The BOB is a typical sea with a dynamic and complex nature. In addition, the abrupt increase in depth and significant tidal forcing favor the formation of IWs over the BOB. The study region and underlying bathymetry are as shown in Fig. 1. The observation of IWs through SAR imagery is particularly amenable. However, to observe these IWs in SAR images, they are significantly strong enough to manifest the ocean surface in such a way that they appear as alternating dark and bright bands against a gray background. Their appearance in SAR images also depends upon local environmental conditions, such as wind speed and direction, surface currents, and the presence of surface films.15. Earlier studies on SAR identification of IW activity were often restricted to the region between 17.5–20.5°N and 83.5–87.5°E in the northern BOB16, 9, 10. However, the present study shows that they generate and propagate all over the continental shelf edge/rim of the BOB. Figure 2 shows the selected ALOS PALSAR L-band SAR images revealing the IWs. Their chief generation mechanism is the perturbation of stratified layers over continental shelves by tidal forces and shoreward propagation, as also suggested by earlier studies. They can also be generated by lee waves, tidal beam resonance, plumes, and the transformation of the internal tide15. 3 and 10 computed the IW characteristics, such as the wavelength, phase speed, propagation direction, and amplitude, with the aid of observational data using SAR images over the same region and frequent IW activity observed from September to May. All these studies were primarily confined to the head or north BOB. Although observational (in situ) and modeling studies pertaining to IWs have been carried out over the BOB (as discussed earlier in the introduction section), studies using SAR imagery are rather limited. The details of the SAR images used in this study are as shown in Table 1.
As the BOB experiences northeast (NE) monsoon, southwest (SW) monsoon, and pre- and postmonsoon seasons, the latter two seasons are more favorable for the formation of low-pressure systems as well as IWs. However, in this study, IW activity was observed even in the monsoon season, although strong winds prevailed during this season. This reveals that stratification is present even in the monsoon period as the IWs propagate along the differing density layers. This may be due to the persistence of freshwater discharge from rivers during monsoons and may be due to the low-pressure systems during pre- and postmonsoon periods. This may indicate the persistence of fresh water throughout the year in the northern and eastern BOB, as reported by 17, 18, 19 and 13. The observed locations of the IWs in the SAR images and the sources of river discharge into the bay are as shown in Fig. 3. The processed ALOS PALSAR L-band SAR images showing IW features over the BOB are as shown in Fig. 4. They vary from a single soliton to a large group containing more than 20 individuals. They are often observed in groups or in packets. Although they appear throughout the year, they interact with the underlying bathymetry and local oceanographic conditions to exhibit different IW morphological features. IW morphology is the study of the shape and structure of IWs.
Jackson et al.15 provided an overview of IW detection theories in SAR imagery and the factors that influence IW morphological signatures, including surface, subsurface, and IW properties. In this study, we investigated the morphological features of SAR-observed IWs in the BOB. As shown in Fig. 4, except for the ALPSRP139980350 (single soliton) image, in all the ALOS PALSAR images, the observed IWs are either in groups or in packets. In addition, different types of patterns, such as bright bands followed by dark bands, dark bands followed by bright bands, and single bright bands, are also present. The morphology of the IWs in the ocean can be affected by a number of factors, including the density difference between the different ocean layers, the wavelength of the wave, the depth of the ocean, and the presence of any other oceanic phenomena such as currents or waves 20. Da Silva et al.20, 21 classified SAR observations of IW signatures as single positive signs (+) for the bright band, single negative signs (-) for the dark band, or double signs (+/-) for the dark and bright bands. The most common pattern is the IWs of depression, which have nonlinearity, appearing as a bright band followed by a dark band (single positive sign). The characteristics of this signature pattern can be influenced by various factors, such as the environment at the ocean surface (wind speed, wind direction, presence of surface films) and the properties of the IWs themselves (mode, half-width, amplitude, and currents). The extracted wind speed and direction plots for the respective images on the respective day of the SAR images from CCMP v3.1 data are shown in Supplementary Fig. 1.
In most of these SAR images, IWs appear as a bright band on a gray or black background (single positive sign). A bright band-only signature is observed in the ALPSRP139980350 image (single soliton), and this morphology appears when the modulations induced by the breaking event occur. In addition, a dark band against a gray background (single negative sign) also appeared in the ALPSRP132690320, ALPSRP085280400, and ALPSRP190450400 images. In this study, the scene IDs ALPSRP132690320, ALPSRP144210410, ALPSRP131670240, and ALPSRP085280400 exhibited peculiar behavior. SAR images with local bathymetry overlaid to study their nature and characteristics are as shown in Fig. 5. These four images show IW signatures apart from those generated by the local topography. These IWs generated over the BOB exhibit complex and peculiar characteristics.
