On the wave-current interaction during the passage of a tropical cyclone in the Bay of Bengal

Deep–Sea Research II xxx (xxxx) xxx

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Deep-Sea Research Part II journal homepage: http://www.elsevier.com/locate/dsr2

On the wave-current interaction during the passage of a tropical cyclone in the Bay of Bengal Kumar Ravi Prakash, Vimlesh Pant * Centre for Atmospheric Sciences, Indian Institute of Technology Delhi, New Delhi, 110016, India

A R T I C L E I N F O

A B S T R A C T

Keywords: Wave-current interaction Coupled model Momentum budget Wave-breaking Bay of bengal

The impact of waves on currents and vice-versa is an integral part of the complex coastal dynamics. The wavecurrent interaction is prominent in the coastal shelf-slope regions, particularly during the passage of a tropical cyclone. In the present study, we describe the importance of wave-current interaction in the northern Bay of Bengal (BoB) using a fully coupled three-dimensional Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) modelling system. The COAWST model is applied to the case of a very severe cyclonic storm Phailin that passed over the BoB basin during 10–15 October 2013. To represent the interaction between waves and currents, we utilized the newly implemented vortex-force method in the coupled model. Numerical experiments with different coupling configuration within the COAWST modelling framework were performed to separately identify the effects of wind, tide, and wave-current interaction process. A comparison of model results with the buoy observations of water elevations, currents, and wave measurements shows a good agreement between model and observed data. Various terms of the momentum balance were calculated from the model simulated and diagnosed parameters. A comparison of the horizontal momentum balance term identifies the wave-breaking induced acceleration as one of the leading terms along the storm affected the east coast of India. Further, an increase in the apparent bed roughness caused by waves found to affect the values and distribution of the bottom shear stress. The pressure gradient term showed significant changes to the pure tidal case. The study highlights that the changes in the momentum balance caused by waves includes contributions from the variations in the water level and currents. The most relevant effect on the coastal hydrodynamics was in the form of a waveinduced setup near the location of landfall of the cyclone.

1. Introduction The BoB, a semi-enclosed basin in the northeastern Indian Ocean, exhibits unique geographic and hydrographic characteristics. On the eastern BoB, a wider area of shallow water exists as compared to the western side of the bay where the sea-bed dips to 2000 m after narrow coastal strip along the east coast of India (Kay et al., 2018). The East India coastal current (EICC), the western boundary current in the BoB, undergoes seasonal reversal under the influence of southwest (June–September) and northeast (December–February) monsoons (Shankar et al., 1996; Schott et al., 2009; Durand et al., 2009). The BoB is well-fed with a large volume of freshwater flux from several rivers including the Ganges-Brahmaputra-Meghna (GBM) river system, which is one of the world’s largest river runoff into the ocean. The GBM delta in the northern BoB is the source of the world’s largest sediment fan (Curray et al., 2002; Weber et al., 2003). The transport of sediments

through currents, tidal and wind waves modulate the local bathymetry in the coastal regions of the bay, particularly during the occurrence of TCs. The excess precipitation over evaporation adds to the freshwater input into the BoB. The surplus freshwater leads to low-salinity (ranging from 26 psu in the north to 34 psu in the south BoB) waters in the upper ocean with a seasonal variation (Rao and Sivakumar, 2003; Sandeep et al., 2018). This strong haline stratification results into shallow oceanic mixed layer (ML) which, in turn, leads to the warmer sea surface temperature (SST) in the bay (Shenoi et al., 2002; Rao and Sivakumar, 2003; Thadathil et al., 2007) as compared to the Arabian Sea, another semi-enclosed basin in the northwestern Indian Ocean. Weller et al. (2016) highlighted the crucial role of near-surface freshwater on the air-sea interactions in the BoB utilizing in-situ observations and one-dimensional ocean model. The shallow ML and warmer (>28 � C) SST makes the BoB an active region for the formation of tropical cyclones (TCs) (McPhaden et al.,

* Corresponding author. E-mail addresses: [email protected], [email protected] (V. Pant). https://doi.org/10.1016/j.dsr2.2019.104658 Received 12 March 2019; Received in revised form 2 October 2019; Accepted 2 October 2019 Available online 7 October 2019 0967-0645/© 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Kumar Ravi Prakash, Vimlesh Pant, Deep–Sea Research II, https://doi.org/10.1016/j.dsr2.2019.104658

