We describe the seasonal cycle of mixing in the top 30–100 m of the Bay of Bengal as observed by moored mixing meters (χpods) deployed along 8°N between 85.5° and 88.5°E in 2014 and 2015. All χpod observations were combined to form seasonal-mean vertical profiles of turbulence diffusivity KT in the top 100 m. The strongest turbulence is observed during the southwest and postmonsoon seasons, that is, between July and November. The northeast monsoon (December–February) is a period of similarly high mean KT but an order of magnitude lower median KT, a sign of energetic episodic mixing events forced by near-inertial shear events. The months of March and April, a period of weak wind forcing and low near-inertial shear amplitude, are characterized by near-molecular values of KT in the thermocline for weeks at a time. Strong mixing events coincide with the passage of surface-forced downward-propagating near-inertial waves and with the presence of enhanced low-frequency shear associated with the Summer Monsoon Current and other mesoscale features between July and October. This seasonal cycle of mixing is consequential. We find that monthly averaged turbulent transport of salt out of the salty Arabian Sea water between August and January is significant relative to local E − P. The magnitude of this salt flux is approximately that required to close model-based salt budgets for the upper Bay of Bengal.
The Bay of Bengal (the Bay) is the eastern semi-enclosed basin of the north Indian Ocean. The shallow salinity-controlled stratification in the upper Bay allows for rapid coupling with the atmosphere, and modulation of sea surface temperature (SST) within the Bay of Bengal has been linked to variations in the South Asian monsoon (e.g., Vecchi and Harrison 2002; Roxy 2014). The influence of processes controlling upper-ocean stratification thus extends beyond the physical footprint of the Bay. The Bay has a particularly strong influence on rainy and dry periods over the Indian subcontinent, termed active and break periods, respectively. Much of central India’s annual rainfall results from convective systems that originate over the Bay and then propagate northwestward over the Indian subcontinent between June and September (Gadgil 2003; Goswami et al. 2003). Interannual variations in mean rainfall are strongly correlated with fluctuations in India’s agricultural output (Gadgil and Rupa Kumar 2006), lending significant social relevance to the problem of understanding air–sea interaction and near-surface ocean dynamics that influence the Bay’s SST.
The Bay’s physical oceanography is characterized by two major features. First, its circulation reverses seasonally under the influence of the Indian Ocean monsoon—the seasonal reversal of winds north of approximately 10°S in the Indian Ocean basin. Second, it receives an immense amount of freshwater—more than 50% of the freshwater runoff into the entire tropical Indian Ocean (Sengupta et al. 2006; Gordon et al. 2016).
The Indian Ocean monsoon and its associated precipitation is visualized in Fig. 1 using seasonal mean wind stress from the Tropflux estimate (Kumar et al. 2012) and precipitation from the Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis dataset (Huffman et al. 2007). Between May and September [southwest (SW) monsoon], the winds are strong and southwesterly throughout the Indian Ocean basin. Precipitation over the Indian subcontinent is substantial (Fig. 1c). The months of October and November [postmonsoon period (SWNE)] are characterized by weak mean wind stress over most of the basin including the Bay (Fig. 1d). Seasonal averaging hides the episodic presence of strong cyclones in the Bay that bring large amounts of rain and significantly affect lives of those residing along the perimeter of the Bay. Recent examples of cyclones that strengthened over the Bay and made landfall resulting in loss of life and severe damages, include category 5 Tropical Cyclone Phailin in October 2013 and category 4 Tropical Cyclone Hudhud in October 2014. The mean winds strengthen in December and switch to being northeasterly up until February [northeast (NE) monsoon]. These winds are weaker than those during the SW monsoon. Nations on the Bay’s Rim, that is, India and Sri Lanka, receive relatively little rainfall during this period and the precipitation maximum is located over the Bay (Fig. 1a). The months of March and April are a period of weak winds and almost no precipitation north of 4°N [northeast–southwest transition (NESW); Fig. 1b].
The monsoon imprints seasonality on the Bay’s circulation (Schott et al. 2002; Shankar et al. 2002). The East India Coastal Current (EICC) spins up at the Bay’s western boundary during both monsoons, flowing northward between May and October and then southward between December and April. The EICC is readily visible in seasonally averaged estimates of near-surface ocean velocity [vectors in Figs. 2a–e from the Ocean Surface Current Analysis Real-Time Product (OSCAR); Bonjean and Lagerloef 2002]1 The EICC exists as a discontinuous flow with many recirculation loops and is visible as a local maximum along India’s eastern coast in maps of geostrophic eddy kinetic energy (colored field in Figs. 2a–e; Durand et al. 2009). Here (ug, υg) are geostrophic velocity anomalies computed from delayed-time sea surface height estimates as measured by multiple satellite altimeters by the Copernicus Marine Environment Monitoring Service (CMEMS).2 Apart from the EICC, one other major circulation feature is the Summer or Southwest Monsoon Current (SMC). The SMC is visible in the seasonal mean during the SW monsoon as an eastward jet along 8°N between 85° and 92°E in Fig. 2d (vectors). Peak velocity in the SMC can exceed 1.5 m s−1 and northward transport has been estimated to be in the range 10–27 Sv (1 Sv ≡ 106 m3 s−1), likely an overestimate due to the presence of recirculations (Wijesekera et al. 2016; Vinayachandran et al. 1999; Webber et al. 2018). The southwestern and south-central Bay is a site of energetic mesoscale variability during the SW monsoon (our Fig. 2d; Chen et al. 2018). The elevated EKE reflects at least three mesoscale features: a westward propagating anticyclone (Wijesekera et al. 2016), a large cyclonic eddy that spins up annually off the coast of Sri Lanka (the Sri Lanka Dome; Vinayachandran and Yamagata 1998) and the SMC which threads a pathway between the Sri Lanka Dome to the north and the anticyclone to the south (Vinayachandran et al. 1999; Wijesekera et al. 2016). During the NE monsoon, the mean circulation in southern Bay reverses and the Northeast Monsoon Current flows westward with a weaker signal in EKE (Figs. 2a,b).
