially eliminates the problem of
grid orientation. The study domain comprises of 280 9 220 grid points in the horizontal
plane with a higher resolution of about 1.6 km near to the coast and 2.1 km in the open
ocean. In Fig. 1, two vertical cross sections are considered from south to north at
Visakhapatnam and Paradeep as shown by the straight lines. Star mark along the cross
section off Visakhapatnam represents the observation location for 18–20 October 2006 and
23–25 February 2007 where the station depth is about 110 m. The model has 23 vertical
levels: the first 12 levels from the sea surface are at 10 m intervals, the next 4 levels are at
20 m intervals, and thereafter the rest of the levels follow at 50, 50, 100, 200, 400, 500,
1000 m intervals, respectively, till the total depth reaches 3000 m. The simulation time
step is considered as 120 s based on CFL criteria.
Monthly climatological temperature and salinity fields are derived from World Ocean
Atlas (2009) of National Oceanographic Data Centre and are taken as initial fields representing the background density (Locarnini et al. 2010; Antonov et al. 2010). The model
uses surface relaxation for sea surface temperature (from daily AVHRR data) and sea
surface salinity (from monthly climatology of WOA09) for every 10 days during its
integration. Relaxation at the surface provides a constraint at the air-sea interface that
compensates possible model drift due to errors in the surface heat and momentum fluxes
(Ravichandran et al. 2013). The model surface forcing is derived from the daily QuikSCAT
winds of 0.25 horizontal resolution (www.remss.com) for the experiments. A bilinear
interpolation was used for bathymetry, temperature, salinity and winds to generate input
data for the model at the computational grid points.
The present study incorporates tidal forcing by including additional forcing terms in the
zonal and meridional momentum equations (Khatiwala 2003; Guo et al. 2011) to drive the
model. The model was initially developed exclusively for the tides by prescribing tidal
constituents, M2, S2, K1 and O1 in the model equations as per the lunar and solar phases.
Tidal amplitudes in the north are large by almost three times compared to the south
(figure not shown) that is consistent with the observations made in the earlier studies by
Rao et al. (2010). The Orlanski radiation boundary conditions (Orlanski 1976) are prescribed in the open boundaries which allow any disturbance generated in the domain to
pass through without any significant distortion. In the present study, the hydrostatic version
of the MITgcm is used, as the focus is mainly to simulate low-frequency IWs of diurnal
and semi-diurnal nature in response to tidal forcing. The present model resolution is
sufficient enough to resolve all the low-frequency IWs. The model integration was performed for a period of 60 days for both late winter monsoon and post-monsoon seasons
bearing different ocean stratifications. The model takes spin-up period of about 10–12 days
to reach the steady-state condition. However, the initial period was not considered for
analysis due to lack of observations. In the first experiment, the model was initialized with
the density climatology for December and integrated from January to February 2007 with
daily wind forcing. Similarly, the second experiment was carried out for September–
October 2006 with initial climatology density of August. Both these experiments were
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forced with real-time tides. Results are analysed for the observational period of February
2007 and October 2006 and accordingly inferences are drawn.
3 Data and methodology
Model validations were performed with available observations of temperature collected
during the post-monsoon season from 18 to 20 October 2006 at a station depth of 110 m
off Visakhapatnam (17° 23.70 N, 83° 28.50 E) using thermistor chain. Another set of data
was also collected nearly at the same location during the late winter period from 23 to 25
February 2007. Data were collected using thermistor chain with five sensors to record
temperature at five depths (5, 25, 50, 75 and 100 m) at 2-min interval. CTD data were
available hourly for 32 h only during February 2007. The observed data are used to
validate the model simulations.
Spectral analysis is made for the time series of temperature/density from observations
and simulations using fast Fourier transform algorithm (Cooley and Tukey 1965) to
examine the spectral characteristics of temperature/density oscillations. Energy spectra of
temperature (2-min interval) at different depths are computed for the observational period
in February 2007 and October 2006.
4 Results and discussions
The model vertical temperatures are compared at five depths with the observed temperatures averaged for 23–25 February 2007 and 18–20 October 2006 as shown in Fig. 2a, b.
The model simulations are in agreement below 50 m depth; however, there are differences
Fig. 2 Simulated vertical temperature profile for a February 2007, b October 2006. Star indicates observed
temperature at specific depths collected from thermistor chain and solid line represents model. Isopycnal
displacement computed from c model, d observations
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noticed at the surface layers. This difference between model and observations could be
attributed to the surface fluxes considered in the model. Isopycnal displacement for
February 2007 as calculated by Nash et al. (2005) is also shown in Fig. 2c, d. The model
computes an isopycnal displacement (Fig. 2c) of about 15 at 60 m depth which compares
well with the observations (Fig. 2d).