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2009; Neetu et al., 2012). A larger number of TCs form over the BoB during the pre-monsoon (May–June) and post-monsoon (October–De­ cember) seasons when the favourable meteorological conditions prevail for the TC formation (McPhaden et al., 2009). These TCs impact heavily on the large population residing along the Indian coast. The storm surge and associated inundation associated with these TCs pose a threat to the infrastructure, biodiversity, and livelihood in the coastal regions. The TCs can also modify the coastal geometry and bathymetry by means of coastal erosion/accretion and sediment transport, respectively (Dufois et al., 2018). The effects of surge and erosion can be altered due to the nonlinear wave-current interaction during a cyclone. An accurate pre­ diction of the TC track and intensity are crucial for calculation of inundation due to the combined effect of the surge, tide, and wind waves (Rao et al., 2012; Murty et al., 2014). Murty et al. (2014) used a para­ metric wind model to generate the wind field applied to coupled ocean circulation-wave model to analyze the impact of wave setup on storm surge and total water elevation. Several coupled atmosphere-ocean models developed in the past have shown an improvement in the air dynamics due to better representation of air-sea fluxes than the atmo­ spheric model with prescribed SST (e.g. Ren et al., 2004; Seo et al., 2007; Bender et al., 2007; Yao et al., 2008). Further, the recent application of atmosphere-ocean-wave coupled model found to be a useful tool for a better simulation of TC track and intensity, and upper oceanic param­ eters as compared to uncoupled models (Warner et al., 2010; Zambon et al., 2014; Prakash et al., 2018). Several studies have demonstrated the importance of ocean waves in ~ os-Sanchez et al., 2005; coastal hydrodynamics (Moon, 2005; Bolan Kang and Di Iorio, 2006). The wave-current interaction deals with the non-linear interaction of propagating waves on the inhomogeneous, dispersive, dissipative and moving medium, which interacts with the wave (Rusu and Soares, 2011). The wind-induced surface gravity waves contribute a residual flow to the background current, with implications in the momentum, mass, and energy conservation equations and the applied boundary conditions. The waves enhance the turbulence, impact the near-surface currents and, thereby, play a crucial role in the upper-ocean mixing. The interaction of waves with currents modulates the total water level in the coastal zone, which is relevant to the beach management and navigation. Samiksha et al. (2017) used a coupled ocean circulation and wave model to study the wave-current interaction and its effect on total water level during Hudhud cyclone in the BoB. The wind-induced currents can interfere with tidal currents which depend on the phase of the tide. The interaction between the currents, waves, and tides influence the magnitude and direction of the wave-field and coastal currents. In the regions of river entrances into the ocean, the wave en­ ergy propagates from offshore to the river entrance and, thereby, de­ creases (increases) the wave height during the flood (ebb) condition (Gonzales et al., 1985). The radiation stress, i.e. the flux of momentum due to waves, controls the formation, evolution, and breaking of the waves (Longuett-Higgins and Stewart, 1964). The radiation stress is balanced by a pressure gradient associated with a change in the local water depth. Grant and Madsen (1979) presented an analytical theory to describe the combined motion of waves and currents in the vicinity of a rough bottom and the associated boundary shear stress. They reported that when the waves and currents co-exist then the turbulence generated by the wave-current interaction at the bed alters the shear stresses associated with wave and current. This leads to greater resistance to the currents above the wave boundary layer than at the physical bottom (Grant and Madsen, 1979). Using the measurements from wave buoy and near-shore pressure gauges together with the ADCIRC model, Smith et al. (2000) showed that wave breaking over Willapa bar was the dominant transformation process for waves in the bay whereas the tidal elevation was found to govern the energy dissipation. The interaction of waves with strong coastal currents (Gulf Stream, Kuroshio, and Agulhas) was studied by Holthuijsen and Tolman (1991) and Komen et al. (1994). Early theo­ retical studies derived basic equations that dealt with the interaction of