Large outflows from the Ganga, Brahmaputra, and Irrawaddy Rivers, and substantial precipitation make the Bay a strongly salinity-stratified basin in its near-surface depths particularly toward the north. The annual river discharge peaks toward the end of the SW monsoon and the freshwater is eventually exported out along the Bay’s western and eastern margins (Sengupta et al. 2006). The exported water is saline with S ≈ 34–35 psu. Hence maintaining the Bay’s long term salt balance requires both an inflow of salty water from outside the Bay and the upward turbulent transport of that imported salt so as to permanently modify the near-surface freshwater (Vinayachandran et al. 2013).
The western half of the north Indian Ocean, the Arabian Sea, is generally considered the source of the required salty water (e.g., Jensen 2001), although recently Sanchez-Franks et al. (2019) used a multiyear model to argue that the original source of the salty water is the western equatorial Indian Ocean. Regardless of specific source, both observations and models agree that the SMC is the dominant pathway for salty water entering the Bay (Jensen 2001; Vinayachandran et al. 2013; Webber et al. 2018).3 The salty signature of the SMC is visible in maps of the depth of the 34.75-psu isohaline surface, which shallows by 25 m or so in the southwestern Bay during the summer monsoon (Figs. 2k–o; Murty et al. 1992; Vinayachandran et al. 2013). The shallow depth of the S = 35-psu isohaline in the southwestern and south-central Bay relative to the northern Bay led Vinayachandran et al. (2013) to hypothesize that the southern Bay is a site of enhanced mixing and associated salt fluxes that may be an important contributor to the salt budget of the Bay. In agreement with this hypothesis, model studies have implicated vertical mixing as the primary mechanism for diluting the immense amount of freshwater the Bay receives during the southwest monsoon (Akhil et al. 2014; Benshila et al. 2014; Wilson and Riser 2016).
Here, we summarize yearlong direct observations of turbulence at three moorings along 8°N in the south-central Bay (white dots in Figs. 1 and 2). We show that the seasonal cycle of winds and currents described above is imprinted on mixing in the Bay with near-molecular mixing during the quiet transition period giving way to elevated mixing during both monsoon periods primarily associated with near-inertial shear (sections 3c and 4a). The observed seasonal cycle in mixing is likely significant for the Bay’s salt budget as has been previously hypothesized (section 4c). We find that the upward turbulent salt transport out of subsurface high salinity water at 8°N is comparable to freshwater gained through precipitation (less evaporation).
All presented turbulence quantities were obtained using χpods: self-contained instruments each consisting of two fast-response FP-07 thermistors, a pitot-static tube for high-frequency speed measurements, a pressure sensor, a compass, and accelerometers (Moum and Nash 2009; Moum 2015). Refinement over many years has resulted in a system that can return records of turbulent temperature fluctuations for up to a year or more. The two thermistors on the χpod record temperature fluctuations at 100 Hz. Temperature gradient spectra are computed using 1-s data intervals and are fit to the theoretical spectrum of Kraichnan (1968) in the viscous–convective range (Moum and Nash 2009). The Kraichnan spectrum is a function of two quantities: the turbulence dissipation rate of temperature variance χ and the turbulence dissipation rate of kinetic energy ε but the χpods only record one quantity, temperature. The dependence on ε arises from the Batchelor (1959) wavenumber that marks the end of the viscous–convective range. Since χpod thermistors do not resolve the Batchelor wavenumber typically (e.g., Lueck et al. 1977), fitting the Kraichnan spectrum requires specification of ε. In the absence of an independent estimate of ε, we assume that the turbulence diffusivities of temperature and density are equal with mixing efficiency Γ = 0.2 for stratified turbulence (Osborn and Cox 1972; Osborn 1980; Gregg et al. 2018). This yields a relationship between χ and ε,
and a solution is obtained by fitting the spectrum through the iterative procedure described in Moum and Nash (2009). The buoyancy frequency N and vertical temperature gradient Tz are estimated using two CTD instruments deployed above and below the χpod. In situ comparisons between χpod estimates and more “standard” estimates from vertical microstructure profiles are favorable under stably-stratified sheared conditions (Perlin and Moum 2012; Pujiana et al. 2018). Total temperature and salt diffusivities KT and KS, respectively, heat flux , and salt flux are estimated from a time series of χ using
where κT, κs are the molecular diffusivity of temperature and salinity, respectively, and Tz, Sz are background temperature and salinity gradients (usually obtained by differencing nearby CTDs on the moorings; subscript z indicates z derivative). Again we have assumed that high Reynolds number geophysical turbulence mixes all scalars at the same rate so that the turbulence diffusivities of both temperature and salinity are equal, that is, .
