Eddy induced trapping and homogenization of freshwater in the Bay of Bengal
Nihar Paul, Jai Sukhatme, Debasis Sengupta, Bishakdatta Gayen
EEddy induced trapping and homogenization of freshwater in the Bay of Bengal
Nihar Paul , Jai Sukhatme , , Debasis Sengupta , and Bishakdatta Gayen , Centre for Atmospheric and Oceanic Sciences, Indian Institute of Science, Bangalore - 560012, India. Divecha Centre for Climate Change, Indian Institute of Science, Bangalore - 560012, India. and Mechanical Engineering Department, University of Melbourne, Australia.
Freshwater from rivers influences Indian summer monsoon rainfall and regional tropical cyclones by shallowingthe upper layer and warming the subsurface ocean in the Bay of Bengal. Here, we use in situ and satellite datawith reanalysis products to showcase how river water can experience a significant increase in salinity on sub-seasonal timescales. This involves the trapping and homogenization of freshwater by a cyclonic eddy in the Bay.Specifically, in October 2015, river water is shown to enter a particularly long-lived eddy along with its attractingmanifolds within a period of two weeks. The eddy itself is quite unique in that it lasted for 16 months in theBay where average lifespans are of the order of 2-3 months. This low salinity water results in the formation of ahighly stratified surface layer. In fact, when freshest, the eddy has the highest sea-level anomalies, spins fastest,and supports strong lateral gradients in salinity. Subsequently, observations reveal progressive homogenizationof salinity and relaxation of sea-level anomalies and salinity gradients within a month. In particular, salty waterspirals in, and freshwater is pulled out across the eddy boundary. Lagrangian experiments elucidate this process,whereby horizontal chaotic mixing provides a mechanism for the rapid increase in surface salinity on the orderof timescale of a month. This pathway is distinct from vertical mixing and likely to be important in the eddy-richBay of Bengal.
I. INTRODUCTION
The Bay of Bengal (BoB) is a semi-enclosed basin lyingbetween 6-22 ◦ N, 80-100 ◦ E, connected to the equatorial In-dian Ocean to the south. The Ganga-Brahmaputra-Meghna(GBM), Irrawaddy, Godavari, and Mahanadi river systems arethe major sources of fresh water to the BoB [37]. The climato-logical annual mean discharge from the GBM and Irrawaddy,the largest of these rivers, is approximately . × m s − and . × m s − ; about 70% of discharge comes in thesummer monsoon season June-September [6, 13, 37]. Thefreshwater from rivers is stirred into the interior of the Bay ofBengal by large-scale circulation, mesoscale eddies, and di-rectly wind-driven flow [53]. In the open ocean, river waterforms a shallow, low-salinity layer with strong density strat-ification at its base [48]. Apart from a well-defined seasonalcycle [43], lateral advection gives rise to intraseasonal vari-ability in near-surface salinity, as seen in Argo float and satel-lite data [23, 38, 62]. Freshwater in the Bay of Bengal hasprofound impacts on regional climate, not only does it affectthe local circulation [50] and sea surface conditions [26, 49],the shallow stratification and thin mixed layers in turn influ-ence regional cyclones [34] and the monsoon itself [44, 51].The seasonally reversing East India Coastal Current (EICC)flows northward along the western boundary of the Bay inspring, and southward in autumn [41, 47]. In situ data, as wellas model simulations, show that the EICC transports freshwa-ter from the GBM, Mahanadi, and Godavari rivers in the formof a narrow, fresh “river in the sea” in the post-summer mon-soon season [6, 52, 67]. The southward transport of freshwaterby the EICC has been analyzed in numerical models [65, 66];in particular, recent efforts suggest that vertical diffusion playsan important role in the gradual increase of surface salinity ona seasonal timescale [1, 3]. While dynamical mechanisms arenot particularly clear, on shorter timescales, Lagrangian salin-ity change maps from August to October of 2013 also show an increase in saltiness with southward advection [31]. In thiscontext, the role of eddies in stirring the salinity field has beenrecognized [20, 28, 53]. In fact, eddy induced variability insea surface salinity has been recently observed in other oceanbasins such as the tropical Pacific [16] and the Arabian Sea[63].The fact that eddies are likely to play an important role in theevolution of the salinity field is not surprising given their in-fluence on the mixing of passive fields on the surface of theBay [39], as well as the broader observation that they trapand transport salt and heat in the global oceans [17]. Further-more, eddies are ubiquitous in the BoB [14] and their prop-erties have been documented on intraseasonal and interannualtime scales [9, 10, 54, 61]. In this work, we examine the inter-action of freshwater and a cyclonic eddy in the BoB. In partic-ular, our interest is on timescales of the order of a month, andwe showcase the trapping and progressive homogenization oflow salinity water that enters the Bay in the postmonsoon sea-son. The trapping of freshwater is explained from a dynamicalsystems perspective by appealing to the eddy’s attracting man-ifolds. Then, the exchange of material by means of extendedsalty (fresh) filaments being wrapped into (out of) the eddyresults in the homogenization of freshwater that is quantifiedby vertical profiles and horizontal cross-sections in and acrossthe eddy. This chaotic mixing of fresh and salty water is elu-cidated via Lagrangian passive tracer simulations. Further,these processes are also identified in reanalysis data. Finally,the results are discussed and a hypothesis on the dynamicalcause of horizontal mixing is presented.
