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Submesoscale motions and their seasonality in the northern Bay of Bengal
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Lanman Li1, Xuhua Cheng1, 2, *, Zhiyou Jing3, Haijin Cao1, Tao Feng1, 2
Acta Oceanologica Sinica | 2022, 41(4) : 1 - 13
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Acta Oceanologica Sinica | 2022, 41(4): 1-13
• Physical Oceanography, Marine Meteorology and Marine Physics •
Submesoscale motions and their seasonality in the northern Bay of Bengal
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Lanman Li1, Xuhua Cheng1, 2, *, Zhiyou Jing3, Haijin Cao1, Tao Feng1, 2
Affiliations
  • 1 College of Oceanography, Hohai University, Nanjing 210098, China
  • 2 Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519080, China
  • 3 State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou 510301, China
Published: 2022-04-25 doi: 10.1007/s13131-021/1847-6
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The unbalanced submesoscale motions and their seasonality in the northern Bay of Bengal (BoB) are investigated using outputs of the high resolution regional oceanic modeling system. Submesoscale motions in the forms of filaments and eddies are present in the upper mixed layer during the whole annual cycle. Submesoscale motions show an obvious seasonality, in which they are active during the winter and spring but weak during the summer and fall. Their seasonality is associated with the mixed layer instability that depends on the mixed layer depth (MLD). During the winter, the MLD provides a much greater reservoir of the available potential energy, which promotes mixed layer instability to develop active submesoscale motions. The variations of MLD are likely modulated by the larger scale motions and the influxes of freshwater. Further investigations imply that the MLD and the stratified barrier layer are combined to determine the vertical structure of the submesoscale motions. The shallow MLD and strong stratification below during the summer and fall seem to prevent the downward extension of submesoscale motions. But in spring when the weak stratification exists, the penetration depth exceeds the base of the barrier layer.

submesoscale motions  /  seasonality  /  northern BoB  /  mixed layer instability  /  stratification
Lanman Li, Xuhua Cheng, Zhiyou Jing, Haijin Cao, Tao Feng. Submesoscale motions and their seasonality in the northern Bay of Bengal[J]. Acta Oceanologica Sinica, 2022 , 41 (4) : 1 -13 . DOI: 10.1007/s13131-021/1847-6
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1 Introduction
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The Bay of Bengal (BoB) is a semiclosed bay of the northeastern Indian Ocean, where the hydrologic and dynamic characteristics are remarkably different from those of other regions. The BoB is forced by the semiannual reversal monsoon that is southwest from June to September and northeast from November to January (Schott et al., 2009). The basin is dominated by a strong cyclonic circulation during the northeast monsoon and by an anticyclonic circulation during the southwest monsoon (Eigenheer and Quadfasel, 2000; Somayajulu et al., 2003; Qiu et al., 2007). The enormous amount of precipitation caused by the strong and wet southwesterly wind, combined with runoff discharged mainly by the Ganges-Brahmaputra and the Irrawaddy River, directly discharge abundant freshwater into the bay during the summer and fall. This creates shallow freshwater pools and strong salinity stratification near the surface (Behara and Vinayachandran, 2016; Rahaman et al., 2014). Stratification usually leads to the defining vertical structure of this region: a shallow mixed layer, thick barrier layer (BL), and temperature inversion layer (TIL) (Dandapat et al., 2020; Han et al., 2001; Howden and Murtugudde, 2001; Thadathil et al., 2016). TIL that is fully formed during the winter (Thadathil et al., 2016) maintains the warm surface temperature by vertical mixing (Sengupta et al., 2008; Thadathil et al., 2016). BL starts to develop during the fall and is thickest during the winter (Ma et al., 2020; Thadathil et al., 2007; Qiu et al., 2012). Strong stratification prevents the exchange of cool interior water and warm upper water, consequently maintaining warm surface temperatures that intensify the tropical cyclones (Balaguru et al., 2012; Neetu et al., 2012).