A challenge with analyzing χpods deployed in the Bay’s thermocline is the frequent occurrence of weakly turbulent and near-laminar flow for extended periods of time as has been recorded with microstructure measurements in the Aegean Sea (Gregg et al. 2012) and in the Arctic (Scheifele et al. 2018). Analyzing microstructure measurements in such environments is challenging given that the usual assumptions of isotropy, steadiness, and homogeneity break down (Rohr et al. 1988; Itsweire et al. 1993; Gargett et al. 1984). In weakly turbulent environments, the χpod records “bit noise” when the turbulent temperature fluctuations are below the FP-07 sensor’s detection threshold. We can account for such behavior using knowledge of the circuit components involved ( appendix B). When the recorded temperature variance of a 1-s subset of data is within an arbitrary factor of 1.5 of the inferred noise variance of the sensor, we set ε to NaN and χ to 0 resulting in total diffusivities KT, KS being set to molecular values κT, κS and the resulting fluxes being that due to molecular diffusion [Eq. (2)]. We do so following Gregg et al. (2012) with the understanding that setting χ to any nonzero value during such periods seems unjustifiable.
b. The 2014–15 Bay of Bengal deployment
As part of the U.S. Office of Naval Research’s Air Sea Interaction Regional Initiative (ASIRI) and the Naval Research Laboratory’s (NRL) Effects of Bay of Bengal Freshwater Flux on Indian Ocean Monsoon (EBoB) programs a number of moored mixing meters (χpods; Moum and Nash 2009) were deployed on moorings in the southwestern Bay. This paper focuses on three moorings deployed along 8°N east of Sri Lanka in late December 2013 (Fig. 3a and Table 1). The χpods ended up at a variety of depths and returned data up to February 2015 (Table 1, Figs. 3b–i; Wijesekera et al. 2016). Nearly all were predominantly in the main thermocline (Figs. 3b–e) and sampled the high salinity water associated with the SMC during the summer monsoon (Figs. 3f–i). This region experiences a significant seasonal cycle in near-surface velocity and mesoscale eddy kinetic energy (Figs. 2a–e). The moorings were displaced by up to 50 m (blowdown) by mesoscale features when present.
Two Teledyne RD Instruments ADCPs were deployed at the top of each mooring: an upward-looking Workhorse 300 kHz sampling every half hour in 2-m bins and a downward-looking Long Ranger 75 kHz sampling every hour in 8-m bins (further details are available in Wijesekera et al. 2016). A data gap in velocity coverage exists between the two ADCPs that is approximately 21 m wide. The shallower χpod was deployed within the blanking zone of the downward looking ADCP, so shear can be directly estimated only at the deeper χpod. We estimate shear by first linearly interpolating the velocities over the gap in depth, central differencing the interpolated velocity over three 8-m-wide bins, and then reintroducing the gap. Each mooring contained more than 15 temperature sensors of various kinds distributed between the buoy and 352 m below the buoy. Salinity coverage was coarser with four sensors deployed within a 50-m depth below the buoy and one sensor at 352 m (Wijesekera et al. 2016). Three of the four shallow salinity sensors were concentrated around the two χpods that were deployed 12 and 32 m below the buoy.
We now describe a seasonal cycle in thermocline turbulence that coincides with a seasonal cycle in thermocline shear. The seasonal variation in turbulence will be discussed along with the seasonal variation in the shear field, decomposed into three components as described below. Bursts in near-inertial shear will be linked back to surface winds using an approximate estimate of mixed layer wind energy input obtained using a slab mixed layer model, also described below. First we introduce and rationalize our decomposition of the shear field.
a. Seasonal cycle in observed vertical shear
At all three moorings, Eulerian rotary spectra of vertical shear at 152-m depth4 are dominated by a broad peak at −f0 (40%–60% of sampled variance), narrow secondary peaks at ( is the M2 tidal frequency, 5%–10% variance) and distributed variance at frequencies less than 10 days reflecting meanders of the Summer Monsoon Current (20% variance). These spectra are presented in Figs. 4a, 4c, and 4e (clockwise in black, counterclockwise in red). The narrow peaks at are a sign of vertical advection or pumping of near-inertial shear layers by the M2 tide which Doppler-shifts spectral energy from −f0 to (Alford 2001). The effect of tidal pumping can be removed by estimating the spectra in isopycnal space (e.g., Alford et al. 2017). Given the sparse sampling in salinity, we instead estimate spectra in isothermal space. The peaks at are much less prominent at the T = 18°C isotherm at all moorings (annual mean depth 150 m; Figs. 4b,d,f), leading us to interpret the near-tidal peaks in the Eulerian spectra (Figs. 4a,c,e) as primarily being near-inertial shear that is Doppler shifted to near-tidal frequencies. Ideally we would interpret the χpod mixing estimates using a time series of isothermal shear that is filtered to isolate the low frequency and near-inertial components. It is not possible to obtain a gapless estimate of these filtered components given the gap in ADCP coverage. Instead we proceed by conducting our analysis in the Eulerian frame as follows.
We decompose the total vertical shear Stotal by linearly interpolating over the sampling gap in the vertical and then using a second-order Butterworth filter applied forwards and backward to split the shear time series into four components: (i) low-frequency shear Slow (low pass with half power point 9 days), (ii) near-inertial shear Sin (bandpass between half power points 7 and 2 days respectively), (iii) near-tidal shear (bandpass between half power points 15.3 and 10.4 h)5, and (iv) a residual Sres. These frequency ranges are shaded in Fig. 4. Given the previous discussion, we incorporate near tidal shear with Sin. The combined sum Sin+ represents any shear associated with near-inertial waves, advection of near-inertial waves by the tide as well as any tidal shear.