II. DATA SOURCES AND METHODS
A variety of in situ , satellite and reanalysis data are usedin this study: Daily mean sea level anomalies and sur-face geostrophic currents (MSLA-UV; . ◦ × . ◦ ) are a r X i v : . [ phy s i c s . a o - ph ] J a n from AVISO. Daily sea surface temperature (SST) is fromthe Group of High Resolution Sea Surface Temperature(GHRSST) product that is produced at . ◦ × . ◦ res-olution, and nighttime SST from Advanced Very High-Resolution Radiometer (AVHRR) instrument of METOP2satellite on a 1.1 km grid. 8-day running mean sea surfacesalinity (SSS) estimates are from the Soil Moisture ActivePassive (SMAP) satellite [19] at 60 km resolution, interpo-lated to a . ◦ × . ◦ grid. Total surface currents are fromthe Bay of Bengal current and advection estimation (BoBcat),based on a combination of AVISO geostrophic currents anddirectly wind-forced Ekman currents at 1 m depth on a gridresolution of . ◦ × . ◦ [4, 53]. Temperature and salin-ity profiles are from Argo floats with 5-day sampling, fromNOAA’s Atlantic Oceanographic and Meteorological Labora-tory [2]. We also use drifter data from the Surface VelocityProgram (SVP), NOAA’s Global Drifter Program [5].The ocean reanalysis is the GLORYS12V1 global product thatuses the NEMO ocean model (1/12 ◦ horizontal resolution, or-der 1 m vertical resolution in the upper ocean, 50 vertical lev-els) surface forcing from ECMWF ERA-Interim reanalysis,covering the satellite altimetry era 1993-2018. Observationsare assimilated using a reduced-order Kalman filter, with a3D-VAR scheme used to correct for the slowly-evolving large-scale biases in temperature and salinity [7, 30].The Lagrangian advection of tracers is performed by BoB-cat surface currents from a given initial position by integrat-ing the surface flow field using a Runge-Kutta fourth-ordermethod. The velocities are interpolated using a bi-linear in-terpolation scheme to a grid of resolution 0.01 ◦ × . ◦ . Theequations involved are described in the supplementary mate-rial text S1 (Equation 1). Lagrangian measures such as attract-ing Lagrangian Coherent Structures (a-LCSs) or backward Fi-nite Time Lyapunov Exponents (b-FTLEs) [25, 35, 68] havealso been computed to understand the pathway of freshwatertrapping further. Details of the calculation of these metrics areprovided in the supplementary material (text S1). Given thetimescales of interest here, the backward advection time hasbeen taken as 20 days to calculate b-FTLEs (a-LCSs). III. THE EDDY AND THE ENTRY OF FRESHWATER
Snapshots of the particular eddy for every month that we useto highlight interaction with freshwater is shown in Figure1. In particular, we show the eddy center (star), sea-levelanomaly, and geostrophic currents. Consistent with priorwork [11], this eddy was born at the eastern edge of theBay. After its genesis (around April 2015), the eddy movedsouthwest towards the central BoB, then took a northwest-ward route from September 2015 onward (Figure 1(a),(b),(c)).After the monsoon, the eddy remained close to the westernboundary of BoB. Interestingly, the eddy appeared to decay insize towards the end of 2015 but re-intensified, and its size in-creased on the arrival of the northward-flowing EICC [21] dur-ing spring of 2016 (Figure 1(g)). Finally, the eddy moved east-ward, off of the western boundary, towards the central BoB and dissociated around June 2016 (Figure 1(h),(i)). The west-ward (eastward) drift of the eddy early (late) in its life is suc-cinctly captured by the Hovm¨oller diagram in Figure S1(a). Inparticular, the speed of translation in these two periods is seento be approximate − cm/s and cm/s, respectively. Further,while near the western coast, the Rossby number ( Ro ) — de-fined as ξ/f , where ξ is the relative vorticity of the eddy and f is the Coriolis parameter — of this eddy was approximately . suggestive of geostrophic balance. Given that the aver-age life span of eddies in the BoB is about two-three months[9, 11], this particular eddy was remarkable in that it lasted forabout sixteen months. Indeed, such a long life span of eddycan be sustained in BoB has not been highlighted so far in theliterature as far as we are aware.In the post-monsoon season, the eddy translated along west-ern boundary of the Bay and trapped freshwater as shownin the SSS maps with surface currents in Figure 2(a). Start-ing in early October, freshwater is pulled inward from thewestern boundary and enters the eddy over a period of about10 days. Coincidentally, five drifters were also trapped andformed loops within the eddy during this period as shown inFigure S1(b). Signs of chaotic advection [36] of the salinityfield, that are visible via the stretching of the salinity field inFigure 2(a), are brought out in Figure 2(b) via a tracer experi-ment [39], wherein a passive field is initialized with the samevalue as the freshwater salinity (SSS ≤ psu) on 01/10. Thebackward finite time Lyapunov exponents (b-FTLEs; see Sup-plementary Material text S1 for definition and computationdetails) [32, 40] for the BoBcat surface flow are also shown forclarity. As is evident, the freshwater (and tracer) is pulled inalong these attracting manifolds [18, 29] and “fills” the eddyin a span of about 10 days. Thus, in less than two weeks,the eddy which contained salty water (around 01/10), pullsin freshwater that forms a layer on its surface (by 21/10). Therole of mesoscale features in restricting freshwater to the northBay has been suggested in other tracer experiments too [3]. IV. HOMOGENIZATION OF FRESHWATER IN THEEDDY
The freshwater that entered the eddy by means of horizontalchaotic advection remains trapped for more than a month asseen in the SSS maps in Figure 3(a). Figure 3(b) shows snap-shots of the evolution of a passive field (SSS ≤
28 psu; violetcolor) within the eddy for this time period. As with SSS, thepassive tracer remains contained in the eddy for the most part,though there is a systematic exchange of material across theeddy boundary. Specifically, some salty water (SSS >
28 psu;marked by red color) spirals into the eddy while freshwater(violet) is stretched out in the form of extended filaments thatmix into the exterior Bay. For example, the intrusion of redfilaments that get wrapped into the eddy and violet streaksthat are stretched out of the eddy can clearly be seen in Figure3(b) on 03/11 and 20/11. This exchange of material acrossthe “kinematic” boundary of the eddy is a hallmark of chaoticmixing (see, for example, [27], for a discussion of this mixing