waves with currents and included the radiation stress component (Longuet-Higgins and Stewart, 1960, 1964), wave action in slowly varying current (Bretherton and Garrett, 1968), and diffraction effects (Booij, 1981; Kirby, 1984; Dingemans, 1985). Later, a few studies used laboratory experiments to demonstrate that the distribution of the spectral energy of the waves changes when the current meets a wave system in a multi-directional wave basin environment (Nwogu, 1993; Guedes Soares et al., 2000; Soares and de Pablo, 2006). The wave-action conservation equation, which takes into account wave refraction and vertically sheared weak currents, was described using both perturbation and numerical methods (Kirby and Chen, 1989). Propagation of waves along with strong currents changes the wave characteristics with refraction, bottom friction and blocking (Kudryavtsev et al., 1995; Ris et al., 1999). Also, the mean flow gets affected by the addition of momentum and mass fluxes due to waves. The wave processes that affect the coastal environment are: (i) cyclone-induced waves, (ii) wave-current interactions, and (iii) wave breaking activity. The cyclone-induced waves contribute significantly to storm surge and inundation. Beardsley et al. (2013) found that addition of waves in the model resulted in larger areas of Massachusetts Bay being flooded. Interaction of waves and currents increases the bottom friction and, hence, the bottom stress. Wave breaking activity influences surface currents; for example, studies by Carniel et al. (2009) and Zhang et al. (2011) reported improvements in the accuracy of surface drifter tracks in the Adriatic Sea and surface boundary layer thickness in the Yellow Sea, respectively, when wave breaking was included in their models. However, waves propagating in a direction opposite the current shows a reduction of the current intensity near the sea-bed (Carniel et al., 2009; Zhang et al., 2011). Several observational studies reported that the effect of wave-current interaction is not restricted to the near-bottom region but also affects the entire water column (Kemp and Simons, 1982, 1983; Klopman, 1994). These effects mainly depend on the direction of the wave and current propagation. A better represen­ tation of air-sea momentum transfer in the model is crucial for improvement in the simulation of wind wave and storm surge, which are sensitive to wind direction and intensity (Kim et al., 2010; Olabarrieta et al., 2012). Most of the ocean circulation models which include wind-wave induced currents, use three different formulations to add the wave impact on currents in the 3D-primitive equations: (i) by means of the radiation-stress gradient (Mellor, 2011), (ii) with the vortex force (VF) formalism (Uchiyama et al., 2010; Kumar et al., 2012), and (iii) GML (Generalized Lagrangian Mean). The VF formalism splits the flow into irrotational and rotational components (McWilliams and Restrepo, 1999) or between waves, infragravity waves, and currents (McWilliams et al., 2004). The VF formalism-based model presented by Uchiyama et al. (2010) separates the effects of wave forcing into conservative (Bernoulli head and vortex force) and non-conservative (wave dissipa­ tion induced acceleration) contributions. In this study, we explore the importance of wave-current interaction in the northern BoB. We use a three-dimensional coupled ocean-wave model by utilizing the VF method to examine the wave-current inter­ action during the passage of a tropical cyclone in the BoB. The VF method is used in the present study to accomplish (i) enhanced mixing implementation using the Generic Length Scale (GLS) scheme with the addition of wave-induced mixing in the form of surface boundary con­ dition and (ii) improved vertical structure of depth-limited wave dissi­ pation induced acceleration that scales with the wave height. Since the wave-current interaction becomes more crucial under high wind con­ ditions associated with a cyclone, the VF method is implemented in the model for a cyclone case in the BoB. The interaction between waves and currents are more prominent under the high wind conditions associated with a cyclone. Olabarrieta et al. (2012) investigated atmosphere–ocean–wave interactions during hurricane Ida and Nor’Ida. Inclusion of ocean roughness in their model experiments showed an improvement in the estimation of wind 2

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intensity, wind waves, surface currents, and storm surge amplitude. In view of the fact that the coastal regions along the east coast of India are prone to natural disasters caused by the TCs that form over the BoB, the wave-current interactions during the passage of a cyclone in the bay are crucial to examine. The wave-current interactions are especially important in shallow coastal regions where they can influence coastal dynamics, storm surges, and sediment transport. A set of numerical experiments are performed to examine the wave-current interaction in the BoB and coastal regions along the east coast of India. Model simu­ lated waves are compared with buoy measurements. A comparison of the horizontal momentum balance terms is made with different model configurations to identify the individual effect of wave-breaking-induced acceleration, bed-roughness caused by waves, distribution of bottom stress, and the pressure gradient term on the overall wave-current interaction in the BoB.

Fig. 1. Schematic of the model configuration. Uwind, Vwind – zonal and meridional wind components, Patm - atmospheric pressure, RH - relative hu­ midity, Tair - air temperature, Cloud - cloud fraction, Rain - precipitation, Evap - evaporation, Swrad – shortwave radiation, Hwave - significant wave height, Lmwave - mean wavelength, Dwave - wave direction, Tmbott - bottom wave period. Qb - percentage wave breaking, DISSwcap - wave energy dissipation, Ubot - bottom orbit velocity, U and V - ocean surface current components, ubar and vbar - depth average current velocity, T - ocean temperature, ssh - sea surface height, and salt - salinity.

2. Data and methodology 2.1. Model details A coupled ocean-wave model as a part of the ‘Coupled OceanAtmosphere-Wave-Sediment Transport’ (COAWST) modelling system (Warner et al., 2010) was used in this study. The ‘model coupling toolkit’ (MCT) was used to couple the ocean model Regional Ocean Modeling System (ROMS) and the wave model Simulating Waves Nearshore (SWAN) (Larson et al., 2004; Jacob et al., 2005). To examine the mag­ nitudes of wave-current interactions, the coupling was activated be­ tween ROMS and SWAN models only. The atmospheric model Weather Research and Forecasting (WRF-ARW) was run in uncoupled mode, and the generated atmospheric data are provided as the surface boundary forcing to ocean and wave models (Prakash et al., 2018). The coupled ocean-wave model was configured over the northern BoB domain covering the east coast of India with a maximum horizontal resolution of 3 km for both ROMS and SWAN models. The numerical simulations with the coupled model were carried out from 00 GMT on 10th October 2013 to 00 GMT on 15 October 2013 when the tropical cyclone Phailin, a very severe cyclonic storm, originated and passed over the BoB (IMD Report, 2013). To investigate the interaction between wave and current, we included VF formulation in the ROMS model. ROMS is a free-surface, hydrostatic, primitive equation ocean model that solves finite differ­ ence approximations of the Reynolds averaged Navier-stokes assump­ tions (Chassignet et al., 2000; Haidvogel et al., 2000) with a split-explicit time stepping algorithm (Haidvogel et al., 2008; Shche­ petkin and McWilliams, 2005). The wave model ‘Simulating WAves Nearshore’ (SWAN) is a spectral model specifically designed for shallow water that solves the wave action balance equation in both spatial and spectral spaces (Booij et al., 1999). In the COAWST modelling system, ROMS feeds SWAN with the free surface elevations (ELV) and currents (CUR). The currents are computed using the formulation given by Kirby and Chen (1989). The wave-averaged momentum balance equations are based on McWilliams et al. (2004) and Uchiyama et al. (2010), which were implemented in the COAWST modelling system by Kumar et al. (2011). The primitive equation of momentum balance is used to analyze the effect of wave-current interaction in the BoB. The simplified momentum balance equation including the VF approach can be obtained by removing the curvilinear term plus body force horizontal and vertical mixing. Following Kumar et al. (2012), the momentum balance equation in the Cartesian coordinates is given by