Depth–time maps of the mean squared shear for three shear components Slow, Sin+, Sres along with the total shear Stotal are shown in Fig. 5 (normalized by the temperature contribution to stratification ). At all three moorings, energetic shear is observed in January, February, and for an extended period between July and November. The shear field is relatively weak between mid-March and the beginning of June. Episodic energetic bursts in near-inertial shear are seen at all three moorings outside these months. All three moorings see a large rise in low-frequency shear between July and November. This is an indication of the Sri Lanka Dome and a large anticyclonic eddy through the array as the meandering of the Summer Monsoon Current (note EKE maximum inferred from altimetric data in Figs. 2a–e). The magnitude of the low-frequency shear is comparable to that of near-inertial shear at all three locations during the SW monsoon. The residual Sres is generally weak relative to the Slow and Sin+. The episodic nature of near-inertial shear events prevent a confident estimation of the magnitude of its seasonal cycle given that only one full annual cycle was recorded. However the seasonal signal in total shear high shear between June and February, and low shear between March and June is robust and consistent across all three moorings.
b. Seasonal cycle in near-inertial energy input
We provide context for the observed near-inertial shear events by using a slab mixed layer model to estimate wind-forced energy input Π in to the mixed layer. We follow Alford (2003) and obtain a slab model estimate of Π, denoted Πslab, by forcing a slab ocean mixed layer model with reanalysis 10-m winds at hourly frequency [Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2); Gelaro et al. 2017] and using climatological monthly mixed layer depths from the Monthly Isopycnal Upper-Ocean Climatology with Mixed Layers dataset (MIMOC; Schmidtko et al. 2013). Details of the solution are described in appendix A.
The SW monsoon winds drive moderate near-inertial flux nearly uniform throughout the Bay (Figs. 2f–j). The largest near-inertial fluxes over the year are confined to latitudes south of 10°N until the months of October and November when strong input associated with the passage of Tropical Cyclone Hudhud (5–14 October 2014) occurs between 12° and 16°N. Intense near-inertial input in the Bay is forced by the passage of cyclonic systems as in the midlatitudes (Alford 2003)—the tracks of Very Severe Cyclonic Storm Madi (7–11 December 2013) and Depression BOB01 (2–6 January 2014) are readily visible in the near-inertial input field for the NE monsoon. There is little to no near-inertial energy flux into the mixed layer during March (northern Bay) and April (entire Bay).
c. Seasonal cycle in mixing
We illustrate the seasonal cycle of turbulence in two ways: (i) by first presenting a time series of daily-averaged observations at a single mooring (NRL5, Fig. 6) and (ii) by presenting a seasonally averaged vertical profile of diffusivity that synthesizes observations from all three moorings (Fig. 7).
1) A prototypical time series (NRL5; 8°N, 88.5°E)
We present the seasonal cycle of winds, turbulence, shear and stratification at mooring NRL5 using daily averaged quantities in Fig. 6. We choose to highlight mooring NRL5 for two reasons. First, it experiences the least blowdown and is least contaminated by the associated space–time aliasing (10–20 m, Fig. 6f). Second, the turbulence quantities in Fig. 6 are inferred from measurements recorded by the deep χpod at 105 m. This instrument is the deepest deployed in the Bay to date, and recorded the longest period of weak turbulence observed during the transition months of March and April. The filtered shear components shown in Fig. 6d are obtained by first subsampling the filtered depth–time fields along the χpods trajectory and then normalizing by 30-day low-pass-filtered N2. Time series recorded at the other moorings are presented in the online supplemental material.
Mixing events during the NE monsoon are episodic and relatively weak (KT ≤ 10−6 m2 s−1) while the transition months of March and April are a period of extremely weak mixing. The χpod measures sustained and relatively high mixing between the months of May and October—a period of energetic mesoscale activity and moderately large near-inertial energy input Π in the south-central Bay (Fig. 2). The Summer Monsoon Current arrived at NRL5 in July, bringing in high salinity water and reducing N2 (Fig. 6d). Its arrival coincided with the rise of KT to sustained values greater than 10−6 m2 s−1. However KT was still consistently below and rarely exceeded the canonical midlatitude thermocline value of 10−5 m2 s−1 (50κT, Fig. 6b). Heat flux is likewise small and exceeds 10 W m−2 for only a few days in the entire year (Fig. 6c).
2) A seasonally varying vertical profile of diffusivity KT
We synthesize all χpod observations along 8°N by constructing approximate seasonally averaged vertical profiles of KT, presented in Fig. 7, as follows:
We label every averaged KT measurement with the density value of the parcel as well as the depth of measurement.
All measurements are then binned by density with bin edges [1018, 1021, 1022, 1022.5, 1023, 1023.5, 1024.25, 1029] kg m−3.
For each season, we construct a PDF of KT in each bin and calculate the mean and standard deviation of the depths of measurement.
The PDFs are presented at the mean depth of the density bin as a vertical profile (Fig. 7). Each PDF is labeled with the mean density in each bin; means and medians are marked by circles and diamonds respectively (see caption).
Some considerations must be kept in mind while interpreting Fig. 7. First, our definition of seasons need not line up perfectly with periods of relatively high or relatively low winds or mixing at every mooring. Second, the χpods on the NRL3 mooring appear to be within the mixed layer and the isothermal but salinity-stratified barrier layer for a few weeks in February. These measurements are excluded since we do not have enough observations to construct meaningful averages for the mixed and barrier layers. Third, Fig. 7 ignores all spatial variability.