FIG. 1: (a)-(i) Mean sea level anomaly (SLA) contours in units of centimeters with geostrophic velocity quivers overlaid on 1st day of themonth for May, July, September, October, November, December 2015, and February, April, June 2016. The contours of SLA are in the rangeof -25 cm to 25 cm with 5 cm intervals. The track of the cyclonic eddy is shown with “star” indicating the SLA minimum of the eddy and“dot” denoting the position in preceding months from its origin.FIG. 2: (a) Sea Surface Salinity (SSS) with BoBcat current quivers on 01/10, 07/10, 13/10, 21/10, respectively. (b) Advected passive scalarmaps with tracer initialized to SSS < psu on 01/10 for days as in (a). In addition, attracting Lagrangian Coherent Structures (a-LCS) orb-FTLE computed by integrating backward for 20 days are shown on the top of the tracer field. Only values above . day − (stronger stablemanifolds) are shown. process and an example from the atmosphere) and is antici-pated to homogenize salinity inside the eddy. In fact, as canbe seen from the SSS values in Figure 3(a), the freshwater on22/10 is much saltier after a month’s time.The vertical structure of water mass is obtained from Argo AOML-5904302 data which was trapped in this eddy from24/10 to 24/12 (Figure S1(b)). In particular, the evolution ofpotential temperature ( θ ), salinity (S), potential density ( σ θ ),square of the Brunt-V¨ais¨al¨a frequency (N = − g ¯ ρ dρdz ) where θ , σ θ and N has been computed using Gibbs-SeaWater Oceano- FIG. 3: (a)(i)-(vi) shows Sea Surface Salinity (SSS) with BoBcat current quivers on 22/10, 30/10, 03/11, 07/11, 14/11, 20/11, respectively.Star marks the center of the eddy. (b) Tracers with SSS ≤
28 ( >
28) psu initialized on 22/10/2015 are marked in violet (red) colors. These areadvected forward in time by BoBcat currents and shown for 22/10, 03/11, and 20/11 of 2015 with contours of SLA overlaid on the top. graphic Toolbox [33], and is shown in Figure S2. The ho-mogenization suggested by Figure 3(a) is confirmed via this in situ data by comparing vertical profiles of θ , S and N inthe early (24/10), middle (18/11) and late (14/12) parts of theaforementioned period. Specifically, as per Figure 4(a), onthe entry of freshwater (24/10), we clearly see a very shal-low layer (about 5 m) of low salinity water, a small temper-ature inversion, and high buoyancy frequency below the baseof this fresh layer. This results in a stratified upper layer inthe eddy with N max = 1 . × − s − . In a few weeks,by 18/11, the surface salinity (temperature) shows signs of in-creasing (decreasing) and the buoyancy frequency has reduced(N max = 4 . × − s − ). In about a month’s time, i.e., on14/12, it becomes clear that surface salinity has increased byalmost 10 psu in this point measurement and its vertical struc-ture is weaker. Further, the surface of the eddy has cooledand there is a marked inversion in temperature at about 25 m[57]. The buoyancy frequency has also reduced significantly(approximately N max = 1 . × − s − ) and is fairly uniformwith depth. Thus, these profiles of water mass clearly indi-cate a progressive homogenization of fields and a decrease invertical gradients over the course of a month. The evolution of mean surface potential temperature ( θ ), SSS,sea-level anomaly of the eddy center, and a maximum speedof the surface currents over a circle of diameter km acrossthe eddy center is shown in Figure 3b(i),(ii), respectively as itmoves along the western coast of the BoB. Here, we see thatduring the entry of freshwater (09/10 till 30/10), SSS dropsby 5 approximately psu. Then, consistent with the Argo floatdata, surface salinity starts increasing. The initial rate of in-crease is relatively high rate till about 13/11 (approximately 3psu in a week), thereafter, the rate of increase of salinity slowsdown, and by 14/12 the mean eddy salinity is about 30-31 psu.This indicates that the homogenization of salinity possibly in-volves multiple stages with different mixing rates. Further,along with this increase in SSS over a month’s time, there issystematic surface cooling from about . to . ◦ C and anincrease in the sea-level anomaly of the eddy center within theeddy.Longitudinal variations across the center of the eddy of sealevel anomaly, θ , and SSS and during pre-freshening (01/10),freshening (31/10), and post freshening days (15/12) areshown in Figure 5. The sea-level anomaly is minimum (about FIG. 4: (a)(i),(ii),(iii) shows S (psu), θ ( ◦ C) and N (s − ) with depth for upper 60 m on 24/10, 18/11 and 14/12 from Argo AOML-5904302,respectively. (b) Daily time series of (i) mean θ , SSS (with straight lines to guide the eye) and (ii) maximum current speed and minima of SLAover a circle of diameter 300 km around the eddy center from 01/10/2015 to 31/12/2015.FIG. 5: (i), (ii), (iii) shows SLA, θ and SSS cross-sections through the center of the eddy on 01/10, 31/10, and 15/12 representing pre-freshening, freshening, and post-freshening days, respectively. − cm) and the rate of spinning is at its fastest when fresh-est water is in the eddy as compared to pre and post fresh-ening periods. Consistent with vertical profiles in Figure 5athe potential temperature decreases across the eddy with timeafter the entry of freshwater. Interestingly, as seen in Fig-ure 5, there is a strong gradient in salinity across the eddyof approximately 6 psu in 200 km on 31/10 when freshwaterfilled the eddy. This horizontal gradient relaxes in a month(by 15/12), and not only is the salinity is much higher, butsea-level anomalies also become smaller (about − cm) andthe rate of spinning slows down. Thus, the surface propertiesand horizontal sections go hand in hand with Argo data andsupport the progressive homogenization of freshwater in theeddy. V. OCEAN REANALYSIS AND DISCUSSION
