The Michaung cyclone initially formed as a cyclonic circulation in the south of Thailand on 26 November 2023. Following a westward path, by 1 December 2023, it had strengthened into a depression over the southeastern BoB, as shown in Fig. 1. The cyclone continued its northwestward path, off the coastlines of northern Tamil Nadu and southern Andhra Pradesh, until 4 December 2023. It strengthened further into a severe cyclonic storm (SCS) over the western–central and adjacent southwestern BoB. Later, it experienced landfall as an SCS near Bapatla in the afternoon of 5 December 2023, with maximum sustained winds of 90–100 kmh-1. It then moved nearly northwards, parallel and close to the coast of southern Andhra Pradesh. In the North Indian Ocean, Michaung was the sixth cyclone to have formed in the same year, with maximum sustained winds surpassing 55 knots (101 kmh-1). A lot of flooding was observed around Chennai due to cyclone-induced precipitation and intense gale winds that hit the coastal regions of southern Andhra Pradesh and northern Tamil Nadu. A maximum SS of about 1.0–1.5 m was observed and flooded low-lying parts of southern coastal Andhra Pradesh. The entire cyclone track covered a long distance of about 1150 km (RSMC report, 2023).

The study utilizes the 2D depth-integrated hydrodynamic advanced circulation (ADCIRC-2DDI) model developed by Luettich et al. (1992) and Kolar et al. (1994). Luettich et al. (1992) provided a detailed explanation of the ADCIRC-2DDI hydrodynamic model. More information about the model can be found at https://adcirc.org/home/documentation/users-manual-v50/ (last access: 9 February 2025). The momentum and continuity equations of the ADCIRC-2DDI model are solved on an unstructured grid using the Galerkin finite-element method. The model solves the generalized wave continuity equation (GWCE) to determine the maximum water elevation and the vertically integrated momentum equation for the currents. The model's governing equations are approximated using Boussinesq, incompressibility, and hydrostatic pressure. The ADCIRC incorporates boundary conditions such as normal flux per unit width and free-surface elevation from different tidal components at the open boundary.

The model employs a hybrid bottom friction formulation with a minimum drag coefficient of 0.0015 to compute SS; the chosen value is due to model stability. The duration of the ramp function for all simulations is around 1 d. The weighting factor (τ0) in GWCE is 0.05, according to Pandey and Rao (2018), while the eddy viscosity is 2 m2s-1, as reported by Cyriac et al. (2018). τ0 weighs the relative contribution of the primitive and wave portions of the GWCE. The ramp function simply scales the applied forcing, making it a unitless value that varies from 0 (no forcing) to 1 (full forcing). The detailed formulation for the hybrid friction is mentioned in Luettich et al. (1992). The drag coefficient, ramp function, and weighing factor are dimensionless. The simulations utilize the wind drag formulation proposed by Garratt (1977).

Wind stress and horizontal variations in surface air pressure primarily produce SSs. The inverse barometric effect results from the impact of changing air pressure on the sea surface. The sea level rises by 1 cm for each hectopascal (hPa) decrease in atmospheric pressure. The wind stress on the sea surface leads to a notable fluctuation in sea level, influenced by the maximum wind speed and geographic distribution of winds (Ross, 1854). The study uses a cutting-edge wind module (Holland et al., 2010, cited as H10) as an input in the model to compute horizontal cyclonic winds. H10 is a revised, more advanced version of the earlier model by Holland (1980), known as H80, that uses an improved estimation of the wind speed and wind direction near the cyclone eye, optimizes the information that is essential to determine the Rmax, resolves bimodal wind profiles, and provides a higher spatial resolution for a more precise assessment of the wind parameters in TCs. Murty et al. (2020) used the H10 wind module in the hydrodynamic and wave model in the BoB.