Despite these caveats, Fig. 7 presents a useful summary of observed mixing along 8°N. There is a clear seasonal cycle in turbulent diffusivity in the upper 30–100 m at all mooring locations that mirrors the seasonal cycle at NRL5 in Fig. 6. Vertical profiles of both mean and median values of KT are always surface intensified (tables of both means and medians are provided in appendix B). The amplitude of the seasonal cycle in mean diffusivities is roughly an order of magnitude with mean KT ≈ 10−4 m2 s−1 during both monsoons. Median KT is approximately an order of magnitude larger during the SW monsoon as compared to the NE monsoon (10−6 m2 s−1 versus 10−7 m2 s−1) indicating that energetic mixing events are rarer during the NE monsoon. The most striking feature of Fig. 7 is the near-complete lack of mixing in the south-central Bay’s thermocline during the months of March and April—median diffusivity values are only slightly greater than molecular diffusivity κT at depths greater than 60 m. The observation of near-molecular diffusivity at the deep χpod at NRL5 is thus consistent across the other two moorings.
a. A seasonal cycle in shear and turbulence
1) NE monsoon (December–February)
During the NE monsoon, mean KT ≥ 10−5 m2 s−1 (50κT) and medians are lower by one to two orders of magnitude across all three moorings (Fig. 7). All three ADCPs recorded the passage of energetic packets of near-inertial energy in January and February (Figs. 5 and 6e). These packets are likely associated with the passage of Cyclonic Storm Madi and Depression BOB01, whose tracks are visible in the near-inertial input Πslab (Fig. 2f). Between December and February, the deep χpod at NRL5 records relatively weak turbulence with maximum KT ≈ 10−6 m2 s−1. Note that the near-inertial event is weakest at NRL5, Fig. 5i.
2) Transition (March–April)
Arguably our most dramatic observation is that the χpod at 105 m recorded near-laminar flow, that is, near-molecular values of KT in the thermocline during the entire month of April. Similar periods of low to negligible mixing are present at other χpods, but for shorter periods of time. Median in most thermocline density bins (deeper distributions in Fig. 7), so the observation of weak to negligible mixing is consistent across all locations. The transition months of March and April are a period of weak thermocline currents, weak thermocline shear, weak winds, high net surface heat flux, and low near-inertial energy flux (Figs. 2, 5 and 6). These conditions are consistent with the observations of weak mixing. Weak pulses of near-inertial shear are seen in Figs. 5 and 6e; again this is consistent with weak wind forcing at the surface (Figs. 2k–o). Stratification is relatively high at all χpod depths: N2 ~ 5 × 10−4 s−2.
3) SW monsoon (May–September)
With the onset of the SW monsoon, the χpods observe an order of magnitude increase in mean thermocline diffusivity to KT ≈ 10−4 m2 s−1 (500κT) with peak values of KT ≈ 10−2 m2 s−1 (5 × 104κT) between July and September (Fig. 7). The mean diffusivity is two to four orders of magnitude larger than values observed during March and April (Fig. 7). Median thermocline diffusivities during the SW monsoon are larger relative to the NE monsoon by a factor of 5–10 (Fig. 7 and Table C2). The medians are also closer to the means during the SW monsoon (Fig. 7), as compared to the NE monsoon, an indication of frequent energetic mixing events.
The SMC and other mesoscale features are visible in Slow at all three moorings during this season though for differing lengths of time (Fig. 5). Both seasonal mean surface velocities from the OSCAR product and mooring ADCP data show the mesoscale to be prominent especially at NRL3 and NRL4, the two westernmost moorings along 8°N (also see Figs. 2a–e and 8; Wijesekera et al. 2016). This inference is consistent with the ADCP measurements (Fig. 5). At NRL5, elevated mixing occasionally lines up with short periods of elevated low frequency shear between May and October (Fig. 6e).
A few high mixing events are also associated with bursts of elevated near-inertial shear that last for one to two weeks at a time at NRL5 (Fig. 6e). The maximum observed diffusivity and turbulence fluxes in Fig. 6 coincide with the passage of a particularly strong set of near-inertial wave packets that forced enhanced turbulence at the χpod’s depth (25 July–7 August, highlighted in white in Figs. 6b and 6c). Zonal shear and KT for this period of intense mixing are shown in Fig. 9. The elevated mixing coincides with the passage of a set of M2 tide packets that vertically displace the isotherms and the near-inertial shear in Fig. 9b. The effect of tidal vertical advection can be removed by interpolating to isothermal or isopycnal space (Alford 2001). We first interpolate total shear to isothermal space and then filter to isolate the near-tidal and near-inertial bands. Squared near-inertial shear is larger than near-tidal shear on both isotherms by nearly an order of magnitude (Fig. 9c). Vertical advection by the M2 tide is Doppler shifting energy to frequencies in Eulerian spectra (Fig. 4). Hence we interpret the apparent modulation of KT at near-M2 frequency (Fig. 9a) as a result of the M2 tide heaving near-inertial shear layers past the χpod, and not mixing forced by tidal shear.
4) Postmonsoon (October––November)
Energetic turbulence is observed at the NRL3 and NRL4 moorings during October and November (see ρ − 1000 = 22.2, 22.8, and 23.2 kg m−3 bins in Fig. 7). Surface velocities in the OSCAR dataset suggest that the SMC ceases to exist as a continuous inflow through the Bay’s southern boundary at the end of September. Subsequent periods of enhanced low frequency shear in Fig. 6e between October and January appear to be associated with westward propagating features seen in OSCAR surface velocity data (Fig. 8). At NRL3, energetic mixing is recorded by the shallower χpod during October; unfortunately the gap in ADCP coverage prevents us from attributing this turbulence to a specific shear event. At NRL4 the χpods record high mixing during November; again this coincides with a downward propagating near-inertial wave (Fig. 5h). There are two strong wind events at the surface in October and November (Fig. 6a) that are likely responsible for downward propagating near-inertial energy during this season (Fig. 5; also see enhanced Πslab in Figs. 2f–j). At NRL5, there appears to be some mixing associated with a low-frequency shear peak in October (Figs. 6b,e).