The northern BoB features abundant multiscale dynamical processes. The results from the satellite observations and numerical models reveal that mesoscale eddies are rich in the northern bay, and their features and variability have been substantially studied (Babu et al., 1991; Chen et al., 2012; Cheng et al., 2013, 2018). The northern coast of the BoB is influenced by the coastally trapped Kelvin waves that propagate from the equator (Vialard et al., 2009; Cheng et al., 2013; Suresh et al., 2013). Tides in the area are ample, with amplitudes typically greater than 2 m, and display the most variable seasonality in the global ocean with typical amplitudes ranging from 10 cm to 20 cm (Tazkia et al., 2017). The interaction between tides and topography easily produces internal waves that are often observed during nonmonsoons (Jithin et al., 2020; Phaniharam et al., 2020). As the spatial resolution of satellite observations increases, submesoscale motions in this region are noted. Based on high-resolution (~5 km) observations from the moderate-resolution imaging spectroradiometer (MODIS), the sea surface temperature reveals that fine temperature filaments and fronts at typical scales of O (10) km are ubiquitous in the northern bay (Fig. 1) and are richer during the winter (Fig. 1b).
Submesoscale processes with a horizontal scale of O (1–10) km and a temporal scale of O (1) day provide a conduit for the energy cascade between multiscale (Capet et al., 2008d; McWilliam, 2016; Molemaker et al., 2010). Their strong vertical motions are vital for the upper ocean heat budget and biogeochemical characteristics (Klein and Lapeyre, 2009; Mahadevan, 2016; Su et al., 2018). In the open upper ocean, frontogenesis and mixed layer instability are considered as the dominant generation mechanisms for submesoscale processes (Callies et al., 2015; Mcwilliams, 2016; Thomas et al., 2008).
The seasonality of submesoscale motions exhibits geographical dependency (Lin et al., 2020; Zhang et al., 2020; Dong and Zhong, 2018; Dong et al., 2020; Brannigan et al., 2015; Mensa et al., 2013; Wang et al., 2018) associated with distinct background dynamical features. Based on observations, previous studies have revealed that salinity-controlled fronts with lateral scales of O (1–10) km are ubiquitous in the upper northern BoB (Ramachandran et al., 2018; Sengupta et al., 2016). Strong submesoscale fronts in this region are associated with frontal instabilities, subsequently effecting the vertical and horizontal variability of properties, such as stratification, potential vorticity, temperature, and salinity (Pham and Sarkar, 2019; Ramachandran and Tandon, 2020; Sarkar et al., 2016). The submesoscale dynamics in the Indian Ocean has received much fewer attentions compared with other oceans. Strong horizontal density gradient and stratification in the northern BoB provide a favorable condition for the occurrence of submesoscale processes. Due to the lack of observations and model simulations, it is still a great challenge to systematically investigate the submesoscale processes in the BoB.
This study provides a basic description of the seasonal features of submesoscale motions in the northern BoB and their corresponding mechanisms based on the regional oceanic model system (ROMS) with high spatial resolution. Under the presence of stratification, their effect on the characteristics of submesoscale motions is interesting. This article is constructed as follows: Section 2 describes the configuration of ROMS; Section 3 presents the seasonal variations in submesoscale motions; Section 4 discusses the potential mechanisms that are probably responsible for the seasonality; Section 5 explores the relationship between stratification and submesoscale motions; Conclusions and discussion follow in Section 6.
2 Data and methods
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2.1 Data
2.1.1 Observation data
The vertical temperature and salinity data provided by the daily Research Moored Array for African-Asian-Australian Monsoon Analysis and Prediction (RAMA) buoy and the gridded monthly reconstructed Argo products are compared with the ROMS simulation in Section 5.1. The RAMA buoy located at 15°N, 90°E for a period from January 2009 to February 2010 is chosen. The Argo products range from 2002 to 2015, with a spatial resolution of 0.5°×0.5°. Vertically, the temperature and salinity for two datasets are available at discrete depth intervals. They have been interpolated by 1 m interval above 100 m.
2.1.2 Model setup
The model that was applied to explore submesoscale motions in this study was ROMS (Shchepetkin and McWilliams, 2005). To capture the submesoscale motions, ROMS used one-way nesting to increase the resolution from parent grid simulation. The parent zone covers the North Indian Ocean and the northwestern Pacific Ocean (Fig. 2a) with a lower horizontal resolution (LR) of ~7.5 km, while the child zone covers the BoB (Fig. 2b) with a higher resolution (HR) of ~1.5 km. The vertical resolution is 60 levels, which includes 25 layers at the upper 200 m. The vertical mixing scheme for momentum and tracers is based on the K-profile parameterization (Large et al., 1994). The bathymetry is derived from the GEBCO_08 (General Bathymetric Chart of the Oceans) dataset.