In the first set of experiments (Exp1), the recent cyclone of Michaung, which experienced landfall in the same region, is considered. The information for the cyclone is taken from the IMD's best-track data (https://rsmcnewdelhi.imd.gov.in/report.php?internal_menu=MzM=, last access: 2 August 2024). The INCOIS website provides the tide gauge data used in this study (https://incois.gov.in/portal/datainfo/drform.jsp, last access: 9 February 2025). In Exp2 and Exp3, the tides are not considered in the model; however, in Exp1, the tides are simulated in the model to compute storm tides (STs) during the Michaung cyclone period. The model uses 13 tidal constituents (K1, M2, N2, O1, P1, S2, K2, L2, 2 N2, MU2, NU2, Q1, and T2) at the open boundary, extracted from the Le Provost tidal database (Le Provost et al., 1998) for the simulations of tides. With these configurations, model simulations are performed with a standalone ADCIRC model to compute SS. However, we are interested in plotting maximum SS at any location during the cyclone period, denoted here as PS. Among all PS values along the coast, the maximum PS is referred to as the MPS.

The eastern coast of India has a very irregular coastline consisting of concave, convex, and straight coastlines, as shown in Fig. 2. To understand the effect of concave, convex, and straight coastlines on the generation of SSs, the concave-shaped coastline near Machilipatnam is selected for the study as this area is frequently affected by SSs. The bathymetry of the region also follows a concave-shaped coastline.

For the experiments (Exp2), different ellipse-shaped concave and convex meshes are designed with distinct a and b values, as shown in Fig. 3. Each designed shape has different a and b values compared to the actual one because a and b values are very small along the actual coastline. Therefore, domains of concave and/or convex shapes are designed based on the use of diverse a and b values. Figure 3ii–vii represent different concave shapes, with a=50, 100, 150, 200, 250, and 300 km, respectively, retaining the same value of b=150km. These shapes are named CC1, CC2, CC3, CC4, CC5, and CC6, respectively. Similarly, Fig. 3viii–xiii represent a convex shape, with a=50, 100, 150, 200, 250, and 300 km, respectively, keeping the same b=150km. These shapes are named CV1, CV2, CV3, CV4, CV5, and CV6. Figure 3xiv shows the straight-coastline domain. All the above concave and convex domains represent the ellipse shape, where b acts as the semi-major axis and a acts as the semi-minor axis until a=150km (circular shape), after which a becomes the semi-major axis and b becomes the semi-minor axis.

A total of 13 meshes are created (six for concave, six for convex, and one for straight coastline) using the surface water modeling system (SMS) application (http://www.aquaveo.com/products, last access: 9 February 2025), with a maximum resolution of 200 m near the coast and 15 km in the open ocean. The bathymetry of the domain is generated using a constant continental shelf width of about 50 km, which is an average value for the region. The depth contours follow the coastline, with a maximum depth of 3500 m in the open ocean. As shown in Fig. 3i, five idealized parallel cyclone tracks are considered, with a maximum pressure drop of 50 hPa. The translational speed of all cyclone tracks is maintained at about 13 kmh-1, which is the average speed of a cyclone observed in this region based on past historical data. The wind field for each track is calculated by taking a constant radius of maximum (Rmax) winds of 30 km, based on observations of the past cyclones in this region (Mohapatra and Sharma, 2015; Sharma and Mohapatra, 2017). These tracks are named T0 for the center, T1 and T2 for the tracks experiencing landfall 30 and 50 km north of the center, and T-1 and T-2 for the tracks experiencing landfall 30 and 50 km south of the center track. All the tracks experience landfall at the same time (at the 48th hour). The curvature of the mesh increases from west to east for both the concave- and convex-shaped coastlines, as shown in Fig. 3ii–xiii.

In the last set of experiments (Exp3), the model domain incorporates actual coastline geometry and the prevailing bathymetry, which is complex in nature, including coastal water features (river channels, lakes, etc.). The analysis area for this experiment only covers 15° N and 80° E to 16.50° N and 82° E along the eastern coast of India, as shown in Fig. 2. The domain mesh uses several digital elevation models (DEMs) (airborne, CARTO2, and SRTM30) and bathymetry datasets (ETOPO-2 and MIKE-CMAP) (Mandal et al., 2020), as in Exp1.

The model's landward boundary is considered for up to 10 m of contour from the shore, assuming the surge never exceeds 10 m topography. The mesh has a high resolution of about 100 m near the coast and of 18 km in the open ocean. Since the study focuses only on the generation of surges at the coastline, the computation of associated coastal inundation is not a part of this study. Therefore, the land is masked to counteract the impact of river openings or the presence of other waterbodies. For the sensitivity experiments, cyclones of parallel, oblique, and straight tracks are considered to have the same intensity as in the previous experiment. Refer to Table 1 for the detailed set of experiments used in the study.