Despite the above noted tendency, near-inertial shear did not always correspond with high mixing. For example, negligible mixing is associated with a burst in near-inertial shear in November (Figs. 6b,e). This wave packet appears to have forced turbulence at a depth not sampled by the χpods, if at all. Enhanced near-inertial shear need not necessarily lead to mixing. Alford and Gregg (2001) observe that peak mixing associated with a downward propagating near-inertial wave occurs at the stratification maximum. As they point out, the presence of strong mixing at the stratification maximum is consistent with WKB scaling: the Froude number scales with stratification Fr = S/N ~ N1/4 so shear instability is expected where N is large. A χpod would need to be recording at the right depth relative to the stratification structure to observe turbulence forced by near-inertial energy—a major caveat to our analysis.
There is a strong seasonal cycle in thermocline mixing (Fig. 7) that appears to be linked to a seasonal cycle in thermocline shear (Fig. 5). The seasonal cycle in shear results from (i) the seasonal presence of the Summer Monsoon Current that greatly increases low-frequency shear Slow between July and October, and (ii) episodic energetic downward propagating near-inertial waves observed outside March and April. At times, Slow is of comparable magnitude to near-inertial shear Sin+ (Fig. 5). The seasonal cycle in low-frequency shear is expected from the well-established seasonal spinup and spindown of the SMC and the Sri Lanka Dome (Schott and McCreary 2001; Vinayachandran and Yamagata 1998). A seasonal cycle in near-inertial shear is perhaps expected from the seasonal cycle of winds. However our ADCP record cannot sufficiently characterize the magnitude of the seasonal cycle in near-inertial energy, given the small number of large magnitude near-inertial events at all three moorings (Fig. 5).
b. Weak turbulence in April
The χpod observations of near-molecular diffusivity values in April is consistent with previous in situ finestructure- and microstructure-based profiles of turbulence quantities in the Bay. For example, Jinadasa et al. (2016) report vertical profiles of N2 ≈ 10−3 s−2 and ε ≥ 10−9 W kg−1 from which we infer minimum diffusivity at 16°N, 87°E, 30 m (their Fig. 2). Similarly St. Laurent and Merrifield (2017) also infer for depths between 40 and 120 m by combining a mean vertical profile of ε and mean N collected by glider-based sensors over seven days. Their mean profile of ε shows ε ≥ 10−9 W kg−1 in the top 120 m. Lucas et al. (2016) infer KT ≤ 10−6 m2 s−1 for depths deeper than 40 m using a χpod sensor on a vertical profiling platform (Wirewalker; Pinkel et al. 2011). Finally, finestructure estimates of dissipation estimated using LADCP shear profiles for the GO-SHIP6 I01 section at approximately 10°N in the Bay of Bengal yield Kρ ≈ 10−6 m2 s−1 (5κT; Kunze et al. 2006).
A nondimensional parameter that characterizes the transition from laminar to turbulent flow is the buoyancy Reynolds number Reb = ε/(νN2) (e.g., Itsweire et al. 1993). When ε ≈ 10−9 W kg−1, N2 ≈ 10−3 s−2 (Jinadasa et al. 2016; St. Laurent and Merrifield 2017), and molecular viscosity , Reb ≈ 1. At such low values of Reb, overturning turbulence ceases to exist and total diffusivity asymptotes to κT in direct numerical simulations as well as experiments (e.g., Ivey et al. 2008, their Fig. 2; Itsweire et al. 1993). The microstructure ε measurements of Jinadasa et al. (2016) and St. Laurent and Merrifield (2017) then independently indicate that weakly turbulent flows with near-molecular diffusivities are present in the Bay.
Low thermocline diffusivities are predicted by the finestructure internal-wave scaling of Henyey et al. (1986) and have been observed previously at low latitudes in the Pacific and Atlantic: Kρ ≈ (1–3) × 10−6 m2 s−1 (5–15κT) for latitudes south of 10°N in Gregg et al. (2003). Our lowest observed values during March and April at approximately 80–100-m depths are frequently lower than those observations (Figs. 7 and 6b). The extended period of low KT values is perhaps unsurprising given the observations summarized above and that the transition months of March and April are a period of very low wind energy input, that is, weak inertial shear; weak mean flows, that is, weak low-frequency shear; and considerable stratification (note low S2/N2 in Fig. 5). However, these χpod observations are the first to show that extremely low mixing (KT ≤ 1–10κT) persists for multiple weeks at multiple locations in the south-central Bay (Figs. 6b and 7).