In the Sections so far, we saw the trapping and homogeniza-tion of freshwater via in situ and satellite data. Here, wecheck if similar features can be detected in the NEMO re-analysis product. Quite clearly, freshwater can be seen insidethe eddy over a similar time period (Figure 4a). Further, earlyon, around 28/10 the water in the eddy is freshest and its salti-ness progressively increases over the next three weeks (via the progressively lighter blue colors in Figure 6). Given therelatively higher spatial resolution of NEMO reanalysis, wecan see the exchange of water mass across the kinematic eddyboundary. This is especially clear on 13/11 and 21/11 wheresee freshwater (blue) being pulled out in the south-east cornerof the eddy while salty water (red) pushes in on its north-eastedge. The three-dimensional nature of reanalysis also allowsfor a clearer view of the eddy itself — Figure 7(a) shows itsvertical structure via the meridional velocity (averaged from28/10 to 21/11) up to a depth of 350 m across the section ABmarked in Figure 6(i). The jets supported by this eddy havethe highest speeds that are approximately 0.35 m/s at a depthof about 20 m, and most of the eddy signature dies out by 300m. Through this period of trapping, the reanalysis salinityalso shows a freshwater layer restricted to within 10 m fromthe surface (Figure 7(b); second panel). Further, the inver-sion noted due to surface cooling in the in situ data (Figure4(a)) is also captured here at a depth of approximately 25 mas seen in the first panel of Figure 7(b). Thus, in addition toa detailed view of the eddy, while the actual numbers differslightly, the overall picture of the trapping of freshwater andits progressive homogenization due to lateral mixing is seenin the reanalysis data too.Given the inflow of low salinity water to the Bay every yearand the ubiquitous presence of eddies on the western coast ofthe Bay, we suspect that this process of trapping and subse-quent homogenization of surface salinity within an eddy onthe timescale of a month may not be uncommon. The rate ofhomogenization is about 2-3 psu in a week which is compa-rable to mixing during strong wind events, for example, trop-ical cyclone Phailin in 2013 off the west coast of north BoBcaused a change of about 1-4 psu via wind-induced verticalmixing [8]. In fact, the increase in SSS by about 5-7 psu inthe eddy is of the same order as that noted through the courseof the winter season in the northern BoB [1]. Of course, theoutstanding issue that remains is the dynamical cause of mix-ing in the eddy. Given the strong stratification on the arrival offresh water, vertical overturning is likely inhibited [58], evenwith the observed surface cooling [31]. While the scale ofthe eddy (approx 300 km) is in a balanced regime [55], thereare clear indications toward the formation of smaller scalesfrom the SSS and SST fields shown in Figure 8(a) and (b).For SSS (Figure 8(a)), which is relatively coarse in resolution,salty water can be seen pushing into the eddy on its north-eastcorner. This is seen in much greater detail with finer scalesalong with the cold and warm tongues in the higher resolutionSST map on the same day in Figure 8(b). Indeed, lobe likestructures can be seen around the eddy on multiple days dur-ing the homogenization period (Figure 3(a), especially, 30/10,03/11, and 07/11). This is reminiscent of the development ofnon-axisymmetric features via baroclinic and barotropic insta-bility during the adjustment of rotating-stratified shallow vor-tices that are of a lower density [12, 22, 46, 64] or fresher [56]than the ambient fluid. These features, especially smaller-scale vortices within the parent eddy, are also visible in re-analysis data shown in Figure 6 and Figure S3.Indeed, the large gradients observed on the arrival of fresh-water are probably even sharper as per ship-based measure-ments in the BoB [42]. At these fine scales of O(1-10 km)frictional as well as diabatic surface fluxes can play an im-portant role in potential vorticity extraction or injection togenerate instability and subsequent sub-mesoscale turbulence[15, 42, 45, 59, 60]. In effect, we suspect that the SST inFigure 8(b) just provides a glimpse into the horizontal mixingand turbulence triggered by the adjustment process in suchfreshwater eddies and motivates further study based on situ observations along with high resolution modeling to under-stand the mechanism behind the homogenization of salinity atsub-mesoscales.
VI. CONCLUSIONS
By using satellite, in situ and reanalysis data, we have shownthat freshwater discharged into the Bay of Bengal was trappedin a cyclonic mesoscale eddy during the postmonsoon seasonof 2015. The eddy responsible for trapping freshwater wasitself unique in that it lasted for almost sixteen months in theBay, where the usual lifetimes of eddies are of the order oftwo months. During its lifetime, the eddy remained close tothe Bay’s western coast for almost three months in the post-monsoon season. In this period, entry of low salinity water into the eddy began in early October. In particular, freshwa-ter was directed along with the eddy’s attracting manifoldsand bore the hallmarks of chaotic advection. In a time spanof approximately ten days, the eddy, which contained warmand salty water, had a surface layer of cool freshwater. Thisled to a strongly stratified surface layer, deep sea-level anoma-lies, high spin rates, and strong lateral gradients in salinity anddensity across the eddy.The trapped freshwater in the eddy was then observed to beprogressively homogenized with its environment. Specifi-cally, satellite maps showed an increase in salinity in about amonth after the freshwater entered the eddy. This was corrob-orated by in situ vertical profiles from Argo data that showedan increase in surface salinity along with surface cooling andthe formation of an inversion layer. Concomitantly, horizontalgradients of salinity and density relaxed over the next month.The homogenization process was illustrated via Lagrangiantracer experiments that showed the horizontal mixing that tookplace, wherein salty water was advected into the eddy. Fresh-water was expelled in thin meandering filaments into the openBay. The trapping, freshwater surface layer, and its homog-enization were also seen in reanalysis data. Thus, in contrastto seasonal timescales where vertical diffusion is important,we have shown that freshwater becomes significantly saltierwithin a month’s timescale, apparently by horizontal mixingwhen trapped in a mesoscale eddy.