In the Exp1, maximum STs are computed for the Michaung cyclone by considering tides in the model during the cyclone period, as shown in Fig. 5i. The amplitude of the local tide coincides with the spring tide at Krishnapatnam, which is observed to be about 0.5 m (not shown in the figure) at the time of the cyclone's crossing of this region. It is observed that the STs are simulated along the coast on both the western and eastern sides of the track as the cyclone moves northwards, parallel to the southern coast, before its landfall. The ST of about 1.6 m is computed on the eastern side of the track on the concave-shaped coast near Bapatla. Moreover, STs of 1.25 m are also generated along the coast near Ongole on the western side of the track. The STs of 1.0 m are also seen along the coast near Diviseema.

Validation of the model-simulated ST is conducted with the only available tide gauge data at Krishnapatnam, which falls to the west of the cyclone track, located about 30 km from the track and 160 km from the landfall point, as shown in Fig. 5i.

As shown in Fig. 5ii, at Krishnapatnam, the maximum STs from the model and tide gauge are noted as 0.63 and 0.66 m, respectively, occurring 36 h before landfall. On the other hand, the ST values are reduced at the time of landfall to 0.08 and 0.28 m, respectively. However, the simulated maximum ST at Krishnapatnam is qualitatively in agreement with that of the tide gauge observations. The computed correlation coefficient, mean absolute error (MAE), mean square error (MSE), mean bias error (MBE), and root mean square error (RMSE) are 0.91, 0.146, 0.032, 0.04, and 0.16 m, respectively. Though some gaps in the tide gauge data are seen, no missing data are found during the maximum ST or landfall time. The reason for the generation of lower STs may be due to the location of Krishnapatnam, located to the west of the cyclone track, which was mostly influenced by the offshore winds during the cyclone period. This experiment confirms the hypothesis that the concave coasts are always subjected to more vulnerability in terms of SSs whenever a cyclone approaches, irrespective of whether the coast is to the east or west of the cyclone track.

Numerical simulations are carried out without tides using different parallel cyclone tracks, as described for Exp2, to delineate their effect on the generation of SSs in the concave and/or convex domain. The model is integrated for 3 d, out of which the cyclone experiences landfall after 2.5 d. Figure 3i shows the computational domain, along with five idealized parallel cyclone tracks experiencing distinct landfalls within the domain. In this study, parallel tracks (T-2 to T2) are considered, and the central track, T0, experiences landfall at the vertex of the domain. The distributions of PS while moving from track T-2 (south) to track T2 (north) within the same domain and between differently shaped domains are depicted in Fig. 6.

The computed MPSs for different concave domains are shown in Fig. 6i. For the track T-2, the value of the MPS does not vary much for different concave shapes (CC1 to CC6), and a maximum difference of only 0.04 m is observed. There is an increasing trend in the MPS for the track T-1 as the curvature of the domain increases from CC1 to CC6, with a maximum difference of 0.075 m. On the other hand, for the central track T0, the value of PS increases up to CC4 and then decreases marginally. It is noticed that the trend is seen to decrease linearly with the increase in the curvature of the domain from track T-2 to track T2.

The maximum difference in the MPS between CC1 and CC6 is computed to be about 0.38 and 0.60 m for the tracks T1 and T2, respectively. The decrease may be attributed to the curvature of the coastline, which becomes more convergent from CC1 to CC6. This indicates that, as the cyclone track and the landfall position move northwards from the vertex or center of the concave coast, the MPS value decreases in correspondence with the increasing convergence. Further investigation is done in this regard and is explained in the subsequent sections.

Figure 6ii shows the MPS trends for different convex domains. It is noted that there is a linear decreasing trend in PS from CV1 to CV6, and the decrease is substantial as the curvature increases. The maximum differences in MPS values between CV1 and CV6 range from 0.02 to 0.83 m for tracks T-2 to T2. It is observed that, if the curvature of the convex shape increases, the MPS values for a particular track decrease significantly. This also underscores the influence of coastline shape and landfall position on surge computation. Furthermore, these simulations quantify the behavior of the MPS distribution for both concave and convex shapes.

