Energetics and spatio-temporal variability of semidiurnal internal tides in the Bay of Bengal and Andaman Sea

Highlights

• Eastern Andaman Sea and head bay are the main areas of frictional tidal dissipation.

• One-third of M2 tidal energy (19 GW) dissipates by generation of internal tides.

• About two-third of internal tide energy dissipates away from the generation sites.

• Seasonal variability in energy conversion is strong in the northern bay.

• Changes in mesoscale circulation alter the path of internal tide propagation.

Abstract

Energetics of semidiurnal barotropic and internal tides in the Bay of Bengal (BoB) and Andaman Sea (AS) are studied using the simulations from a high-resolution ocean general circulation model. Barotropic M${}_2$ tide, which is the largest tidal constituent in this region, loses about 65.5 GW of energy in the BoB and AS. Most of this barotropic energy (46.5 GW) is dissipated by means of bottom friction in the shallow regions, such as the head of the bay and the Gulf of Martaban. Due to the interaction of barotropic tides with bottom topography, about one-third of the barotropic M${}_2$ energy (19.1 GW) gets converted into internal tides and most of this conversion (84%) occurs over the Andaman–Nicobar (AN) Ridge. On the contrary to the estimates in earlier studies, our results show that a large part (59%) of this internal tide energy in the BoB and AS gets dissipated far away from the generation sites. Compared to the BoB, energy dissipation rates are found to be large over the entire AS and it could result in enhanced vertical mixing in this region. Further, analysis of the temporal variability of conversion within the model domain shows that energy conversion in the semidiurnal band varies between 11 to 27 GW over a spring–neap cycle. Seasonal variability in the stratification due to river runoff significantly changes the conversion of tidal energy at the generation sites in the northern BoB and AS. Our study revealed that westward radiating internal tides from AN Ridge undergo path alteration (refraction) due to the time-varying mesoscale circulation and such path alterations cause large intraseasonal variability in internal tide activity and redistribution of internal tide energy available for mixing in the remote areas such as the continental margins of the western BoB.

Introduction

Barotropic tides supply about 3.7 terawatts (1 TW $=$ 10¹² watt) of energy into the ocean globally, and about 25%–30% of this energy gets converted to baroclinic energy in the deep ocean due to the generation of internal tides (Egbert and Ray, 2000). The rest of the energy is dissipated in the shallow regions by means of bottom friction. It has been estimated that about 2 TW of mechanical energy is required to maintain the abyssal stratification and meridional overturning circulation in the ocean (Munk and Wunsch, 1998). Earlier studies have shown that about half of this energy is supplied by breaking of internal tides, which are generated by the interaction of barotropic tides with the bottom topography (0.7–1.3 TW). The other half is provided by the near-inertial waves, which are generated by the change in the wind stress acting on the ocean surface (Waterhouse et al., 2014).

Unlike the generation of near-inertial waves, which is highly variable over temporal and spatial scales, most of the internal tide generation occurs at some specific topographic features such as continental slopes and mid-oceanic ridges (Alford, 2003). Based on microstructure measurements, earlier studies have reported enhanced diapycnal mixing over the rough bottom topography due to the conversion of barotropic energy into the baroclinic energy (Ledwell et al., 2000). In addition, though the observed distribution of diapycnal mixing in the ocean is extremely patchy in space, varying both in depth and location, it has a noticeable spatial correspondence with internal tide energy dissipation (MacKinnon et al., 2017). Therefore, the identification of pathways of internal tide energy conversion, radiation and dissipation is important to understand the spatial distribution of diapycnal mixing in the ocean and thereby to provide better representation of mixing processes in numerical models. As the observations on vertical mixing are limited, estimates of the internal tide energetics using regional models with very high grid resolution have a greater role in perceiving their spatio-temporal variability and internal tide-induced mixing (Carter et al., 2012).