VII. ACKNOWLEDGEMENT
We thank Dr. Jared Buckley and Prof. Amit Tan-don for sharing the BoBcat dataset for 2015 ( https://github.com/jbuckley-BoBcat/BoBcat ). NPwould like to acknowledge Dr. J Sree Lekha andDr. Dipanjan Chaudhuri for discussions. The authorswould like to acknowledge the following data sources:National Oceanic and Atmospheric Administration’s At-lantic Oceanographic and Meteorological Laboratory, Physi-cal Oceanography Division ( ) for distributing Argo and Drifter data;Copernicus Marine and Environment Monitoring Service(CMEMS) for Ssalto Duacs/gridded multimission altime-ter products from AVISO and GLORYS12V1 productdriven by the NEMO model ( https://resources.marine.copernicus.eu/ ); Physical Oceanography Ac-tive Archive Centre for distributing SMAP (Soil MoistureActive Passive) satellite sea surface salinity data ( https://doi.org/10.5067/SMP43-3TPCS ) and Group forHigh Resolution Sea Surface Temperature (GHRSST) data( https://podaac.jpl.nasa.gov/GHRSST/ ). Wealso thank the Divecha Centre for Climate Change, IISc, Ban-galore, for providing financial assistance. JS would like to ac-knowledge support from the University Grants Commission(UGC) for funding via 6-3/2018 under the 4th cycle of theIndo-Israel joint research program. DS acknowledges supportfrom the National Monsoon Mission, IITM, Pune. NP and JSwould like to thank Pattabhi Rama Rao E, Dr. N. Srinivasa
FIG. 6: (i)-(iv) SSS (psu) (with contours) at 0.5 m from NEMO reanalysis from 28/10 to 21/11 (freshwater trapping days) with 8-day interval.AB denotes the cross-section of the eddy from 83 ◦ E-89 ◦ E shown in subpanel (i).FIG. 7: (a) Mean meridional velocity profile along the longitudinal section AB of the eddy up to a depth of 350 m shown in Figure 6(i)averaged over freshwater trapping days (28/10–21/11) from NEMO reanalysis data. The vertical black lines indicate the contours of maximumspeed on each side of the lobes of the eddy. (b) Variation of mean potential temperature ( θ ) (upper panel) and mean salinity (lower panel)within upper 50 m of the eddy averaged for the same section and time period as in (a). Rao and Geetha Gujjari of ESSO - Indian National Centrefor Ocean Information Services ( https://incois.gov.in/ ), Ministry of Earth Sciences, Government of India forsharing the METOP2-AVHRR SST data.
VIII. SUPPORTING INFORMATION FOR “EDDYINDUCED TRAPPING AND HOMOGENIZATION OFFRESHWATER IN THE BAY OF BENGAL”A. SI: Text
Attracting Lagrangian Coherent Structures (a-LCSs orBackward Finite Time Lyapunov Exponents (b-FTLEs) :The mixing of freshwater is characterized from a Lagrangian
FIG. 8: (a) SSS (psu) with BoBcat currents (b) METOP2-AVHRR SST ( ◦ C) on 13/11/2015. perspective via so-called backward Finite Time Lyapunov Ex-ponents (b-FTLEs) [68]. These are ridges that represent at-tracting Lagrangian coherent structures in a flow [24]. Tocompute the b-FTLEs, we first advect fluid parcel by integrat-ing the following equations backward in time, dφdt = u ( φ, λ, t ) R cos( λ ) , dλdt = v ( φ, λ, t ) R . (1)Here, φ , λ , u and v are the latitude, longitude, zonal andmeridional velocity, respectively. R is the radius of the earth.The time span is t = t to t = t o − τ and the numerical methodemployed is the 4th order Runge-Kutta scheme. The velocitydata ( u, v ) is given on a fixed grid and the flow has been inter-polated by a bilinear interpolation scheme. We then computethe right Cauchy-Green Lagrange tensor C tt associated withthe flow map F tt ( x ) , which is defined as, C tt ( x ) = ( ∇ F tt ( x )) T ∇ F tt ( x ) . (2) F tt ( x ) denotes the position of a parcel at time t backwardin time, advected by the flow from an initial time and posi-tion ( t , x ). C tt ( x ) is symmetric and positive definite, itseigenvalues ( λ (cid:48) s ) and eigenvectors ( ξ (cid:48) s ) can be written as, C tt ( x ) = λ i ξ i , < λ ≤ λ , i = 1 , . (3) The gradient of the flow map ∇ F tt ( x ) is computed usingan auxiliary grid about the reference point [35], and can bewritten as, ∇ F tt ( x ) ≈ (cid:18) α α α α (cid:19) , (4)where, α i,j ≡ x i ( t ; t , x + δx j ) − x i ( t ; t , x − δx j )2 | δx j | . (5)Finally, the largest b-FTLE [24, 25, 32] associated with thetrajectory x ( t, t , x ) over the time interval [ t , t ] is definedas, λ τ ( x ) = − | t − t | log( (cid:113) λ max [ C tt ( x )]) . (6)The backward integration time | τ | = | t − t | has been taken as20 days and computed on a finer grid resolution . ◦ × . ◦ . B. SI: Figure (S1, S2, S3) [1] V. Akhil, F. Durand, M. Lengaigne, J. Vialard, M. Keerthi, V. V.Gopalakrishna, C. Deltel, F. Papa, and C. de Boyer Mont´egut. A model-ing study of the processes of surface salinity seasonal cycle in the Bay ofBengal.
Journal of Geophysical Research: Oceans , 119(6):3926–3947,2014. doi: 10.1002/2013JC009632.[2] Argo. Argo float data and metadata from global data assembly centre (Argo GDAC).
SEANOE , 2000. doi: 10.17882/42182.[3] R. Benshila, F. Durand, S. Masson, R. Bourdall´e-Badie,C. de Boyer Mont´egut, F. Papa, and G. Madec. The upper Bayof Bengal salinity structure in a high-resolution model.
OceanModelling , 74:36–52, 2014. doi: 10.1016/j.ocemod.2013.12.001.[4] J. M. Buckley, B. Mingels, and A. Tandon. The impact of lateral advec-
FIG. S1: (a) Hovm¨oller diagram of Rossby number ( ξ/f ) computed from geostrophic currents averaged over 16.625 ◦ N-17.625 ◦ N shown forthe year 2015-2016. (b) Track of Argo float (AOML-5904302) and trajectories of Surface Velocity Program (SVP) “drifters” (drouged at 15m depth) within the eddy from 01/10 to 31/12 of 2015 and entire track of eddy in inset from the first day of April 2015 to June 2016 in aninterval of a month.FIG. S2: (i) Potential temperature ( θ ), (ii) salinity (S), (iii) potential density ( σ θ ) and (iv) squared Brunt-v¨ais¨al¨a frequency (N ), respectivelywith depth using Argo AOML-5904302 data for the upper 50 m from October to December, 2015. tion on SST and SSS in the northern Bay of Bengal during 2015. DeepSea Research Part II: Topical Studies in Oceanography , 172:104653,2020. doi: 10.1016/j.dsr2.2019.104653.[5] L. R. Centurioni, J. D. Turton, R. Lumpkin, L. Braasch, G. Brassington,Y. Chao, E. Charpentier, Z. Chen, G. Corlett, K. Dohan, et al. Globalin-situ observations of essential climate and ocean variables at the air-sea interface.