Figures 6iii–iv depict the tendency of the MPS within the concave and convex domains, respectively, as the tracks move from south to north (T-2 to T2). For all the concave and/or convex curvatures, the MPS initially increases from T-2 to T-1, which is followed by a decrease. However, the MPS is noticed at T-1 in both shapes, though it is more apparent for the concave coast, being that it is a convergent type. The value of the MPS varies from 3.62 to 3.7 m for CC1 to CC6, while it ranges from 3.60 to 3.51 m for CV1 to CV6, as depicted in Fig. 6iv. The reason for simulating a higher MPS for T-1 may be due to the value of Rmax that lies at the vertex of the curvature as it provides maximum winds in this region. For the straight coastline (not shown here), the MPS is simulated at about 3.6 m, which falls mostly between the concave and convex values. From the above analysis, it is noted that there is not much difference in terms of the MPS computed for CC1 as the track moves from south to north. However, the difference increases as the curvature increases for both concave and convex shapes. The maximum differences in the MPS between parallel tracks (T-1 to T2) within the CC1 to CC6 domains are 0.07, 0.14, 0.30, 0.44, 0.59, and 0.74 m, respectively. For the convex-coastline domains, CV1 to CV6, these values are 0.07, 0.20, 0.37, 0.57, 0.71, and 0.80 m. In general, the values of the MPS increase as concave curvature increases because of the accumulation of more wave energy towards the coast. On the other hand, energy gets distributed or dissipated on the convex coast with increasing curvature, which results in a lower MPS along the coast.

This analysis is further explained using a tangent angle at the location of the MPS, which usually coincides with the location of maximum sustained winds along the coast based on the value of Rmax. The detailed calculation of the angle corresponding to the location of the MPS for each track and shape of the domain is explained in Fig. 4. Tables 2 and 3 provide tangent angles corresponding to the location of the MPS generated by various tracks against each domain. Table 2 shows that the difference in the angle between T-1 and T2 increases as the domain curvature increases from CC1 to CC6, while the angle (negative) decreases for the track T-2. A similar observation is also made for the convex domain, as given in Table 3.

These angles have a significant effect on the generation of the MPS, as shown in Tables 2 and 3. It is noted that the maximum-curvature domain (CC6) produces different MPS values for different tracks (T-2 to T2) compared to that of the minimum (CC1). This leads us to infer that the curvature of the coast plays a significant role in the generation of PSs, along with the landfall location of the track in the domain. To understand further whether this angle is also responsible for the spread of PSs, the spatial distribution of PSs along the coast during the cyclone period is shown in Fig. 7 for the domains CC1–CC6 and CV1–CV6 as these two domains represent the minimum- and the maximum-curvature domains. It is noted that the lowest spread of PS is seen at the vertex of the domain when the angle is at its maximum (θ=90°) and is more as the theta decreases on either side of it. This leads us to infer that the spread along the coast increases as the curvature of the domain increases.

As cyclone winds are the primary forcing for the generation of SSs, it is important to investigate the wind distribution along the coast with reference to each curvature of the domain. For this, wind components onshore and alongshore are estimated at the location of the MPS, along with how these components vary due to differently shaped concave and convex coasts. These components provide insight into PS and its distribution along the coast. Storm waters are driven towards the coast by onshore winds originating at sea. Due to the accumulation of water caused by these winds along the coast, PS is enhanced. However, the alongshore wind component influences the distribution or spread and direction of water movement along the coast. Hence, the onshore wind plays a vital role in developing SS at the coast, while the alongshore wind is responsible for the spread of surges along the coast. Figure 8 represents the temporal variation of the onshore and alongshore wind components for the domains CC1, CC6, CV1, and CV6 as calculated at the location of the MPS. From Fig. 8, it is noted that, in general, the onshore wind increases as the cyclone approaches the coast. The negative sign represents the onshore wind towards the west (positive towards the east) and the alongshore wind towards the south (positive towards the north). At the time of landfall, the onshore winds for CC1 are -45.1, -49.0, -48.2, -47.7, and -46.7 ms-1, and the alongshore wind is -25.0, -15.0, -14.3, -15.7, and -23 ms-1 for the tracks T-2, T-1, T0, T1, and T2, respectively. Similarly, CC6 experiences onshore winds of -49.2, -52.3, -46.0, -40.0, and -32.4 ms-1 and alongshore winds of -15.0, -4.0, -22.0, 27, and 40.4 ms-1 for the tracks T-2, T-1, T0, T1, and T2. The onshore wind decreases and the alongshore wind increases from track T-2 to T2 for CC6, which is consistent with the MPS (refer to Fig. 6), as depicted in Fig. 8. Although the maximum wind speed of 54 ms-1 of the cyclone is used for all the tracks, the generation of SS depends upon the strength of the onshore wind at the time of landfall, which varies with the curvature. For the convex domain (CV1), there is not much change in the onshore wind for all the tracks, which is the same as for CC1.