�

�Z

�

�Z

�

�Z

��

∂v 1 ∂ ∂ ∂ þ uvdz þ v ust dz þ v vst dz ∂x ∂y ∂t H ∂x � �Z � �Z �� ust ∂ ∂ 1 ∂P þ udz vdz þ f u þ f ust ¼ ∂y H ∂x ρ0 ∂ y τy τyb þ F wy þ s þ Dhvisc ρ0H ρ0H

(1)

where u and v are horizontal components of velocity, uSt and vSt represent stokes velocity components, H is the total water depth, f is the y Coriolis parameter, τb and τys are bottom and surface stresses, ρ0 is the

reference density, and Fwy is the non-conservative wave forcing. In the wave-averaged momentum equation (1), the first term on the left hand side represents the local acceleration (accel) and the second to fourth terms collectively represent horizontal advection (hadv). The fifth and sixth terms are horizontal and vertical vortex forces (hvf), which were recently added by Uchiyama et al. (2010). The seventh term is the Co­ riolis acceleration (cor) and the eighth term is the Stokes-Coriolis (stcor) acceleration. On the right hand side, the first term represents the total pressure gradient (prsgrd), the second term is the non-conservative wave force (WF), the third and fourth terms are surface stress (sstr) and bottom stress (bstr) respectively, and the fifth term represents horizontal viscosity. In the above momentum equation (1), the wave-induced terms include part of the hadv term, the hvf term, the Stokes-Coriolis term and the non-conservative wave force. The pressure gradient rP is equal to the horizontal gradient of the geopotential function after extracting the vertical vortex force. It can be decomposed into the current contribution Pc , the quasi-static response Pqs , the Bernoulli Head term Pbh , and the surface pressure boundary correction Ppc (Kumar et al., 2011). (2)

rP ¼ Pc þ PWEC ¼ Pc þ Pqs þ Pbh þ Ppc wy

The non-conservative wave force term F includes the accelerations due to surface streaming (Bsf Þ, bottom streaming (Bbf Þ and wave breaking (Bwb Þ (Kumar et al., 2012) F wy ¼ Bbf þ Bsf þ Bwb

(3)

In the present simulations, surface waves included the effects of the vortex force (VF) in the horizontal and vertical, and the Bernoulli head (BH), which is essential for the pressure adjustment in incompressibility conditions (Lane et al., 2007). The VF method separates conservative 3

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Fig. 2. Model domain with bathymetry (m). Track of Cyclone Phailin as simulated by the atmospheric model is denoted by the black line. Location of wave-rider buoy is marked with a white star near Gopalpur (black star). White circle represents Paradeep location.

wave forces (Bernoulli head and vortex force) from non-conservative wave forces (wave dissipation induced acceleration, e.g. wave breaking, wave-current interaction enhanced bottom friction and wave streaming).

Table 1 Summary of model experiments. ELV: water elevation, CUR: current, VF-BH: vortex force and Bernoulli head, BRK: wave breaking.