For example, Fig. 6 shows the IW signatures observed off the Kakinada region having image ID of ALPSRP132690320. Interestingly, the single positive sign and single negative sign signatures coexisted and crossed each other without overlapping in the BOB. This may imply that multiple layers of stratification exist in the BOB. The backscatter profile/transect drawn across these signatures clearly shows the difference in polarity/sign. An extensive study of these kinds of IWs was discussed in 20. In addition, these IWs appear to be approaching different directions, which may indicate that there might be other sources of IW generation (such as high river discharge) or may be due to IW reflection itself (yet to be studied in the future). This triggering of IWs by river discharge has been observed by several studies, as river plumes can also be a significant source for the generation of IWs31. The generation of IWs is due to the high discharge from the Mzymta River22 and the generation of IWs under different discharge conditions, such as subcritical23 and supercritical22 conditions. Similarly, this region is also influenced by Godavari River discharge, and its plume obtained from Landsat 5 images on 22 August 2010 is shown in Fig. 7. Their studies also revealed that IWs can be generated from (even) moderate to high discharge conditions and that their wavelengths and amplitudes vary accordingly. Their study also suggested a general mechanism for river plumes/discharge generating IWs in the coastal ocean in which the river dumps freshwater into the ocean, which forms plumes that spread out due to stratification, and as the plume meets seawater, a zone with a sharp contrast in density forms at the leading edge, called the plume front. Then, the interaction between the plume's flow and this density difference creates a condition where the plume front acts as a moving disturbance called a hydraulic jump23. This disturbance triggers internal waves to propagate away from the plume front with generally negative polarity, as shown in Fig. 6b. Other IWs with negative polarity were observed off the stretch of the Mahanadi-Brahmani River confluence. These depressed IWs generated in deep water appear to propagate toward shallow regions. Similar results were obtained for all four images, as discussed in the earlier paragraph. As these IWs propagate toward coastal regions, they undergo changes in polarity, refraction, etc., and tend to interact with coastal phenomena. Thus, they exhibit complex patterns.
The most common IW manifestation is the bright band, followed by the dark band of mode-1 IWs of depression 15. However, the existence of higher modes is also possible in the BOB due to the presence of different stratification conditions 15. The first and second images of ALPSRP162590150 and ALPSRP162590160 in Fig. 5 are examples of mode-2 IWs. As these mode-2 IWs can persist for more than a day 20, their presence might be observable in the Global Open HYCOM model simulations. It is worth mentioning here that there are not sufficient in situ observations in this region. The daily Global Open HYCOM model simulations of sea surface temperature, U–current, V-current, and SSH data on 11 Feb 2009 showed significant variations, indicating the occurrence of IW activity, as shown in Supplementary Figs. 2 and 3. SAR observation of IWs provides information about their wavelengths, propagation direction, phase speed, polarity, and amplitudes with the aid of in situ data (amplitude computation is not carried out in this study). As previously reported, IWs are generally elevated in this study and are usually generated only when the top layer (H1) is thicker than the bottom layer (H2). However, IWs of depression were also observed, where the top layer (H1) was thinner than the bottom layer (H2). This conversely reveals that IWs provide information about the interior of the ocean, such as stratification/thermocline depth25. The two-layered Kortweg-de Vries (KDV) equation governing these waves is generally used to study their characteristics26,27,28,29,30,25, 31, 10 and is given as
$$\frac{\partial {\eta }}{\partial \text{t}}+{\text{C}}_{0}\frac{\partial {\eta }}{\partial \text{x}}+{\alpha }{\eta }\frac{\partial {\eta }}{\partial \text{x}}+{\beta }\frac{{\partial }^{3}{\eta }}{\partial {\text{x}}^{3}}=0$$
1
The nonlinear and dispersion coefficients are
$${\alpha }=\frac{3}{2}\frac{{\text{H}}_{1}-{\text{H}}_{2}}{{\text{H}}_{1}{\text{H}}_{2}}{\text{c}}_{0}$$
$${\beta }=\frac{1}{6}{\text{H}}_{1}{\text{H}}_{2}{\text{C}}_{0}$$
$${\text{C}}_{0}={\left[{\Delta }{\rho }\text{g}{\text{H}}_{1}{\text{H}}_{2}∕{\rho }\left({\text{H}}_{1}+{\text{H}}_{2}\right)\right]}^{\frac{1}{2}}$$
where η is the interfacial displacement, H1 and H2 are the top and bottom layers of the ocean, respectively, ρ is the density of water, g is the gravity constant, and ∆ρ is the density difference between the two layers.
Generally, the bottom layer (H2) is thicker than the top bottom layer (H1). Then, the displacement becomes
$$\eta \left(x,t\right)=-A sec {h}^{2}\left[\frac{2\left(x-{C}_{t}\right)}{\lambda }\right]$$
2
where A is the amplitude, which represents the soliton of the depression. Its phase speed (C) and wavelength \(\left(\lambda \right)\) are expressed as
$$C={c}_{0}\left(1-\frac{A\alpha }{3{\text{c}}_{0}}\right) ; \lambda ={4\left(\frac{-3\beta }{\alpha A}\right)}^{\frac{1}{2}}$$
The wavelengths computed from the present study vary from 0.17 to 4.8 km. They generally propagate toward the coast. The phase speed ranges from 0.04 to 0.2 m/s. The computed IW phase speed and wavelengths are as shown in Table 2. Further detailed research using more data is required to understand the morphology of these IWs.