However, the change becomes significant as the curvature increases, as shown in Fig. 8vii. At the time of landfall, the onshore winds for CV1 are -45.0, -46.0, -44.0, -43.6, and -43.2 ms-1, and the alongshore wind is -24.1, -23.2, -26.0, -26.8, and -27.3 ms-1 for the tracks T-2, T-1, T0, T1, and T2, respectively, as shown in Fig. 8v–vi. Similarly, CV6 experiences onshore winds of -41.5, -44.8, -40.0, -33.8, and -30.0 ms-1 and alongshore winds of -29.3, -25.7, -30.5, -39.8, and -41.6 ms-1 for the tracks T-2, T-1, T0, T1, and T2, as shown in Fig. 8vii–viii and Table 4. Similarly, the onshore wind does not change much for CV1, but it experiences significant changes for CV6. From all the cases discussed above, the maximum onshore wind is noticed for track T-1 as the Rmax coincides with the vertex of the curvature. Hence, the occurrence of the MPS is observed for track T-1. It is also noted that the distribution of PS along the coast increases as the alongshore wind is enhanced, which is evident from Fig. 7.

Figure 9i–xx describe the generation of positive and negative surges along the coast during the cyclonic period for the shapes CC1, CC6, CV1, and CV6 for all the tracks from T2 to T-2.

Figure 9i–xx show that the distance along the coast is considered with reference to the landfall location, implying positive values on the right and negative values on the left, along with the surge values. The left y axis (red) indicates the landfall location of the cyclone track, and the right y axis depicts the surge value. Figure 9i–v describe surge development for CC1 for all tracks. It is observed that the positive surge occurs close to the landfall on the right side, while the negative surge on the left is generated about 2 h prior to the landfall time. A similar observation is made based on Fig. 9vi–x for CC6. The simulations for different concave coasts (CC1–CC6) suggest that the positive surge decreases for the tracks from T-2 to T2, while the negative surge increases. This can be attributed to the reduction in available domains on the eastern side of any track in CC6 required to drag water masses by means of the onshore winds towards the coast, as considered for T-2 to T2.

As seen from all the simulations for CC6, it is observed that the maximum surge along the coast always propagates towards the center or vertex of the curvature. In the case of convex coasts (CV1–CV6), the surges generated along the coast, in general, diverge or spread from the vertex of the curvature. As the curvature increases from CV1 to CV6, a reduction in PS is seen for all the tracks because of lower onshore and higher alongshore winds (refer to Fig. 8v–viii). The onshore winds are responsible for the accumulation of surge waters towards the concave coasts, while the alongshore winds are responsible for the divergence or spreading of the waters along the convex coasts.

As observed from the earlier simulations, the value of PS in the concave domain increases as the SS waves are propagated towards the coast. The increase in SS can be related to an increase in the corresponding energy flux in the domain. If the shape of the domain becomes narrower and shallower away from the sea, the surge will increase in the domain. This may be known as the funneling effect. If we neglect frictional losses, the wave energy flux will theoretically remain constant as the wave progresses upwards in the domain, and the wave energy density is given by: 3E=ρgA22, where A is the amplitude of the surge wave, ρ is the density of the water, and g is the acceleration due to gravity. The energy density per unit length of the domain is given by EB, where B is the width of the domain. Then the energy flux in the domain given by EBc will be constant (c being the phase speed or energy propagation speed in the shallow water), i.e., 4(ρgA)b(gh)1/22=constantorAαB-1/2h-1/4, where h is the depth.