The parent simulation was forced by the daily mean climatology wind stress from the Quick Scatterometer (QuikSCAT). The heat and freshwater fluxes were provided by the monthly climatology of the International Comprehensive Ocean-Atmosphere Data Set (ICOADS) (Woodruff et al., 2011). The initial and lateral boundary conditions were provided by the monthly averaged climatology of Simple Ocean Data Assimilation (SODA) reanalysis dataset (Carton and Giese, 2008). The parent configuration was spun up for 20 years, then run for an additional 14 months to provide the boundary condition for child simulation. Then both simulations were performed for 14 months and saved every 3 days from January 2 to February 29 of the next year. Both simulated outputs are corresponding to the climatological field rather than the realistic period. This method adopting the climatological forcing has been successfully applied in the simulating submesoscale motions (Gula et al., 2014; Jing et al., 2021; Cao et al., 2021).
Submesoscale motions are highly correlated with the salinity fronts in this region. The monthly-averaged salinity at 5 m depth is compared between ROMS HR (whole year) and Argo (2002–2015) in Figs 3a and b, respectively. Both results show that low salinity water rapidly develops during the summer monsoon. Generally, the monthly evolution of salinity in ROMS is in agreement with the Argo results, illustrating the ability of the model simulation. Note that the simulated salinity is fresher than the Argo result, which may be caused by the differences between initial salinity in the model and Argo salinity. Since we focused on the seasonal variations, this salinity difference has less impact on the result of our study.
2.2 Methods
2.2.1 Flow decomposition
Ocean flows contain multiscale processes that can disturb the analysis of the submesoscale variations. For convenience, the flow field is divided into two parts: large-mesoscale $ \bar{{U}} $ and submesoscale $ {U}' $. A Reynolds decomposition is employed in this study. The submesoscale component $ {U}' $ is obtained by high-pass filtering in spatial domain, with a spectral cutoff on the Fourier transform spectrum to obtain an approximate Reynolds average. The remaining velocity is defined as $ \bar{{U}} $. The partition scales are selected as 15 km based on the scale of the disturbance under the baroclinic instability $ L=NH/f $, where N denotes the buoyancy frequency, $ f $ is the Coriolis parameter, and $ {H} $ denotes the mixed layer depth (MLD). The MLD is computed by the depth at which the density is larger than the surface of 0.2 kg/m3 (Narvekar and Kumar, 2006).
To examine whether 15 km is the typical decomposition scale, a spectral method that counts the ratio of the contributions of divergent and rotational to kinetic energy is used (Torres et al., 2018). When the ratio is close to 0.1, the contribution of the divergent part is not negligible, implying the role of submesoscale motions. The spectral method is provided in supplementary materials. The estimated scale is 16 km, which is close to 15 km. As the minimum scale of the model resolving is 5 times of the horizontal resolution (Lévy et al., 2012), the submesoscale can be resolved in the high-resolution child configuration.
2.2.2 Definition of the vertical structure and stratification
The layer between the mixed layer and isothermal layer is BL (Vinayachandran et al., 2002). The barrier layer thickness (BLT) is defined as the depth difference between the MLD and the isothermal layer depth (ILD), where BLT=ILD−MLD. The ILD is the depth at which the temperature decreases by 0.6°C from the surface (Ma et al., 2020). In this study, the TIL is defined at which the temperature is warmer than that at the surface by 0.1°C (Girishkumar et al., 2013). The BL usually exists simultaneously with the TIL during winter in the northern BoB. Both the BL and TIL are sandwiched between the surface layer and subsurface colder layer.
The density in the mixed layer is relatively uniform. The isothermal layer, as the definition implies, is a layer with uniform temperature. When vertical salinity stratification is absent and the density distribution is entirely controlled by the temperature, the thermocline layer and the mixed layer coincide. Once the halocline shoal to a depth smaller than the thermocline, a BL forms. The BL and TIL are usually associated with high stratification. The squared buoyancy frequency $ {{N}}^{2}=-{g}\partial \rho /\partial z $, indicating the density stratification, is contributed by two components: salinity ${{N}}_{{S}}^{2}=-{{g}}\beta \partial S/\partial z$ and temperature ${{N}}_{{T}}^{2}={g}\mathrm{\alpha }\partial {T}/\partial {z}$, where $ \rho $ is the density, g is the gravity acceleration, S is the salinity, T is the temperature, $ \ \beta $ is the haline contraction coefficient and $ \mathrm{\alpha } $ is the thermal expansion coefficient (Maes, 2008).