Frontiers in Marine Science , 6:419, 2019. doi: 10.3389/fmars.2019.00419.[6] A. Chaitanya, M. Lengaigne, J. Vialard, V. Gopalakrishna, F. Durand,C. Kranthikumar, C. Amritash, V. Suneel, F. Papa, and M. Ravichan-dran. Salinity Measurements Collected by Fishermen Reveal a “Riverin the Sea” Flowing Along the Eastern Coast of India.
BAMS , pages1897–1908, 2014. doi: 10.1175/BAMS-D-12-00243.1.[7] E. Chassignet, A. Pascual, J. Tintor´e, and J. Verron. New frontiers in operational oceanography.
GODAE OceanView , 2018. doi: 10.17125/gov2018.[8] D. Chaudhuri, D. Sengupta, E. D’Asaro, R. Venkatesan, andM. Ravichandran. Response of the salinity-stratified Bay of Bengal tocyclone Phailin.
Journal of Physical Oceanography , 49(5):1121–1140,2019. doi: 10.1175/JPO-D-18-0051.1.[9] G. Chen, D. Wang, and Y. Hou. The features and interannual variabilitymechanism of mesoscale eddies in the Bay of Bengal.
Continental ShelfResearch , 47:178–185, 2012. doi: 10.1016/j.csr.2012.07.011.[10] X. Cheng, S.-P. Xie, J. P. McCreary, Y. Qi, and Y. Du. Intraseasonal vari-ability of sea surface height in the Bay of Bengal.
Journal of Geophysi-cal Research: Oceans , 118(2):816–830, 2013. doi: 10.1002/jgrc.20075.[11] X. Cheng, J. P. McCreary, B. Qiu, Y. Qi, Y. Du, and X. Chen. Dy-namics of eddy generation in the central Bay of Bengal.
Journal FIG. S3: (a) SSS with contours with an interval of 1 psu (b) vorticity with surface current quiver (c) SST with contours with an interval of0.2 ◦ C at 0.5 m depth on 13/11/2015 from NEMO reanalysis data. of Geophysical Research: Oceans , 123(9):6861–6875, 2018. doi:10.1029/2018JC014100.[12] F. Chia, R. Griffiths, and P. Linden. Laboratory experiments on fronts:part II: the formation of cyclonic eddies at upwelling fronts.
Geophys-ical & Astrophysical Fluid Dynamics , 19(3-4):189–206, 1982. doi:10.1080/03091928208208955.[13] A. Dai and K. E. Trenberth. Estimates of freshwater discharge fromcontinents: Latitudinal and seasonal variations.
Journal of hydrometeo-rology , 3(6):660–687, 2002. doi: 10.1175/1525-7541(2002)003 (cid:104) (cid:105)
IEEEJournal of Selected Topics in Applied Earth Observations and RemoteSensing , 9(11):5044–5054, 2016.[15] E. D’Asaro, C. Lee, L. Rainville, R. Harcourt, and L. Thomas. Enhancedturbulence and energy dissipation at ocean fronts.
Science , 332(6027):318–322, 2011. doi: 10.1126/science.1201515.[16] T. Delcroix, A. Chaigneau, D. Soviadan, J. Boutin, and C. Pegliasco.Eddy-Induced Salinity Changes in the Tropical Pacific.
Journal of Geo-physical Research: Oceans , 124(12):374–389, 2019. doi: 10.1029/2018JC014394.[17] C. Dong, J. C. McWilliams, Y. Liu, and D. Chen. Global heat and salttransports by eddy movement.
Nature communications , 5(1):1–6, 2014.[18] F. d’Ovidio, V. Fern´andez, E. Hern´andez-Garc´ıa, and C. L´opez. Mix-ing structures in the Mediterranean Sea from finite-size Lyapunov ex-ponents.
Geophysical Research Letters , 31(17), 2004. doi: 10.1029/2004GL020328.[19] A. G. Fore, S. H. Yueh, W. Tang, B. W. Stiles, and A. K. Hayashi.Combined active/passive retrievals of ocean vector wind and sea surfacesalinity with SMAP.
IEEE Transactions on Geoscience and RemoteSensing , 54(12):7396–7404, 2016. doi: 10.1109/TGRS.2016.2601486.[20] S. Fournier, J. Vialard, M. Lengaigne, T. Lee, M. M. Gierach, andA. V. S. Chaitanya. Modulation of the Ganges-Brahmaputra river plumeby the Indian Ocean dipole and eddies inferred from satellite observa-tions.
Journal of Geophysical Research: Oceans , 122(12):9591–9604,2017. doi: 10.1002/2017JC013333.[21] A. Gangopadhyay, G. Bharat Raj, A. H. Chaudhuri, M. Babu, andD. Sengupta. On the nature of meandering of the springtime westernboundary current in the Bay of Bengal.
Geophysical Research Letters ,40(10):2188–2193, 2013. doi: 10.1002/grl.50412.[22] R. Griffiths and P. Linden. The stability of vortices in a rotating, strat-ified fluid.
Journal of Fluid Mechanics , 105:283–316, 1981. doi:10.1017/S0022112081003212.[23] G. Grunseich, B. Subrahmanyam, and B. Wang. The Madden-Julianoscillation detected in Aquarius salinity observations.
Geophysical Re-search Letters , 40, 2013. doi: 10.1002/2013GL058173. [24] G. Haller. Lagrangian coherent structures from approximate veloc-ity data.
Physics of Fluids , 14(6):1851–1861, 2002. doi: 10.1063/1.1477449.[25] G. Haller and T. Sapsis. Lagrangian coherent structures and the smallestfinite-time Lyapunov exponent.