North-eastern flank of the tropical Indian ocean comprises the Bay of Bengal (BoB) in the west and Andaman Sea (AS) in the east, which are partially separated by volcanically formed Andaman–Nicobar (AN) Islands chain (Fig. 1a). The BoB is deep ($\sim$4500 m) in the south and becomes shallow towards the north. Bathymetry in the AS is complex due to the presence of multiple seamounts and islands. Several straits or passages having varying depths, with maximum depth exceeding 1000 m, along the AN Islands chain connect the AS to the BoB and maintain the exchange of water mass (Chatterjee et al., 2017). This region is bounded by land mass in the west, east and north, whereas the southern part is connected to the equatorial Indian Ocean.

Tides in the BoB and AS are mainly semidiurnal in nature, which enter through the southern boundary of BoB from the equatorial Indian Ocean (Murty and Henry, 1983, Sindhu and Unnikrishnan, 2013). As tides propagate towards the north, their amplitudes gradually increase and they get amplified over wide continental shelves in the northern BoB, Eastern AS and Gulf of Martaban (Sindhu and Unnikrishnan, 2013). Semidiurnal M${}_2$ is the largest constituent followed by S${}_2$ and amplitudes of M${}_2$ vary from 10 cm in the southern side to 90 cm in the head of the bay. Amplitude of diurnal constituents (K${}_1$ and O${}_1$) are relatively weak (less than 12% of M${}_2$) in the BoB and AS (Sindhu and Unnikrishnan, 2013). Though the characteristics of propagation of barotropic tides in this region are fairly well known, the pathways of their dissipation are not understood completely. As noted earlier, a part of this tidal energy can be converted into internal tides. Many previous studies have reported the presence of tidally-generated internal waves (internal tides) in the BoB and AS. Most of these studies explored the energetics of internal tides in the western BoB using numerical simulations (Rao et al., 2010, Rao et al., 2011, Pradhan et al., 2013, Pradhan et al., 2016, Joshi et al., 2016). These studies have reported that internal tides in the western BoB are generated along the continental slopes and relatively strong internal tides occur in the northern parts of the western BoB and in the head of the bay. Later, long-term observations of internal tides in this western BoB from Acoustic Doppler Current Profilers (ADCP) showed that observed baroclinic velocities (of about 15 cm s⁻¹) associated with semidiurnal internal tides on the shelf are stronger than the barotropic tidal currents in this region (Jithin et al., 2017a). They also reported the presence of energetic internal tides in the southern and northern parts off the east coast of India, which could not be explained based on the spatial variation of barotropic tides in the region.

Combining numerical simulations and ADCP observations, Jithin et al. (2019) showed that most of the internal tides observed along the continental margins in the western BoB are not locally generated on the shelf break region, but they are coming from the southern and northern parts of the AN Ridge, which is located about 1000 km away. These internal tides take about 5–7 days to reach the western BoB and cause relatively strong internal tide activity during the neap phase of the local barotropic tides. In addition, the onshore transmission/reflection of these remotely-originated internal tides play an important role in determining the spatial variability of internal tides along the shelf of western BoB. In some areas along the western BoB, where the continental slope is not very steep, these internal waves propagate further onto the shelf and result in relatively strong internal tide activity in the inner shelf regions (Jithin et al., 2019). Shoreward propagating short-period internal waves in the shelf of western BoB, particularly in the northern part of the coast (18${}^{\circ }$–19${}^{\circ }$N), were also identified from Synthetic Aperture Radar imageries (Prasad and Rajasekhar, 2011, Joshi et al., 2016).