Peak density oscillations are found during spring time with its maximum amplitude on 3
and 18 February 2007 (Fig. 3a) in the pycnocline region (at about 75 m depth) where
buoyancy oscillations are the highest (shown in Fig. 3b). Period of maximum amplitude
coincides nearly with the days of maximum astronomical forcing (spring tides). These
oscillations decrease as the neap period approaches on 11th and 26th, respectively. Density
oscillations are also seen near the bottom due to shallow topography over which barotropic
tides interact. Similarly for October 2006 (Fig. 3c), maximum amplitudes coincide with the
spring tides observed during 7th and 22nd and minimum at neap tides during 14th and
30th. The study reveals a large variation of IW amplitude across the neap—spring period
approximately three times higher during spring tide. During October the IW activity is seen
throughout the water column, where it is well stratified with depth, unlike the case during
February 2007. For this period (Fig. 3d), the values of buoyancy oscillations are nearly
invariant throughout the water depth. During winter season, deep mixed layer and temperature inversions persist and slowly fade away by the end of February. In October (postmonsoon period), the coastal bay is filled with low-salinity plumes originating from the
Fig. 3 Model simulated a vertical variation of density for February 2007, b average buoyancy frequency
for 23–25 February 2007, c same as (a) except for October 2006, d same as (b) except for 19–21 October
2006
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major river systems joining the bay and thus provides strong stratification in this region.
Due to the deep mixed layer during February, the IWs are found to occur at depths below
40 m in the pycnocline region, while in October they are seen even at shallow depths of
10 m due to strong stratification.
Spectral estimates for temperature are made based on 2-day data (with 2-min time
interval) where observations are available, i.e. during 23–25 February 2007 (upper panel)
and October 2006 (lower panel) and are presented in Fig. 4 for three depths. It is noticed
that the peak estimate is concentrated in the range of tidal frequency, primarily of semidiurnal (12.4-h time period) corresponding to 0.08cph frequency at all depths. The
observations coincide with the neap period and hence a comparison of the simulations with
observations is limited to the neap time only. In general, comparison of the spectral
estimates associated with the semi-diurnal tide suggests a reasonable agreement at all the
depths for low-frequency IWs. The spectral energy at 100 m (station depth *110 m)
might be due to the combined effect of tides and the sloping bottom with their possible
impact on the stretching of isopycnals vertically.
Similar computations were made for October 2006 off Visakhapatnam (lower panel)
where the stratification is significantly different from that of February 2007. The observational period of 18–20 October 2006 is between the spring and neap time phase.
Computed spectral estimate is mostly concentrated at semi-diurnal frequency, while the
observations show both diurnal and semi-diurnal components. In this case, the maximum
spectral energy for temperature oscillations is found at 50 m among the available observed
depths.
To determine the variability of IWs from spring to neap period, the simulations for
February 2007 and October 2006 were analysed off Visakhapatnam at selected observed
depths, where the model temperature agrees well with observations. Figure 5 depicts
Fig. 4 Comparison of spectral estimate of temperature from observations (dashed line) and model (solid
line) off Visakhapatnam at different depths for a February 2007, b October 2006
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maximum spectral estimates corresponding to semi-diurnal (*0.08 cph) and diurnal
(*0.04 cph) frequencies at different depths for February 2007 (left panel) and October
2006 (right panel). Total number of days considered in this analysis is about 26 days
covering two springs and one neap. The spectral estimate was computed using 2.0-day time
span with 1-day running average. It is clearly seen from spectral estimate that the variability is considerable from spring to neap, with its peak during spring tide. The estimates
at semi-diurnal and diurnal are maximum at a depth of 75 m during a complete tidal cycle
where Brunt–Vaisala frequency is maximum. However, the simulated diurnal component
(Fig. 5c, d) is small compared to semi-diurnal (Fig. 5a, b) which is consistent with the
observations. At this depth (75 m), the estimate is about ten times higher during spring
period compared to that of neap. The estimates during February show a symmetric nature
between the spring and neap except at 50 m depth during the beginning of the month.
These low estimates are attributed to weak IWs due to deep mixed layer depth during this
period (see Fig. 3a). However, the IWs are observed more frequently during the later part
of the month as the mixed layer depth gets reduced. The spectral estimates during October
2006 are less at all depths as seen in Fig. 5b. This could be attributed to the prevailing
stratifications at this location which determine the strength of IWs. These phenomena are
further investigated in detail in the subsequent analysis.
Numerical experiments were performed to understand the IW propagation over the
shelf-slope region along two different cross sections off Visakhapatnam and Paradeep
having different stratifications. Spectral energy is computed for IWs of semi-diurnal frequency or internal tides that contain maximum energy in the energy spectrum. The estimates depicted in the Fig. 6a are for a depth, where the estimates are maximum during
springtime. It is seen from Fig. 6b that the shelf edge is located at about 27 km from the
Fig. 5 Maximum spectral estimate of temperature during neap—spring time for IWs of semi-diurnal
frequency for a February 2007, b October 2006 and diurnal frequency for c February 2007, d October 2006
at different depths. The dash–dot, solid and dashed lines represent 50, 75 and 100 m, respectively
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coast. The peak energy in October occurs much inside the shelf break interior and towards
the coast as compared to that in February (peak energy near the shelf break). To understand
the cause for the inward shift of the energy peak from the shelf break, it is important to
look at the prevailing local stratifications in both these months. Figure 6 c, d provides the
simulated density stratification off Visakhapatnam for February and October, respectively.