Energy density per unit length EB is computed for the concave coasts of CC1 and CC6, as shown in Fig. 10i and ii, using the computed PS (A) at each grid multiplied by the grid resolution (B) for the track T0. It is observed that the maximum EB values of 60 and 58 MJm-1 are computed near the coast for CC1 and CC6, respectively, at the time of the MPS. As seen in the figure, the integrated value of EB is computed across the lines AA^′, BB^′, and CC^′, falling 5 km (LA), 25 km (LB), and 50 km (LC) from the vertex (L) of the domain for the shapes of CC1 and CC6. These values are 1953, 197, and 56 MJm-1 for CC1, while they are 983, 300, and 85 MJm-1 for CC6, as shown in Table 5. The higher energies (AA^′) are seen close to the landfall for CC1 while decreasing significantly for CC6. However, higher values are seen in CC6 much further away from the landfall (BB^′, CC^′) compared to in CC1, implying more spread of EB for CC6. For track T0, the funneling effect is not seen in terms of surge generation (refer to Table 5). The peak EB is associated with the radius of maximum winds (Rmax) in either case. However, the spread or extent of the peak EB is seen more in CC6 compared to in CC1 due to the funneling effect.

The value of the width (B) is reduced as the cyclone gets closer to the concave shore, resulting in an increase in the energy density and EB. This increase in energy is directly responsible for the enhancement of surges in the concave-shaped domains. Since B has a more significant influence on A than h, we have considered only B in the above computations, leaving out h. This explanation holds well for all other concave shapes as well. This formula may not be directly applicable for convex domains. However, it is expected that more energy will dissipate instead of accumulate along the coast for the convex domains, as in the case of concave domains. The simulations for all the concave domains (not shown), in general, suggest that the energy is more focused towards the coast as the tracks move from T2 to T-2.

In the next experiment (Exp3), complex coastal stretch with both concave and convex geometry is selected along the eastern coast of India to investigate the impact of PS in the region. This experiment consists of three parts. The first part computes PS using three independent parallel tracks (Fig. 11). The second part deals with the tracks approaching from different angles at different locations in the domain (Fig. 12). The final part examines the generation of PS with three straight tracks parallel to the coast, with different Rmax values (Fig. 13). In all these experiments, the strength of the cyclone remains the same.

As shown in Fig. 11, three parallel tracks, 1, 2, and 3, are considered in the concave-shaped coast, showing landfall at different locations on the southern, center, and northern sides of the concave coast, respectively. Rmax is considered to be 30 km for all three of the tracks. Track 1 experiences landfall near Diviseema, with an MPS of 3.94 m occurring in the middle of the concave coast, as shown in Fig. 11i. The reason for this is attributed to the prevailing maximum onshore winds associated with track 1, which is found close to the vertex of the concave coast as the Rmax is 30 km. Tracks 2 and 3 experience landfall near Machilipatnam and Antervedi, with MPS values of 3.51 m (Fig. 11ii) and 3.13 m (Fig. 11iii), respectively.

As the tracks move from south to north, a reduction in PS or the MPS and a shifting of its location are perceived. The reason for the reduction is due to the change in landfall location on the concave coast, which leads to a reduction in the onshore winds as the tracks change from 1 to 3. Hence, accumulation of the storm waters is reduced as the tracks move to the north, leading us to deduce that the effect of the concave coast is reduced as the landfall location of the track moves to the north of the coast. It is also important to note that the MPS is also generated to the west of tracks 1 and 2 near Nizampatnam due to the presence of another concave coast close to Bapatla. A convex-shaped coastline is also enclosed between the concave coasts of Nizampatnam and Diviseema.

However, PS is reduced in this region as the tracks shift to the north. The experiments lead us to infer that the concave-coastline geometry is more susceptible to higher SSs, especially when the track experiences landfall to the south of the coast. Additionally, SS computed along the concave-shaped coastline is higher compared to that along the convex coastline, which aligns with the observations made with the idealized concave and convex domains (refer to Sect. 5.2).