Chaos: An Interdisciplinary Journal ofNonlinear Science , 21(2):023115, 2011. doi: 10.1063/1.3579597.[26] S. Howden and R. Murtugudde. Effects of rives inputs into the Bayof Bengal.
Journal of Geophysical Research , 106(C9):19825–19843,2001. doi: 10.1029/2000JC000656.[27] B. Joseph and B. Legras. Relation between Kinematic Boundaries, Stir-ring, and Barriers for the Antarctic Polar Vortex.
Journal of the Atmo-spheric Sciences , 59:1198–1212, 2002. doi: 10.1175/1520-0469(2002)059 (cid:104) (cid:105)
Ocean Dynam-ics , 63:1175–1180, 2013. doi: 10.1007/s102360130652y.[29] Y. Lehahn, F. d’Ovidio, M. L´evy, and E. Heifetz. Stirring of the north-east Atlantic spring bloom: A Lagrangian analysis based on multisatel-lite data.
Journal of Geophysical Research: Oceans , 112(C8), 2007.doi: 10.1029/2006JC003927.[30] J.-M. Lellouche, E. Greiner, O. Le Galloudec, G. Garric, C. Reg-nier, M. Drevillon, M. Benkiran, C.-E. Testut, R. Bourdalle-Badie,F. Gasparin, et al. Recent updates to the Copernicus Marine Ser-vice global ocean monitoring and forecasting real-time 1/12 ◦ high-resolution system. Ocean Science , 14(5):1093–1126, 2018. doi:10.5194/os-14-1093-2018.[31] A. Mahadevan, G. Spiro Jaeger, M. Freilich, M. Omand, E. Shroyer,and D. Sengupta. Freshwater in the Bay of Bengal: Its fate and role inair-sea heat exchange.
Oceanography , 29:72–81, 2016. doi: 10.5670/oceanog.2016.40.[32] M. Mathur, M. J. David, R. Sharma, and N. Agarwal. Thermalfronts and attracting Lagrangian Coherent Structures in the north Bayof Bengal during December 2015–March 2016.
Deep Sea ResearchPart II: Topical Studies in Oceanography , 168:104636, 2019. doi:10.1016/j.dsr2.2019.104636.[33] T. J. McDougall and P. M. Barker. Getting started with TEOS-10 andthe Gibbs Seawater (GSW) oceanographic toolbox.
SCOR/IAPSO WG ,127:1–28, 2011.[34] S. Neetu et al. Premonsoon/Postmonsoon Bay of Bengal tropical cy-clones intensity: role of Air-Sea coupling and large-scale backgroundstate.
Geophysical Research Letters , 46:2149–2157, 2019. doi: 10.1029/2018GL081132.[35] K. Onu, F. Huhn, and G. Haller. LCS Tool: A computational platformfor Lagrangian coherent structures.
Journal of Computational Science ,7:26–36, 2015. doi: 10.1016/j.jocs.2014.12.002.[36] J. Ottino.
The kinematics of mixing: stretching, chaos, and transport , volume 3. Cambridge university press, 1989.[37] F. Papa, S. K. Bala, R. K. Pandey, F. Durand, V. Gopalakrishna, A. Rah-man, and W. B. Rossow. Ganga-Brahmaputra river discharge fromJason-2 radar altimetry: an update to the long-term satellite-derivedestimates of continental freshwater forcing flux into the Bay of Ben-gal. Journal of Geophysical Research: Oceans , 117(C11), 2012. doi:10.1029/2012JC008158.[38] S. Parampil, A. Gera, M. Ravichandran, and D. Sengupta. Intraseasonalresponse of mixed layer temperature and salinity in the Bay of Bengalto heat and freshwater flux.
Journal of Geophysical Research: Oceans ,115, 2010. doi: 10.1029/2009JC005790.[39] N. Paul and J. Sukhatme. Seasonality of surface stirring by geostrophicflows in the Bay of Bengal.
Deep Sea Research Part II: Topical Studiesin Oceanography , 172:104684, 2020. doi: 10.1016/j.dsr2.2019.104684.[40] V. P´erez-Munuzuri. Mixing and clustering in compressible chaoticstirred flows.
Physical Review E , 89(2):022917, 2014. doi: 10.1103/PhysRevE.89.022917.[41] J. T. Potemra, M. E. Luther, and J. J. O’Brien. The seasonal circulationof the upper ocean in the Bay of Bengal.
Journal of Geophysical Re-search: Oceans , 96(C7):12667–12683, 1991. doi: 10.1029/91JC01045.[42] S. Ramachandran, A. Tandon, J. Mackinnon, A. J. Lucas, R. Pinkel,A. F. Waterhouse, J. Nash, E. Shroyer, A. Mahadevan, R. A. Weller,et al. Submesoscale processes at shallow salinity fronts in the Bay ofBengal: Observations during the winter monsoon.
Journal of PhysicalOceanography , 48(3):479–509, 2018. doi: 10.1175/JPO-D-16-0283.1.[43] R. Rao and R. Sivakumar. Seasonal variability of sea surface salinityand salt budget of the mixed layer of the north Indian Ocean.
Journal ofGeophysical Research , 108:3009, 2003. doi: 10.1029/2001JC000907.[44] D. Samanta, S. N. Hameed, D. Jin, V. Thilakan, M. Ganai, S. A. Rao,and M. Deshpande. Impact of a narrow coastal Bay of Bengal sea sur-face temperature front on an Indian summer monsoon simulation.
Sci-entific reports , 8(1):1–12, 2018. doi: 10.1038/s41598-018-35735-3.[45] S. Sarkar, H. T. Pham, S. Ramachandran, J. D. Nash, A. Tandon,J. Buckley, A. A. Lotliker, and M. M. Omand. The interplay be-tween submesoscale instabilities and turbulence in the surface layerof the Bay of Bengal.
Oceanography , 29(2):146–157, 2016. doi:10.5670/oceanog.2016.47.[46] P. M. Saunders. The instability of a baroclinic vortex.