Presence of large amplitude internal waves in the AS, which is mostly generated by tidal currents flowing over the AN Ridge, were identified from in situ temperature profiles and SAR images in the 1980’s (Perry and Schimke, 1965, Osborne and Burch, 1980). Roder et al. (2010) had reported that these internal waves play a crucial role in supporting coral metabolism in the eastern AS by regulating the distribution of organic matter and making them more resilient to disturbance. Recently, based on the simulations from a model having a grid resolution of about 2.5 km, forced with M${}_2$ and S${}_2$ tidal constituents, Mohanty et al. (2018) have shown that about 23 GW of semidiurnal barotropic tidal energy gets converted as baroclinic energy in the AS and most of the energy dissipates near the generation sites itself. Even though they noted the presence of westward radiating internal tides from the AN Ridge into BoB, the fate of these internal tides and their propagation through the BoB are not well documented. In addition, previous studies have also shown that the continental slopes along the head of the bay are also important regions of internal tide energy conversion (Pradhan et al., 2016, Joshi et al., 2016, Jithin et al., 2019). Hence the actual internal tide field in this region can be more complex as the internal tides from multiple sources result in interference patterns and even alter the local energy conversion and dissipation (Rainville et al., 2010). Therefore, to obtain a more accurate picture of the internal tide field and its energy budget in this region, all the potential sources must be included. Moreover, though there are a few studies (Jensen et al., 2018, Jensen et al., 2020) which used high-resolution models for the entire north-eastern basin of Indian Ocean with realistic atmospheric forcing and showed internal tide radiation from the AN Ridge, none of them are thoroughly validated using in-situ observations or explored the internal tide energetics in detail. Unlike earlier studies on internal tides in this region, in which most them uses models with their domain restricted to AS or the western BoB (Rao et al., 2010, Rao et al., 2011, Pradhan et al., 2013, Pradhan et al., 2016, Joshi et al., 2016), simulation from a high-resolution model covering the entire BoB and AS is used in the present study to estimate the energy budget of this region.

BoB is rich in the presence of mesoscale eddies, which play an important role in modulating the circulation and stratification in this region (Chen et al., 2012). Most of the mesoscale eddies in this region are generated along the eastern and western boundaries (Chen et al., 2012). Previous studies have noted that changes in the mesoscale circulation could greatly modulate and redistribute the baroclinic energy and change the paths of the propagation of the internal tides in South China Sea (Xie et al., 2016, Huang et al., 2018) and Hawaiian Ridge (Rainville and Pinkel, 2006, Zaron and Egbert, 2014) and Japan Sea (Park and Watts, 2006). In addition, varying-mesoscale fields also result in the incoherent and intermittent nature of internal tide (Zhao et al., 2010, Van Haren, 2004). Wijesekera et al. (2019) have suggested that vertical mixing gets enhanced 3–5 times by the interaction between internal waves and eddies in the southern BoB. Jensen et al. (2018) reported that the interaction of semidiurnal solitary waves with eddies results in enhanced sub-mesoscale variability in the BoB. However, no detailed investigation has been carried out so far to understand the effect of mesoscale eddies on the internal tide propagation and re-distribution of internal tide energy in the BoB.

The northern parts of the BoB and AS receive large amounts of freshwater from adjacent rivers, stratification in these regions changes significantly from one season to the other (Vinayachandran and Kurian, 2007). River runoff peaks towards the end of the South-west Monsoon (June–September) and the near-surface stratification also becomes high in the subsequent months. Xie et al. (2015) had shown that the barotropic-to-baroclinic energy conversion increased with the upper-ocean stratification because the large variability in stratification impacted the pressure perturbation at the bottom However, the changes in internal tide generation associated with background stratification in this region has not been examined in detail.

Hence, the major objectives of the present paper are to

(i) Estimate barotropic and internal tide energy budget in the BoB and AS

(ii) Provide a comprehensive picture of major sources and pathways of internal tide propagation and dissipation

(iii) Examine the spring–neap and seasonal variations in the internal tide energetics

(iv) Examine the effect of variable mesoscale field on the propagation of internal tides in this region.

The present paper is organized as follows. Section 2 describes the data and methodology. A detailed discussion of barotropic and internal tide energetics and its spatio-temporal variability is given in Section 3. Section 4 summarizes the paper.