3 Main characteristics of submesoscale motions
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3.1 Horizontal distribution of submesoscale motions
Submesoscale motions are characterized by O (1) Rossby number (${Ro}=\zeta /f)$, which means their relative vorticity ($ {\zeta }={v}_{x}-{u}_{y} $) is roughly equivalent to the planetary vorticity f (Thomas et al., 2008). Snapshots of the Ro in four seasons in both HR and LR are shown in Fig. 4. The large Ro features that manifest as filaments and eddies are conspicuous in the maps for different times, indicating that submesoscales are widespread in the northern BoB. Compared with HR (Figs 4a, b), submesoscale motions are greatly underestimated in LR (Figs 4e, f), and the mesoscale processes occupy the domain. Complex patterns with high Ro occur in most of the time except in January (Fig. 4a). High Ro are conspicuous in the region where the water depth is deeper than 50 m (called the offshore region in the following description). The time series of Ro averaged over the whole region (gray line) and the offshore region (blue line) are shown in Fig. 5a. A good correspondence between the two series is noted with a correlation coefficient of 0.97, and their difference is small. The following analyses mainly focus on the offshore region.
Snapshots of Ro suggest that submesoscale motions have a significant variability throughout the year (Figs 4a–d). Submesoscale features are most active during the winter, mainly in the forms of filaments and eddies (Fig. 4a). Then, they gradually weaken from spring to fall. Compared to the winter monsoon (winter and spring), submesoscale motions are relatively quiescent during the summer monsoon (summer and fall). In the northern bay, a clear seasonal cycle of Ro is observed, with a peak in January and a trough in August, indirectly reflecting the variability of submesoscale motions.
3.2 Vertical structure of submesoscale motions
The typical features of submesoscale motions are the high Ro and the strong vertical velocity ($ {w} $). The temporal and vertical distribution characteristics of the regionally-averaged Ro and $ {w} $ are shown in Fig. 5. High values of Ro occur at the upper mixed layer and can penetrate under the MLD. The mean value of |Ro| is 0.17 at the surface and only 0.07 at 200 m depth (Fig. 5a). The time series of regionally-averaged MLD has a good correspondence with $ {\zeta } $ and $ {w} $, indicating that the variability of submesoscale motions is probably related to the mixed layer processes (Figs 5b, c). The vertical structures of Ro and $ {w} $ also show obvious seasonal variations (Figs 5b, c). Strong vertical exchanges induced by submesoscale motions are the most active at approximately 25 m during the winter monsoon (Fig. 5c), especially in the winter. For the boundary condition that near surface $ {w}\approx 0 $, the seasonality of $ {w} $ in the upper 10 m is insignificant. It should be noted that the LR simulation mostly indicates the mesoscale processes (not shown), which tend to have similar seasonality with submesoscale processes, seemingly suggesting that the submesoscale processes are closely related to the local mesoscale processes. The annual cycle of submesoscale motions in this region is distinguished from that in the northern Gulf of Mexico, where a secondary maximum for submesoscale motions emerges during summer (Luo et al., 2016) and is similar to the Gulf Stream region (Callies et al., 2015) and the Kuroshio Current region (Mensa et al., 2013; Qiu et al., 2014). It is noted that the mean |w| is still strong below 100 m from June to February, which is probably induced by the interaction between the current and topography in the northern boundary (Molemaker et al., 2015).
Skewness (Sk) in the distribution of normalized relative vorticity (Ro) is one of the features of submesoscale flows (Buckingham et al., 2016). The probability density function (PDF) and skewness of Ro is one metric for analyzing submesoscale motions. The PDF distributions of Ro at 5 m for both simulations for four seasons are represented in Fig. 6. In HR, the positive vorticity overwhelms negative vorticity for all seasons, indicated by positive skewness. The prevailing positive vorticity has been noted by previous studies (Capet et al., 2008b; Lin et al., 2020; Qiu et al., 2014) and interpreted as being due to submesoscale instability (centrifugal instability). When a large anticyclonic vorticity is present ($ {\zeta } < -{f} $), centrifugal instability arises and suppresses the growth of large negative vorticity motion but has no effect on positive vorticity motion. The probability of positive vorticity in HR continuously decrease from spring to fall, while negative vorticity with the maximum values during the fall (Fig. 6a). The skewness has a maximum of 1.29 in spring, then decreases in winter, and reaches a much lower value in the summer and fall. The extraordinarily large negative vorticity is probably related to submesoscale processes that are induced by the interaction between the southwestward flow and topography. For LR, the maximum positive vorticity is approximately a second of those in HR, showing a rapid decrease in vorticity in the mesoscale resolving simulation. The corresponding skewness is low in LR (Fig. 6b), and the PDF of vorticity becomes more symmetric.