2.2. Model configuration and experiment design The components of COAWST modelling system used in this study comprised of the coupled ocean-wave (ROMS þ SWAN) model config­ ured over the BoB. A schematic diagram showing the component models, variables exchanged, data used as surface forcing, initial and boundary conditions is shown in Fig. 1. The surface open boundary conditions during the passage of tropical cyclone Phailin, i.e. 10–15 October 2013, were derived from the un-coupled WRF-ARW model (Skamarock et al., 2008). The WRF model was initialized on 10 October 2013 at 00 GMT with National Centre for Environmental Prediction (NCEP) Final Analysis (FNL) data. Also, the same data are used to supply lateral boundary conditions at every 6-h interval (see Fig. 1). The ability of WRF-ARW model in simulating track and intensity of TC Phailin was demonstrated by Prakash and Pant (2017). The ocean circulation model ROMS was used with 40-sigma vertical levels. The sub-grid scale parameterization for mixing of momentum and scalars were accom­ plished with K- ε model generic large-scale two-equation turbulence (Umlauf and Burchard, 2003), as implemented by Warner et al. (2005) and Smagorinsky (1963) was used to calculate the horizontal eddy vis­ cosity and diffusivity. Boundary condition of the tides were derived from the TPXO (Egbert and Erofeeva, 2002). These data include tidal current, phase, and amplitude of the M2, S2, N2, K2, K1, O1, P1, MF, MM, M4, MS4, and MN4 tidal constituents along the east coast of India. The tidal input was interpolated from TPXO grid to ROMS computational grid. The bound­ ary conditions in the open ocean included Chapman (1985) and Flather (1976), with small modifications (Shchepetkin, 2000) for the free-surface elevation and 2D momentum variables, respectively. For 3D momentum variables, the radiation boundary condition (Orlanski, 1976; Raymond and Kuo, 1984) was used. The Flather boundary condition allows the free propagation of astronomical tides and wind-generated

Run

ELV

CUR

VFBH

BRK

Remarks

Exp1 Exp2 Exp3

✓ ✓ ✓

✓ ✓ ✕

✕ ✓ ✓

✕ ✓ ✓

Exp4

✕

✕

✓

✓

ROMS (no wave effect) ROMS þ SWAN (fully coupled ROMS þ SWAN (no feedback of currents on waves ROMS þ SWAN (no feedback of currents and elevation on waves

currents along the lateral open boundaries of the domain. ROMS and SWAN models were configured over the same domain in the BoB as shown in Fig. 2. The zonal and meridional grid spacing of 3 and 6 km, respectively were used in the ROMS model with 40 vertical terrain-following sigma levels. The lateral boundary of the model was closed in the north and open elsewhere. The oceanic initial and lateral open boundary conditions in ROMS were derived from the ECCO2 data (https://www.esrl.noaa.gov/psd/.) Ocean bathymetry was derived from ETOPO2 (National Geophysical Data Center, 2006). The surface forcing for ROMS and SWAN were derived from WRF-ARW simulated output with 9-km horizontal resolution. Details of model physics, initial and boundary conditions for WRF model are provided in Prakash and Pant (2017). The Rossby baroclinic radius of deformation over BoB is 60–200 km. Joint North Sea Wave Project (JONSWAP) boundary con­ dition was applied to the boundaries of the domain in the SWAN model. These boundary conditions were derived from Wave Watch III (WWIII) reanalysis (ftp://polar.ncep.noaa.gov/pub/history/waves/) spectral parameters with 24 frequencies (0.04–1.0 Hz). The Komen et al. (1984) closure model was utilized to transfer energy from the wind to the wave field. Dissipation due to depth-induced wave breaking was treated by Battjes and Janssen (1978) spectral formulation with α ¼ 1 and γ ¼ 0.73. Four numerical experiments (listed in Table 1) were carried out to understand the impact of the waves on currents and vice-versa during the passage of TC Phailin in the BoB. 4

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Fig. 3. Time series of significant wave height (m) in upper panel and peak wave direction (degree) in lower panel at the wave rider buoy location.

2.3. JONSWAP spectrum

the JONSWAP spectrum is given below:

To understand the impact of surface currents on the spectral energy density of waves, we computed the Joint North Sea Wave Project spectrum (JONSWAP) on the basis of observed and model-simulated wave parameters. The equation proposed by Goda (1985) to derive

Sðf Þ ¼ βj H

2 1 2 3 Tp 4

=

where,

f

5

SðfÞ

(4)

3

4e ðTp f Þ 5γd 5 4

4

is

spectral

energy

density

Fig. 4. JONSWAP spectra of energy density (m2/Hz) for (a) 11 October, (b) 12 October, and (c) 13 October from buoy observations (black curve), model Exp2 (red dashed curve) and Exp3 (blue curve). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 5

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Fig. 5. Spatial distribution of the model simulated wave energy density spectrum (J m

due to gravity, f is the wave frequency, d ¼ e

2σ 2

Hz

1

degree

1

) on (a) 12 October at 6 GMT and (b) 13 October at 00 GMT.

3. Results and discussion

0:06238 βj ¼ 0:230þ0:0336γ ½1:094 0:01915lnðγÞ� , g is the acceleration 0:185ð1:9þγÞ 1 � �2 f fp

2

3.1. Evaluation of model performance

1

, and fp ¼ T1p is the

The model-simulated peak wave direction and significant wave heights were compared with a wave-rider buoy measurements off Gopalpur at the east coast of India (location of the buoy marked in Fig. 2). Fig. 3 shows the model-simulated (Exp2 and Exp3) significant wave heights (H1/3) and peak wave directions (Tp) at the Gopalpur wave-rider buoy location. Model-computed wave heights match well with the wave rider buoy observations. In both the model experiments, wave height starts with the bias of ~1 m in the initial conditions. The bias could be due to the errors in boundary conditions, wind speed

frequency corresponding to the peak value of energy spectrum, γ is the peak enhancement factor corresponding to change in fp. Here the value � 0:07 f � fp of γ was 3.3 and. σ ¼ 0:09 f > fp