It is possible that an inability to represent the observed low values of mixing has consequences for simulations of the Indian Ocean. Wilson and Riser (2016) find that “negative salinity biases at 50-m depth are associated with positive salinity biases near the surface” between February and May in an assimilative HYCOM simulation of the Bay. They then suggest that “the model is overestimating the strength of vertical mixing in the upper bay for those months and possibly for other times of the year.” This February–May time period is precisely when the χpods observe very little mixing in the southern Bay (Fig. 7). Furthermore, improved upper-ocean state representation in the CFSv2 operational forecast model run by the Indian Institute of Tropical Meteorology for India’s Monsoon Mission program has been shown to improve rainfall forecasts over central India (Koul et al. 2018). Chowdary et al. (2016) show this model to be biased cold in the top 80 m, biased warm below 100 m, excessively saline in the top 500 m and have excessive vertical turbulent heat fluxes in the top 200 m (annual mean). They link the high mixing bias to excess shear and reduced stratification in the model. Climate model configurations that account for the latitudinal variation of internal wave diffusivity noted in Gregg et al. (2003),7 use a background KT ≈ (1–1.7) × 10−5 m2 s−1 (50κT) in the Bay (Danabasoglu et al. 2012, their Fig. 1). This value is an order of magnitude larger than the mean we observe between 80 and 100 m at 8°N during March and April (Table C1; appendix C). Perhaps artificially high background mixing is partly to blame for the biases noted by Chowdary et al. (2016).
c. The importance of turbulence for salt flux at 8°N
Is the observed seasonally enhanced mixing in the south-central Bay’s thermocline between May and November important for the Bay’s salt budget? The climatological depth of the S = 34.75-psu surface at 8°N estimated using the Argo mapped climatology shallows by 20 m or so between May and November relative to other months (Figs. 2k–o and 3f–i). The seasonal shallowing of this isohaline is significant since the observed diffusivity profile is surface intensified (Fig. 7). Mean KT at this isohaline, the thick orange horizontal line in Fig. 7, is approximately 10−4 m2 s−1 between May and November (SW; SWNE). In contrast, KT is an order of magnitude lower during the NE monsoon and near-molecular during the NESW transition. Seasonally averaged surface velocities show the mean path of the SMC to be along the mooring line at 8°N (NRL3, NRL4, and NRL5; Figs. 2a–e). So we now attempt to quantify turbulent salt flux along 8°N in the south-central Bay using our admittedly sparse dataset.
All available hourly averaged estimates of turbulent salt flux are shown as a function of time in both depth and salinity spaces (Figs. 10a and 10b, respectively). Monthly averages of in bins with edges defined by salinity surfaces S = [34, 34.5, 35, 36] psu (Fig. 10c) are interpreted as the mean flux through the 34.25-, 34.75-, and 35.5-psu isohalines, respectively. Bins with less than one instrument month of data are not shown, those with less than two instrument months of data are grayed out, and only one bin has more than three instrument months of data (Fig. 10c). Given the yearlong coverage in the 35 ≤ S ≤ 34.5 salinity bin, we define the high salinity water mass as parcels with salinity S > 34.75 psu (Fig. 10b).8 An estimate of the virtual surface salinity flux S0(E − P), computed using evaporation E from OAFlux (Yu et al. 2008), precipitation P from the TRMM Multisatellite Precipitation Analysis dataset (Huffman et al. 2007), and S0 = 32 psu, and averaged along 8°N between 85° and 90°E is also presented for comparison (Fig. 10d).
The χpods recorded turbulent transport of salt through the S = 34.75-psu isohaline between August and January9 (Fig. 10c). The timing of this turbulent salt flux in Fig. 10d agrees with previous modeling studies that have highlighted the importance of vertical mixing during the SW monsoon and postmonsoon (SWNE) period in restoring the near-surface salinity of the Bay after the large freshwater input in August (Benshila et al. 2014; Akhil et al. 2014; Wilson and Riser 2016). The estimated mean value of is of comparable magnitude to monthly average surface virtual salinity flux S0(E − P) averaged along 8°N between 85° and 90°E (Fig. 10d). For the upper 30 m of the Bay, Wilson and Riser (2016) estimate that the freshwater input is primarily balanced by vertical advection and mixing that averages approximately 2.5 × 10−6 psu m s−1 upward between June and November—this may be interpreted as a flux at the base of the mixed layer. Our observations capture turbulent flux of that magnitude in September and October at depths of approximately 50–75 m (Fig. 10a).
The sampling bias resulting from mooring blowdown suggests that we are underestimating the true magnitude of . For example, all χpods at 8°N are forced down approximately 50 m or so by the Summer Monsoon Current in July during which time they record little turbulent salt flux (Fig. 10a). Inspection of the velocity fields shows that the χpods dive beneath the region of greatest shear in the water column and are likely missing the regions of greatest mixing during this period (Fig. 5). Given these uncertainties, we do not consider Fig. 10c a good estimate of the amplitude of the seasonal cycle of turbulent heat flux but instead interpret it as evidence that climatologically important turbulent fluxes occur in the south-central Bay at least between August and January. Further extended observational efforts are required to properly constrain the magnitude of .
5. Summary and future directions
Yearlong observations of turbulence from moored mixing meters (χpods) revealed a seasonal cycle in upper-ocean turbulence along 8°N in the Bay of Bengal (Figs. 3 and 7 and Table 1). In the Bay’s thermocline, the seasonal cycle of turbulence is influenced by downward propagating near-inertial waves and by low frequency shear associated with the Summer Monsoon Current and other mesoscale features such as the Sri Lanka Dome (Figs. 6, 5 and 9). Multiple χpods recorded extended periods of weak mixing (1–10 κT) between 50- and 100-m depth during the months of March and April—a period of weak winds, weak currents, weak shear, and low near-inertial energy input (Figs. 2, 5 and 6; Tables C1 and C2). It has been hypothesized that mixing in the vicinity of 8°N is necessary to close both heat and salt budgets in the Bay (Shenoi et al. 2002; Vinayachandran et al. 2013; Wilson and Riser 2016). Despite these extended periods of low mixing, our observations suggest that turbulent salt fluxes of the right magnitude are indeed occurring in the south-central Bay (section 3c).