4 Interpretation of the seasonality of submesoscale motions
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The above results show that submesoscale motions are mostly present during the winter and spring, and in the upper layer. The potential generating mechanisms are investigated in this section.
4.1 Frontogenesis
In the upper layer, frontogenesis is an important mechanism for the generation of submesoscale fronts. Frontogenesis is that larger-scale strain intensifies the cross-front density gradients (Hoskins and Bretherton, 1972). Here, strain is defined as ${S}_{t}=\sqrt{{\left(\partial u/\partial x-\partial v/\partial y\right)}^{2}{+\left(\partial u/\partial x+\partial v/\partial x\right)}^{2}}$, where u and v are zonal and meridional velocity, respectively. The strain consists of along-front stretching and the cross-front shear (Mahadevan and Tandon, 2006). As horizontal density gradient is enhanced, the vertical secondary circulation is produced, which suppresses the sharpen of the front and tends to restore the geostrophic balance by tilting isopycnals toward horizontal (Capet et al., 2008c). The evolution rate of the front induced by the strain can be depicted by the frontogenesis rate $ {F} $, $F=\dfrac{{\rm{D}}\left|\nabla _{h}\rho \right|^2}{{\rm{D}}t}= -\left({{u}}_x \rho _x+{{v}}_x \rho _y\right){{\rho }}_{x}- \left({{u}}_{y}{{\rho }}_{x}+{{v}}_{y}{{\rho }}_{y}\right)\rho _y$, where $ {\left|{\nabla }_{h}\rho \right|}^{2} $ denotes the intensity of the front (Capet et al., 2008c; Hoskins, 1982; Hoskins and Bretherton, 1972). Above, $ {u} $ and $ {v} $ denote the zonal and meridional velocity, $ {\rho } $ is the density, and the subscript is the derivative. Strong strain rates and active horizontal density gradients are conducive to the generation of submesoscale motions (Dong and Zhong, 2018; Gula et al., 2014; McWilliams, 2016).
Figure 7a shows the F varied with time and depth. As the resolution becomes finer, the regionally-averaged magnitude of F increases (Figs 7a, b). Positive F almost appears in the upper mixed layer, implying that frontogenesis mainly occurs in the upper ocean, similar to findings of other studies (Brannigan et al., 2015; McWilliams, 2017). High values for F are trapped in the shallow mixed layer during the late summer and fall. For the period with the deep mixed layer (spring and winter), F is in a weak state. The magnitude of frontogenesis in the late summer and fall is an order of magnitude higher than the rest of the time is novel.
The time series of $ \left|{\nabla }_{h}{\rho }\right| $ and St at different depths are shown in Figs 7c and d, respectively. Both St and $ \left|{\nabla }_{h}{\rho }\right| $ are stronger at the 5 m depth where high Ro frequently appears. The temporal variations in F show a good correlation with horizontal density gradients (r=0.82), and is insignificantly correlated with the strain rate (r=−0.26). These results indicate that density gradients are the dominant factors for frontogenesis and that the strain rate has a relatively weak influence. The increasing horizontal density gradients in summer and fall, which may be created by the influxes of freshwater (Shetye, 1993), feed the evolution of frontogenesis and lead to the much higher F (Luo et al., 2016). The correlation between F and |Ro| averaged with the MLD is only −0.39. Frontogenesis seems not to be the controlling factor for the submesoscale motions during the whole year. However, frontogenesis is likely to play an important role during summer and fall.