Fig. 6. Dominant terms in the momentum balance equation for model Exp1 (upper panel) and Exp2 (lower panel) on 12 October. 6

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Fig. 7. Contribution from the zonal (upper panels) and meridional (lower panels) components of the wave breaking and viscosity terms in the momentum bal­ ance equation.

simulation, model resolution, parameterization, inaccurate bathymetry, etc. This order of bias may also arise due to the use of JONSWAP and inadequate swell dissipation in the wave model. Both the model experiments were able to capture the increasing and decreasing trends during the simulation period. However, the model could not capture the sharp (short-duration) changes in the wave height as noticed in the buoy measurements. The model performance with respect to the measurements is analyzed in terms of root-mean-square error (RMSE), correlation coefficient (R), and model performance (skill score, i.e. S) (Willmott, 1981). The model computed peak wave direction (shown in Fig. 3b) was in good agreement with the measure­ ments. The model captured the rapid change in wave direction when the cyclone passed close to the buoy location. Fig. 4 compares the measured and model computed (with and without current effect) JONSWAP spectrum from significant wave height and peak wave periods before and after the landfall of cyclone near the Gopalpur buoy location. The model computed spectrum in Exp2 (with current effect on waves) shows better agreement with the measured spectrum as compared to Exp3 (without current effect on waves). Prior to the TC landfall, the model (Exp2 and Exp3) overestimated the spectrum which was measured as 12 m2/Hz at Gopalpur. The wave energy enhanced up to 93 m2/Hz upon the arrival of cyclone near the buoy location. However, the energy reduced to 43 m2/Hz after the passage of TC. The RMSE and correlation coefficients between the spectrum derived from the model simulations and observations were 1.02 and 0.91 on 11 Oct (for curves on Fig. 4a), 2.10 and 0.98 on 12 Oct (for curves on Fig. 4b), 2.94 and 0.87 on 13 Oct (for curves on Fig. 4c). Therefore, there was good agreement between measured and computed energy density spectra. The differences in the spectrum on 11 October could be due to an overestimation of the wind intensity of the storm over that location and error in the peak wave period simulation. At the location of the JONSWAP spectrum analysis, the peak intensity on 12 October was well represented by the model. Therefore, the discrepancies on 11 October would not strongly influence

our results and conclusions in this study. The spatial distribution of the simulated wave energy density spectrum at 6 GMT on 12 October (during maximum wind condition just before the landfall) and at 00 GMT on 13 October (just after landfall) are shown in Fig. 5. Note that the swell waves (0.05–0.15 Hz) were the major source of energy in the di­ rection between 80 and 135� . Direction of energy propagation changed from southeast to south after the passage of cyclone over the location (see Fig. 5). 3.2. Effect of waves on the momentum balance terms The different terms of the momentum balance equation (Equation (1)) were calculated separately for different numerical experiments performed using the coupled model. It was found that the largest con­ tributions were from the horizontal pressure gradient term (prsgrd) and the bottom friction term (bstr). These two leading terms from the xmomentum and y-momentum equations are plotted for model experi­ ments Exp1 (ROMS alone) and Exp2 (ROMS þ SWAN) on 12 October in Fig. 6. Our results with the momentum budget calculations agree with the findings of Olabarrieta et al. (2011) who also reported the pressure gradient and bottom friction as the two leading terms in their study on the wave-current interaction. In response to the waves, the pressure gradient and bottom stress terms were found to vary all along the wave-breaking zone in the shallow coastal waters. It can be seen that the inclusion of waves (in Exp2) resulted in a considerable enhancement in the magnitude (either positive or negative) of the pressure gradient term and the bottom stress term, particularly in the shallow regions near the east coast of India. This effect was noticeable in both the zonal and meridional components. This change in the pressure gradient term can be attributed to the additional contribution from the surface gravity waves (as suggested by Equation (2), section 2.1) when the SWAN model is coupled to the ROMS model. Further, another two contributory terms viz. the wave-breaking (u-brk, v-brk) and horizontal viscosity (u-hvisc, 7

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Fig. 8. Model simulated barotropic current during ebb tides (a and b), during flood tides (d and e), and the difference between Exp2 and Exp1 during ebb (c) and flood (f).

v-hvisc) to the momentum balance with the inclusion of waves in the coupled model are plotted in Fig. 7. It can be seen from the figure that the wave-breaking induced acceleration force the surface currents by

transferring the momentum from the waves to the currents. In the cyclonic environment, the impact of wave-breaking was found to be higher in the shallow coastal zone where the waves preferentially break.