It is known that the coastal waters during October are well stratified from the surface, while
during February there is a deep mixed layer/temperature inversion. As any hydrostatically
stable stratification supports generation and propagation of IWs, its activity is more
prominent near the coastal waters in October in terms of energy propagation towards the
coast. However, the stratification is not solely responsible for the shift in peak energy; the
shifting of the peak energy offshore in February may be due to the formation of well-mixed
shelf water that acts as a barrier to the propagating IW. This barrier allows the energy to
fall suddenly towards the coast unlike in October where the energy propagates slowly
inwards as the waters are well stratified. This leads to abrupt amplification of the energy
compared to that of October. The shifting of the energy peak from the shelf break towards
the coast over this region is about 9 km in October compared to February.
Similar analysis is made at Paradeep, a northern location of the domain (see Fig. 1), to
confirm the above hypothesis about local stratification. The corresponding computations
are shown in Fig. 7. It is worth noting that the inward propagation of IW energy in October
surpasses by 7.5 km off Paradeep compared to February. This spatial extent of IW energy
propagation may also depend on the distance of the shelf break from the coast, which is
difficult to conclude precisely, as the present model’s minimum resolution is about 1.6 km.
Hence, the rationale for the extent of coastward IW propagation is a twofold mechanism.
The first one is the local stratification which varies significantly from season to season and
secondly the location of the shelf break which varies along the coast.
In order to look at the internal wave activity along the entire coast for February 2007 and
October 2006, spatial distribution of spectral estimates associated with semi-diurnal frequency during spring tide is shown in Fig. 8a, b. In comparison with the estimates between
these two months, it is noticed that the estimates for October are in general higher and are
spread out more towards the coast. This may be attributed to the prevailing highly stratified
coastal waters in October compared to that of February. However, higher estimates noticed
Fig. 6 Analysis off Visakhapatnam a spectral energy over the shelf-slope: red and blue solid lines are for
February and October, respectively (star indicates location of the peak energy), b bottom topography (plus
shows location of shelf break), c vertical variation of density (kg/m3) for February 2007, d vertical variation
of density (kg/m3) for October 2006
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Fig. 7 Analysis off Paradeep a spectral energy over the shelf-slope: red and blue solid lines are for
February and October, respectively (star indicates location of the peak energy), b bottom topography (plus
shows location of shelf break), c vertical variation of density (kg/m3) for February 2007, d vertical variation
of density (kg/m3) for October 2006
Fig. 8 Maximum spectral estimate of internal waves (shaded) associated with semi-diurnal frequency for
spring time during a 17–19 February 2007, b 21–23 October 2006, along with bathymetry (contoured) over
the western Bay of Bengal
along certain coastal strips in both the months may be due to the effect of local topography
which requires further investigation. Though the estimates are less for the diurnal frequency,
similar spatial pattern is noticed as that of semi-diurnal (figure not included).
5 Summary
The study of numerical simulations explores the spectral energy associated with IWs
during neap—spring period in the western part of the Bay of Bengal. The model results
show that the IWs have higher spectral energy when the astronomical forcing is maximum
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(spring time) and lower when the forcing is minimum (neap time). Peak estimates are
confined to the depths of the thermocline during the phase of spring tide. Effect of local
stratification on the extent of IW propagation in the inner shelf is analysed at two cross
sections off Visakhapatnam and Paradeep. The continental shelf edge region generally
remains the zone of maximum internal wave activity. Stratification affects the propagation
of IWs in the inner shelf that is dominated by mixing. The IWs off Paradeep and
Visakhapatnam in February 2007 are restricted to 20 and 18 km away from the coast,
respectively. However, the spectral estimates are found close to the coast during October
2006 due to the extended thermocline up to the surface. Longer time series observations
could provide more insight into the neap—spring variability of internal wave energy under
different stratified ocean conditions. The study is useful to know the extent of IW propagation over the inner shelf for many applications like underwater acoustics and mixing
processes.
Acknowledgments The authors are thankful to Naval Research Board (NRB), Government of India for
the financial support for carrying out this study. Sincere acknowledgements are also due to Dr T. V. Ramana
Murty and his team for providing the data collected under the NRB project. The valuable suggestions and
support of Prof. B. S. R. Reddy for preparation of this paper are gratefully acknowledged. The first author
also appreciates the financial support of CSIR, New Delhi, in the form of his research fellowship.
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