4.2 Mixed layer instabilities
The mixed layer is not entirely homogeneous but has numerous horizontal density gradients overlying the strongly stratified layer (Boccaletti et al., 2007). Baroclinic instability that occurs in the mixed layer is called MLIs and can be measured by the conversion rate of available potential energy (APE) to submesoscale eddy kinetic energy (EKE), that is PK. The PK is defined as the vertical buoyancy flux ($w'b'$) averaged over the mixed layer, which is calculated as $\mathrm{P}\mathrm{K}=\dfrac{\int^{-{\rm{MLD}}}_{0} w{'}b{'}{\rm{d}}z}{{\rm{MLD}}}$ (Boccaletti et al., 2007), where $ {w} $ is the vertical velocity, $ {b} $ is the buoyancy (${b}=-{g}{\rho }/{{\rho }}_{0}$, $ {g} $ is the gravitational acceleration, $ {{\rho }}_{0} $ is the reference density defined as the density averaged over the region and the mixed layer), and the prime indicates the submesoscale component. The scaling of $ {w}'{b}' $ in the upper boundary layer appears to follow a relationship ${\rm{PK}}={\langle w'b'\rangle}_{xyz}\propto {{\langle\left|\nabla {\bar{b}}\right|\rangle}^{2}}_{xyz}\cdot {\langle{\rm{MLD}\rangle}^{2}}_{xy}$ (Fox-Kemper and Ferrari, 2008; Fox-Kemper et al., 2008; Capet et al., 2008a), where ${ \langle \;\;\rangle}_{xyz}$indicates the volume averaged over the domain and MLD. Conceptually, the scaling assumes that horizontal buoyancy gradients and MLD are two main factors influencing MLIs.
As shown in Fig. 8a, PK is always positive, implying the transition from APE to EKE. The high value of PK is mainly concentrated in the mixed layer and becomes small beneath the mixed layer (not shown). It is reasonable to infer that MLIs occur mainly in the mixed layer. Within the mixed layer, PK gradually decreases from the spring to fall, then sharply increases in the late fall, reaching a maximum in winter. The correlation coefficient between the variations of PK and Ro is 0.68. PK in spring are much smaller than that in winter, while submesoscales are as strong as winter. The larger PK in winter is possible related to the scale of the fronts in the background (Fig. S2). The larger scale fronts prevail in spring and turn smaller fronts in winter. These strong fronts combined with deep mixed layer contribute to the generation of submesoscale. The small-scale fronts in winter significantly enhance the $ {b}' $, resulting in a larger PK. There may be other mechanisms for the occurrence of submesoscale processes in spring, which need further exploration with a comprehensive model.
PK scaling has been verified successfully by Capet et al. (2008a) in the Argentinian shelf and by Mensa et al. (2013) in the Gulf Stream. To test the parameterization scheme, ${{\langle\left|\nabla {\bar b}\right|\rangle}^{2}}_{xyz}\cdot {{\langle{\rm{MLD}}\rangle}^{2}}_{xy}$ is shown by the red line in Fig. 8a. Overall, the scaling is appropriate in this region. The time series of ${{\langle\left|\nabla {\bar b}\right|\rangle}^{2}}_{xyz}$ and ${{\langle{\rm{MLD}}\rangle}^{2}}_{xy}$ are plotted in Fig. 8b. MLD obviously displays an opposite seasonality with respect to horizontal density gradients. MLD is deep in the winter and spring, consistent with the strong submesoscale motions. A significant enhancement of buoyancy gradients can be observed during the summer and fall, which does not have a significant influence on the formation of MLIs. The results illustrate that the MLD is potentially the main controlling factor in submesoscale motions formation.
The seasonal variations in MLD can be partially linked to vertical stratification in the ocean. The vertical sections of density and salinity along 19°N in spring, winter, and fall are shown in Fig. 9. In spring and winter, the outcropping isopycnals accompany deep MLD, which provide a favorable condition to store APE that feeds the development of submesoscale motions (Figs 9a, b). In contrast, the MLD is shallowest in fall, when the stratification is the strongest and the upper thin mixed layer is isolated from the interior (Fig. 9c). Strong stratification is likely to limit the generation of submesoscale motions by inhibiting the formation of vertical recirculation along the fronts.
When the averaged surface salinity is compared with the MLD and horizontal buoyancy gradients, we find that these three-time series are better correlated, with correlation coefficients reaching 0.96 and −0.91, respectively (Fig. 10a). The salinity gradually decreases from June to October. As reported by Akhil et al. (2014), the freshest water appears in the northern BoB especially during and post the summer monsoon. The seasonal cycle of salinity is highly correlated with the influxes of the runoff and precipitation, which further produce strong salinity stratification and a shallow MLD (Narvekar and Kumar, 2006; Vinayachandran et al., 2002; Rao and Sivakumar, 2003). After the injection of freshwater encounters salty seawater, enormous salinity fronts (high buoyancy gradients) are formed. The influxes of freshwater in this region are a critical factor influencing the variations in MLD and buoyancy gradients, especially in the summer and fall. In addition, the vertical and annual cycles of the eddy kinetic energy (${\rm{EKE}}=1/2({\bar{u}}^{2}+{\bar{v}}^{2})$) are shown in Fig. 10b. Active mesoscale processes may be another factor supporting the submesoscale motions generated during the winter monsoon, and probably indirectly through modulating the deepening of the mixed layer. The periphery of mesoscale eddy is usually accompanying the active submesoscale motions (Yang et al., 2017).