Fig. 9. Time series of model simulated sea surface elevation (m) from Exp1 (a) and Exp2 (b). Time series of currents (represented by vectors in ms 1) at a location (marked as a white circle in Fig. 2) from Exp1 (c) and Exp2 (d). 8

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This wave-breaking activity can force the movement of sediments from the sea-bed in the shallow coastal zone and act to re-suspend sediments into the water column. This wave-breaking effect, together with the enforcement of the coastal current (i.e. EICC), enhances the sediment transport in the northwestern BoB. The frequent TCs in the pre- and post-monsoon seasons in the bay affect the local bathymetry which, in turn, influences the total water levels and surge. 3.3. Effect of waves on currents In order to examine the effect of waves on the currents, the local barotropic currents are analyzed from the coupled and uncoupled model simulations. Fig. 8 shows the barotropic current obtained from numer­ ical experiments Exp1, Exp2, and the difference between the two ex­ periments at the time of maximum ebb and maximum flood conditions on 12th October. The peak barotropic current magnitude of ~1.3 ms 1 was found in the coastal region in the vicinity of the cyclone on 12th October during flood tides. After the passage of cyclone during the ebb period, the current magnitude reduced to ~1.1 ms 1. The difference plot (Fig. 8c) between the two model experiments reveals the large impact of waves on the coastal circulation (i.e. offshore currents along the east coast of India) during the ebb period. The wave-forced barotropic cur­ rent strengthened by ~0.1 ms1 as compared to currents without waves during the ebb condition. Interestingly, the wave effect on the current reversed (i.e. barotropic current weaken) during the flood condition in the shallow water regime. The intensification of current during the ebb time was because of wave-breaking induced acceleration in the wavebreaking (surf) zone. On the other hand, the effect of apparent bed roughness operated to slow-down the barotropic current during the flood. A time series analysis was carried out at a coastal location (marked with a white circle in Fig. 2) where the magnitude of wave-current interaction appeared large from the momentum balance equation. The time series of model-simulated (Exp1 and Exp2) sea surface elevation are shown in Fig. 9a and b and profiles of current vectors are presented in Fig. 9c and d. The flood and ebb conditions at this location can be seen in the figure. The maximum flood was at 18 GMT on 12 October, and maximum ebb was towards the end of 13 October. At the initial time of

Fig. 10. Significant wave height (m) simulated using coupled model including the effect of currents on waves (a), without the current effect on waves (b), and the difference between the two (c) during the peak intensity of Cyclone Phailin.

Fig. 11. The difference of model simulated (Exp2 – Exp3) significant wave height (Hs) (a, c) and mean wave period (Tmbot) (b, d) representing the effect of currents on waves during maximum ebb (i) and maximum flood (ii). 9

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Fig. 12. Wave direction (degree) during (i) ebb and (ii) flood simulations using coupled model including the effect of currents on waves (a, c) and without the current effect on waves (b, d).

track. During the flood condition, the current impact on waves was negative (decreases wave height). The positive impact is mainly attrib­ uted to the wave refraction mechanism whereas the negative impact is associated with the shoaling effect. The opposing current to the waves causes a significant decrease in the wavelength which results in nar­ rowing of the wave crest and trough that leads to an increase in the elevation of wave crest (Liu et al., 2016). During the entire study period, the offshore swell waves broke over the shoal during the ebb and finally, dissipated their energy. The energy dissipation primarily depends on the local depth of the ocean. Sheng et al. (2010) analyzed the effects of waves on storm surges, currents, and inundation during hurricane ’Isabel-2003’. They found that the wave-induced stresses and radiation stress have a greater effect as compared to wave-induced bottom stresses on the total water levels. The spatial variation of absolute wave mean period (Tm) and wave direction for Phailin from model Exp2 (with current effect included on waves) and Exp3 (without current effect on waves) during the maximum ebb and flood conditions are shown in Fig. 11b,d, respectively. The large mean wave period (~11 s) found on the right side of the cyclone track, whereas the mean wave period was about 7 s on the left side of the track for both the model experiments during ebb conditions. The difference between Exp3 and Exp2 highlights a positive impact of currents on the waves, i.e. wave height increases with increasing current magnitude during the ebb condition near the cyclone location. During the flood condition, the large mean wave period reaches to ~15 s in Exp3 (without current effect) whereas in Exp2 (with current effect), the wave period remains ~11 s. Therefore, it can be perceived from Fig. 11 that the current has a negative (positive) impact on the wave parameters during the flood (ebb) condition. The present study confirms the doppler shift of intrinsic wave frequency in an environment of active wavecurrent interaction in cyclonic condition. At the time of ebb condi­ tions, the waves and current were in the same direction which indicates the positive impact of waves on current (i.e. intensify the current magnitude) when the wave forces were included in the coupled model.