In this part of Exp3, the impact of various approach angles and the location of the landfall on the generation of PSs along the concave coastline is explored. The approach angles and landfall locations considered in this study are based on the history of the cyclones formed in this region, which include the 1977 Andhra Pradesh cyclone and the Ogni (2006), Khaimuk (2008), Laila (2010), Helen (2013), Lehar (2013), and Roanu (2016) cyclones.

The model domain is the same as that of Sect. 4.6. Here, three landfall locations along the concave coast are considered in relation to three different approach angles. Though some tracks cross the coast multiple times, PS is studied at selected landfall locations in the concave domain, as discussed in the above section. As a part of this exercise, PS is simulated in the concave-shaped coastline with approach angles of 45, 165, and 180°, as experienced at the landfall location (east, center, and west), represented as tracks 1, 2, and 3, as shown in Fig. 12. The reason for selecting these tracks is that some generate PS over the region that is west of the track. The track angle is measured clockwise, with the tangent drawn parallel to the landfall location. These tracks are chosen so that they have more influence on the occurrence of PS in the concave domain. The tracks that strike on the eastern side of a concave coastline near Antervedi generate MPS values of about 2.56, 3.08, and 3.15 m for tracks 1, 2, and 3, respectively, as shown in Fig. 12i–iii.

The MPS is also computed in the neighboring concave-shaped coastline near Bapatla at about 2.01 and 3.02 m for tracks 2 and 3, respectively. The MPS for track 1 is computed on the eastern side, while for tracks 2 and 3, it is on the western side due to the concave nature of the coastline. In Fig. 12iv–vi, tracks 1, 2, and 3 experience landfall at the center of the concave domain near Machilipatnam, and the associated MPS values are about 2.83, 3.59, and 3.62 m, respectively. Tracks 2 and 3 also generate MPS values in the adjacent concave-shaped coastline near Bapatla of about 2.75 and 3.27 m, respectively. The simulations shown in Fig. 12vii–ix correspond to the landfall location near Diviseema, with different approach angles. The simulated MPS values for tracks 1, 2, and 3 are approximately 3.34, 3.61, and 3.67 m, respectively, each exhibiting higher SSs in the concave domain compared to in any other landfall locations. This suggests that the occurrence of the MPS is not always confined to the eastern side of the cyclone track if a cyclone experiences landfall towards the concave geometry with unique approach angles. These simulations lead us to infer that the generation of PS depends on both the track approach angle and the landfall location in the concave domain.

In the past, many parallel cyclonic tracks along the eastern coast of India were seen passing through the coastal stretch covering Kothapatnam to Antervedi, which has a complex geometry with concave- and convex-shaped coastlines. Though the cyclones may not experience landfall in this region, this coast is prone to higher SSs due to its irregular coastline geometry. Hence, this experiment is designed to study the effect of PS with equally spaced (20 km) tracks moving parallel to this coast and with different Rmax values of 20, 30, and 40 km for tracks 1, 2 and 3, respectively, as shown in Fig. 13. The PS in the domain is depicted in Fig. 13i–iii as the cyclonic tracks move parallel to the coast, with Rmax of 20 km. It is important to note from the simulations that all these parallel tracks generate SSs along the coast. However, the MPS of 2.85 m is simulated with track 1, and the minimum of 2.0 m is simulated with track 3. Similarly, the experiments are carried out with Rmax of 30 and 40 km, as shown in Fig. 13iv–vi and vii–ix, respectively. The pattern of surge development at the coast is very similar to that of an Rmax value of 20 km. However, the MPS simulated for track 1 is 3.1 m, and that for Rmax values of 30 and 40 km is 3.2 m. It is also observed that the MPS values for track 3 are 2.5 and 3.0 m for Rmax values of 30 and 40 km, respectively. It is worth noting that PS is generated only to the west of the concave coasts due to strong associated onshore winds, and the maximum is produced along the coast, with Rmax of 40 km. It is observed from the simulations made for Rmax of more than 40 km (not shown here) that the effect of SS on the coast is reduced as the tracks move away from the coast. Moreover, the concave coast in the north, covering Diviseema to Antervedi, experiences higher SS compared to that of the adjacent concave coast lying in the southern part of the domain at Bapatla. The increase in Rmax does not affect the magnitude of the wind but modifies the cyclonic horizontal wind distribution. Higher surges are expected to be generated at coastal locations far from the landfall point as Rmax increases.