5 Relationship between stratification and submesoscale motions
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The above descriptions imply that MLD is an important factor for the spatial distribution of submesoscale motions. The deeper the MLD is, the submesoscale motions can penetrate deeper. Previous studies suggested that thick BL and a TIL exist in the northern BoB in winter (Ma et al., 2020; Thadathil et al., 2007, 2016), which tends to shrink the thickness of the MLD. BL and TIL are a highly stratified layers. Their possible influence on submesoscale motions in the northern BoB has been less studied.
5.1 The BL and TIL in the model
Time-depth sections of temperature, salinity, MLD, ILD, and TIL in the northern BoB from the model and observations are displayed in Fig. 11. The BL exists persistently for the whole year but obviously thickens during the fall and then fully develops during the winter. The reproduced BL in ROMS is basically in concert with the observations. Notably, the annual cycle ILD in ROMS is weaker than the observations. The probable reasons may be the climatological daily atmospheric forcing used in the model. During the fall and winter, temperature inversion is evident, which weakens the stratification in the upper ocean and potentially has impacts on the submesoscale motions.
The annual means of BLT and TIL are shown in Fig. 12, and they display a spatial difference. The thickest BL and TIL occur in the northern bay and gradually weaken to the central bay. Their thickness in the northern bay is approximately 3 times larger than that in the central bay. The submesoscale processes in two sub-regions, the northern region (NR) and the central region (CR), are further analyzed in the next section. The distribution of the annual mean BL in the model is consistent with that in Thadathil et al. (2007). The freshwater from runoff and precipitation in the upper layer significantly influence the forming of BL and TIL (Vinayachandran et al., 2002; Thadathil et al., 2016). They create a thin freshwater surface layer and a more strongly stratified interior below, which are favorable for the development of BLT and TIL. As far away from the coast, the inflow of runoff decreases, their effect on the formation of BLT and TIL weaken.
5.2 Potential impact of BL and TIL on the submesoscale motions
The temporal-vertical evolution of Ro and $ {w} $ in NR and CR are shown in Fig. 13, superimposed with the MLD, ILD, and TIL. Although submesoscale motions are mainly confined in the upper mixed layer, high values of Ro also appear under the mixed layer (Figs 13a, b). During the summer monsoon, submesoscale motions are relatively weaker and concentrate within the mixed layer in both NR and CR. However, in the winter and spring, they can penetrate far beneath the base of the mixed layer and into the BL, even into the thermocline layer. For example, the active submesoscale motions extend to 65 m in March in NR, when the MLD is only 30 m. In CR, high Ro signals reach 50 m, which exceeds the MLD of approximately 30 m in February. Strong submesoscale motions can even reach beneath the isothermal layer, such as over NR and CR in May. The vertical motions obviously strengthen when the mixed layer is deeper (Figs 13c, d). The deeper MLD seems to provide a favorable condition for horizontally tilting of outcropping isopycnals and subsequently inducing strong vertical exchange.
The depth-time evolution of N2, $N_S^2$, and $N_T^2$ averaged over NR and CR is shown in Fig. 14. As expected, the BL and TIL are high stratification layers (Figs 14a, b). The upper stratification is dominated by salinity rather than temperature (Figs 14c, d). The blue contours in Fig. 14 are the regionally-averaged Ro of 0.18. The 0.18 of Ro represents the discrimination between the strong and weak submesoscale motions.