Journal of Phys-ical Oceanography , 3(1):61–65, 1973. doi: 10.1175/1520-0485(1973)003 (cid:104) (cid:105)
Progress in Oceanography , 51(1):1–123, 2001. doi:10.1016/S0079-6611(01)00083-0.[48] D. Sengupta, G. Bharath Raj, M. Ravichandran, J. Sree Lekha, andF. Papa. Near-surface salinity and stratification in the north Bay of Ben-gal from moored observations.
Geophysical Research Letters , 43(9):4448–4456, 2016. doi: 10.1002/2016GL068339.[49] H. Seo, S.-P. Xie, R. Murtugudde, M. Jochum, and A. J. Miller. Seasonaleffects of Indian Ocean freshwater forcing in a regional coupled model.
Journal of Climate , 22:6577–6596, 2009. doi: 10.1175/2009JCLI2990.1.[50] D. Shankar, P. Vinayachandran, and A. Unnikrishnan. The monsooncurrents in the north Indian Ocean.
Progress in oceanography , 52(1):63–120, 2002. doi: 10.1016/S0079-6611(02)00024-1.[51] S. Shenoi, D. Shankar, and S. Shetye. Difference in heat budgets of thenear-surface Arabian Sea and Bay of Bengal: Implications for the sum-mer monsoon.
Journal of Geophysical Research , 107:283–316, 2002.doi: 10.1029/2000JC000679.[52] S. Shetye, A. Gouveia, D. Shankar, S. Shenoi, P. Vinayachandran,D. Sundar, G. Michael, and G. Nampoothiri. Hydrography and circula-tion in the western Bay of Bengal during the northeast monsoon.
Journalof Geophysical Research: Oceans , 101(C6):14011–14025, 1996. doi:10.1029/95JC03307.[53] J. Sree Lekha, J. Buckley, A. Tandon, and D. Sengupta. Subseasonaldispersal of freshwater in the northern Bay of Bengal in the 2013 sum-mer monsoon season.
Journal of Geophysical Research: Oceans , 123(9):6330–6348, 2018. doi: 10.1029/2018JC014181.[54] B. Subrahmanyam, T. CB, and V. Murty. Detection of intraseasonal os- cillations in SMAP salinity in the Bay of Bengal.
Geophysical ResearchLetters , 45(14):7057–7065, 2018. doi: 10.1029/2018GL078662.[55] J. Sukhatme, D. Chaudhuri, J. MacKinnon, S. Shivaprasad, and D. Sen-gupta. Near-surface ocean kinetic energy spectra and small scale inter-mittency from ship based ADCP data in the Bay of Bengal.
Journal ofPhysical Oceanography , 2020. doi: 10.1175/JPO-D-20-0065.1.[56] B. Tartinville, E. Deleersnijder, P. Lazure, R. Proctor, K. Ruddick, andR. Uittenbogaard. A coastal ocean model intercomparison study for athree-dimensional idealised test case.
Applied mathematical modelling ,22(3):165–182, 1998. doi: 10.1016/S0307-904X(98)00015-8.[57] P. Thadathil, V. Gopalakrishna, P. Muraleedharan, G. Reddy, N. Araligi-dad, and S. Shenoy. Surface layer temperature inversion in the Bay ofBengal.
Deep Sea Research Part I: Oceanographic Research Papers , 49(10):1801–1818, 2002. doi: 10.1016/S0967-0637(02)00044-4.[58] R. Thakur, E. L. Shroyer, R. Govindarajan, J. T. Farrar, R. A. Weller,and J. N. Moum. Seasonality and Buoyancy Suppression of Turbulencein the Bay of Bengal.
Geophysical Research Letters , 46(8):4346–4355,2019. doi: 10.1029/2018GL081577.[59] L. N. Thomas. Destruction of potential vorticity by winds.
Journalof physical oceanography , 35(12):2457–2466, 2005. doi: 10.1175/JPO2830.1.[60] L. N. Thomas, J. R. Taylor, E. A. D’Asaro, C. M. Lee, J. M. Klymak,and A. Shcherbina. Symmetric instability, inertial oscillations, and tur-bulence at the Gulf Stream front.
Journal of Physical Oceanography ,46(1):197–217, 2016. doi: 10.1175/JPO-D-15-0008.1.[61] C. Trott and B. Subrahmanyam. Detection of intraseasonal oscillationsin the Bay of Bengal using altimetry.
Atmospheric Science Letters , 20(7):e920, 2019. doi: 10.1002/asl.920.[62] C. Trott, B. Subrahmanyam, H. Roman-Stork, V. Murty, andC. Gnanaseelan. Variability of Intraseasonal Oscillations and Synop-tic Signals in Sea Surface Salinity in the Bay of Bengal.
Journal ofClimate , 32, 2019. doi: 10.1175/JCLI-D-19-0178.1.[63] C. Trott et al. Eddy-Induced Temperature and Salinity Variability in theArabian Sea.
Geophysical Research Letters , 46:2734–2742, 2019. doi:10.1029/2018GL081605.[64] R. Verzicco, F. Lalli, and E. Campana. Dynamics of baroclinic vorticesin a rotating, stratified fluid: a numerical study.
Physics of Fluids , 9(2):419–432, 1997. doi: 10.1063/1.869136.[65] P. Vinayachandran and J. Kurian. Hydrographic observations and modelsimulation of the Bay of Bengal freshwater plume.
Deep Sea Research,Part I , 51:471–486, 2007. doi: 10.1016/dsr.2007.01.007.[66] P. Vinayachandran and R. Nanjundiah. Indian Ocean sea surface salinityvariations in a coupled model.
Climate Dynamics , 33:245–263, 2009.doi: 10.1007/s0038200805116.[67] P. Vinayachandran, T. Kagimoto, Y. Masumoto, P. Chauhan, S. Nayak,and T. Yamagata. Bifurcation of the East India Coastal Current eastof Sri Lanka.
Geophysical Research Letters , 32, 2005. doi: 10.1029/2005GL022864.[68] S. Wiggins. The dynamical systems approach to Lagrangian transportin oceanic flows.