model integration, the current vectors denoted northwestward surface currents which changed to counter-clockwise with the increasing depth and became southward around 15-m depth. Current profiles evolved over time as the cyclone approached and passed-by this location. At the time of nearest proximity of cyclone to this location, the currents became southward from the surface up to a depth of 30 m. The surface currents shifted from southward to northeastward after the passage of cyclone. When the wave forces were included in the model, the current magnitude and direction changed significantly, primarily on 12th October. The changes in current profiles in the presence of waves could have been due to the influence of wave-generated Coriolis and Stokes terms. A few studies also reported the effect of wave-induced Coriolis and Stokes terms on the currents up to a few meters from the sea surface (Liu et al., 2011; Polton et al., 2005). The stress imposed by the breaking waves on the sea surface (and the water column) caused the variations in total water level and current profile in the upper few meters. Rao et al. (2009) highlighted that the mean water level fell with an increase in wave momentum when wave-breaking was not present. However, in the presence of wave-breaking, the radiation stress carried by the waves decreased due to the reduction in wave energy and momentum. 3.4. Effect of currents on waves The spatial distribution of significant wave height (Hs) during the peak wind condition of Cyclone Phailin on 12th October is shown in Fig. 10 using the fully coupled model Exp2 (that includes the current effect on waves) and Exp3 (coupled model without current effect on wave). The Hs magnitudes of more than 12 m were observed in the extreme weather conditions associated with Phailin. The figure shows higher (by about 1.5 m) wave heights in the case when the current effect on waves were not included in the coupled model. The effect of varia­ tions in the barotropic current on the wave generation and propagation was analyzed by comparing the model simulated results from Exp2 and Exp3 (Fig. 11). Fig. 11a,c shows the spatial distribution of the difference (Exp2 minus Exp3) in significant wave height during the maximum ebb and flood time on 12 October. The differences induced by the current on the significant wave height shows a positive impact (increases wave height) of current on Hs during ebb tides on the right flank of the cyclone

4. Summary and conclusions The coupled ocean-wave model as part of the COAWST modelling 10

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system was applied to understand the wave-current interaction process during the very severe cyclonic storm Phailin (10–15 October 2013) over northern BoB. The model computed variables, i.e. significant wave height, peak wave direction, and JONSWAP spectrum agree well with the wave-rider buoy measurements. Numerical experiments were per­ formed to estimate the effect of various wave-current interaction pro­ cesses. To understand the effect of waves on hydrodynamics, the 2D depth-integrated momentum balance with and without wave effect was analyzed. In the momentum balance equation, the pressure gradient and bottom shear stress were found as the leading terms. The wave breaking induced acceleration term was incorporated in the momentum balance. As a result of non-linear wave-current interaction, the pressure gradient, total water elevation, and bottom shear stress terms changed significantly in the coastal shallow water regions along the east coast of India. The study highlights the acceleration induced by wave breaking as one of the crucial mechanism which governs the effect of waves on currents in the coastal wave-breaking zone. The wave breaking-induced acceleration transfers momentum from waves to surface currents, which can result in sediment transport in the shallow coastal zone where waves preferentially break. During the ebb phase, the wave-forced barotropic current strengthens by ~0.1 ms 1 as compared to currents without waves. However, the barotropic current weakens during the flood phase in response to bed roughness. The wave-generated Coriolis and Stokes terms were found to affect the sub-surface current profile in the upperocean. In the shallow depth region, the current-induced refraction takes place that modifies the wave frequency spectrum. In agreement with Olabarrieta et al. (2011), the offshore waves broke while approaching shore and shoal such that the significant wave height inside the inlet was depth limited and changed through tidal waves. The refraction and shoaling induced by currents change the wave direction more than 30� in some places (Fig. 12). However, the change in mean wave period induced by currents was more important for modification of surface currents during the ebb and flood periods. The present study on wave-current interactions is useful in applications such as salt-intrusion in coastal land areas, storm surges, coastal inundation, and sediment transport. Particularly, the study provides crucial information on the wave-current interaction in the BoB, which is a unique hydrographic region and highly impacted by TCs.

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Declaration of competing interest The authors (K R Prakash and Vimlesh Pant) declare no conflict of interest. Acknowledgements Ocean observation program of the National Institute of Ocean Technology (NIOT), Chennai, is gratefully acknowledged for the deployment and maintenance of the wave-rider buoy. Buoy data was acquired from Indian National Centre for Ocean Information Services (INCOIS), Hyderabad. ECCO2 (https://www.esrl.noaa.gov/psd/.) is a contribution to the NASA Modeling, Analysis, and Prediction (MAP) program. The authors acknowledge the funding supports from Space Applications Centre, ISRO and Ocean Mixing and Monsoon (OMM) programme of the National Monsoon Mission, Govt. of India. KRP ac­ knowledges UGC-CSIR for his PhD fellowship support. The High Per­ formance Computing (HPC) facility provided by IIT Delhi and supported by Department of Science and Technology (DST FIST- 2014), Govt. of India are thankfully acknowledged. References Battjes, J.A., Janssen, J.P.F.M., 1978. Energy loss and set-up due to breaking of random waves. In: Proceedings of 16th International Conference on Coastal Engineering. ASCE, pp. 569–587.

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