The vertical distribution of the submesoscale motions seems to correlate with MLD and the stratification below it. Deep MLD favors active submesoscale motions generating, and strong stratification inhibits the deepen of the active submesoscale motion. In NR (Fig. 14a), when the MLD is shallowest and the stratification is strongest (August–October), submesoscale motions are the weakest and strictly trapped in the shallow mixed layer. During the late fall, the strong salinity stratification goes deeper and becomes thicker, but the presence of temperature inversion partially counteracts the salinity stratification (Fig. 14e). Submesoscale motions are mostly restricted in the mixed layer due to the still relatively strong stratification below it. When comes to winter, deep mixed layer and thick BL present. Constrain by the stratification in the thick BL, the strong submesoscale motions only extend to the interior of the BL and TIL. Differently, in the spring, the ILD begins to shoal and the stratified layer turns weak and thin, which is probably due to surface heating and the vertical mixing (Thadathil et al., 2007). Without the constraint, strong submesoscale signals penetrate to larger depths and even pass through the BL.
Similarly, the high Ro processes in CR have a corresponding relationship to the vertical stratification. The columns of high submesoscale motions are potentially limited by the stratification contained in the BL and TIL during the winter monsoon. The maximum extended depth is at the interior of the BL. When the BL is thinner and has weak stratification in spring, the depth of strong submesoscale motions even stretches into the thermocline. When compared with NR, the BL is thinner and the stratification is weaker in CR, and the active submesoscale processes can extend to further distance below the mixed layer.
6 Conclusions and discussion
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Based on high resolution numerical simulation data from ROMS, the features of submesoscale motions in the northern BoB are characterized in this article. Compared with the HR results, submesoscale motions in LR are much weaker. The northern BoB experiences obvious seasonality in terms of the dynamical characteristics of submesoscale motions, with stronger signals in the winter and spring but weaker in the summer and fall. Diagnostic analysis reveals the occurrence of submesoscale motions mainly trapped in the mixed layer, but they can penetrate under the base of the mixed layer. The MLIs appear to play a more important role than frontogenesis in the formation of the submesoscale in this region. The conspicuous seasonality of submesoscale motions is tightly associated with the variations in MLD, which are probably modulated by the influxes of freshwater as well as large and mesoscale motions. Further analysis implies that the mixed layer and the stratification below affect the vertical distribution of submesoscale motions. When the vertical salinity gradients over the BL are weakest, high Ro motions can reach depths far beyond the BL. However, the thick and high stratification BL seems to act as a buffer in which the depth of submesoscale motions is limited.
In this study, we qualitatively study the relationship of the two generating mechanisms and submesoscale motions, respectively. Actually, frontogenesis and MLIs cannot separate from each other, they are tightly related (McWilliams, 2016). The pre-exist weak fronts are sharply intensified by frontogenesis, and accompanied by the MLIs. Our findings display the potential influence of frontogenesis and MLIs on submesoscale motions. Besides, symmetry instability, buoyancy forcing, topography and tides are contributing to the formation of submesoscale motions. Submesoscale characteristics and the mechanisms need further explored with more dedicated numerical simulation outputs with finer spatial resolution and higher frequency temporal interval.
Acknowledgements
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The RAMA buoy data was obtained from https://www.pmel.noaa.gov/gtmba/pmel-theme/indian-ocean-rama. The sea surface height data is distributed at AVISO and can be downloaded from http://marine.copernicus.eu/. The high-resolution SST from MODIS is available at https://oceancolor.gsfc.nasa.gov/. The reconstructed Argo products were obtained from http://www.umr-lops.fr/. The QuikSCAT wind stress data is available at http://www.ifremer.fr/opendap/cerdap1/cersat/wind/l4/quikscat/daily/. The freshwater and hear flux data were produced by the Asia-Pacific Data-Research Center (http://apdrc.soest.hawaii.edu/dods/public_data/iCOADS/). The SODA reanalysis dataset was provided by http://apdrc.soest.hawaii.edu/dods/public_data/SODA/. The GEBCO topography dataset was produced by the British Oceanographic Date Centre (http://data.nodc.noaa.gov/).
Funding
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  • The National Key R&D Program of China under contract No. 2018YFA0605702; the National Natural Science Foundation of China under contract Nos 41876002 and 41776002.
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doi: 10.1007/s13131-021/1847-6
  • Receive Date：2021-02-09
  • Online Date：2025-11-21
  • Published：2022-04-25
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  • Received：2021-02-09
  • Accepted：2021-05-29
Funding
The National Key R&D Program of China under contract No. 2018YFA0605702; the National Natural Science Foundation of China under contract Nos 41876002 and 41776002.
Affiliations
    1 College of Oceanography, Hohai University, Nanjing 210098, China
    2 Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519080, China
    3 State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou 510301, China

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表12种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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