Fully interpreting the observed seasonal cycle of mixing requires understanding the processes that drive and sustain the Bay’s internal wave field. The χpod observations show that enhanced thermocline mixing generally coincides with bursts of near-inertial shear. Understanding the many mechanisms and processes that drive the seasonal cycle of near-inertial shear at depth is thus of prime importance. It is known that the stratified transition layer at the base of the mixed layer can strongly influence the ability of winds to drive energy into the thermocline. Dohan and Davis (2011) studied observations during two different storms. In one case they found that the wind-forced energy deepened the mixed layer with little to no mixing in the transition layer. For a second storm of comparable magnitude, the mixed layer remains unchanged but the transition layer was significantly broadened through mixing in the thermocline. Brannigan et al. (2013) show that shear at the base of the transition layer depends on the alignment between ocean shear and wind stress. Both studies imply that the near-surface freshwater layer that characterizes the Bay could have a significant influence on the internal wave energy that ultimately leads to observed mixing. Lucas et al. (2016) found this to be the case in the Bay—they observed enhanced shear at the base of mixed layer but weak shear at the base of the barrier layer thereby isolating the thermocline from surface forcing. This picture may be complicated by other physics; for example, the interaction of near-inertial energy with lower-frequency mesoscale features in the Bay (Johnston et al. 2016). Another related puzzle is the extended period of weak to negligible mixing during March and April. This observation suggests that the Bay’s internal wave field can be weaker than that expected from the Garrett–Munk spectrum typical of other oceanic regions, again highlighting the need for further study on the Bay’s internal wave field. The Bay’s complex upper-ocean structure, seasonally varying winds, and strong synoptic storm activity offer intriguing opportunities for studying the ocean’s internal wave field and its links to turbulence.
This work was supported by U.S. Office of Naval Research Grants N00014-15-1-2634 and N00014-17-2472. Processed turbulence datasets and EBoB mooring data are available from the authors upon request. We thank two anonymous reviewers as well as the Editor for their fair and critical feedback. We also acknowledge expert engineering and technical contributions from Pavan Vutukur, Kerry Latham, and Craig van Appledorn, and many stimulating discussions with Johannes Becherer, Alexis Kaminski, Sally Warner, Debasis Sengupta, J. Sree Lekha, Dipanjan Chaudhari, Eric D’Asaro, and Jennifer MacKinnon. Many of these discussions were facilitated by a visit to the International Centre for Theoretical Sciences (ICTS) for participating in the program Air-sea Interactions in the Bay of Bengal From Monsoons to Mixing (Code: ICTS/ommbob2019/02). The Ssalto/Duacs altimeter products were produced and distributed by the Copernicus Marine and Environment Monitoring Service (CMEMS) (http://www.marine.copernicus.eu). The OSCAR data were obtained from JPL Physical Oceanography DAAC and developed by ESR (Earth and Space Research). The evaporation product was provided by the WHOI OAFlux project (http://oaflux.whoi.edu) funded by the NOAA Climate Observations and Monitoring (COM) program. Analysis was greatly helped by the use of the xarray Python package (Hoyer and Hamman 2017). Development of xarray was partially supported by NSF Award 1740648 that funds the Pangeo platform.
Near-Inertial Input (Πslab) Calculation
Near-inertial energy input Πslab is calculated following Alford’s (2003) spectral solution of the Pollard and Millard (1970) slab ocean mixed layer model. In this model, mixed layer velocity Z = u + iυ is obtained by solving
where , (τx, τy) is the wind stress, ρ0 is chosen to be 1025 kg m−3, H is the mixed layer depth, f is the Coriolis frequency, and r is a damping coefficient that models the decay of mixed layer near-inertial energy. We follow Alford (2003) and choose r = 0.15f. Near-inertial energy input is estimated by solving for Z in the frequency domain as in Alford (2003). This solution requires specification of wind stress T and mixed layer depth H. We choose to use hourly MERRA-2 reanalysis wind speeds (Gelaro et al. 2017) and monthly mean mixed layer depth from the monthly mean MIMOC climatology (Schmidtko et al. 2013). MIMOC’s mixed layer depth estimates in the open ocean are primarily sourced from Argo profiles (Schmidtko et al. 2013). There are flaws associated with this calculation (Plueddemann and Farrar 2006) but we believe Fig. 2 captures the qualitative large-scale spatial and seasonal variation of the true near-inertial input Π. Another source of errors is that MERRA-2 does not capture the large wind stresses evident in the TropFlux compilation (Kumar et al. 2012) as well as in in situ Research Moored Array for African–Asian–Australian Monsoon Analysis and Prediction (RAMA) mooring sites in the Bay. However one cannot use Tropflux to calculate Π north of approximately 10°N because the inertial period nears 2 days, the Nyquist frequency of the daily resolution TropFlux winds.
Detecting Weak Turbulence
The voltage recorded by the FP-07 temperature sensor in the χpod is differentiated by an analog differentiator circuit and then digitized using an analog-to-digital converter (ADC) whose noise level is 6 voltage levels peak-to-peak. We estimate the spectral energy level of the discretized white noise voltage time series of that amplitude for a 1-s subset of data and combine it with the instrument calibration coefficients as in Becherer and Moum (2017) to get a dimensional spectral energy density level that would result when the ADC records “bit noise.” Multiplying this noise spectral energy density level by frequency bandwidth gives an estimate of the instrument’s “noise floor,” that is, an estimate of the variance in a 1 s interval when the data recorded are bit noise.
Tables of Seasonal Mean and Seasonal Median KT
Current affiliation: National Center for Atmospheric Research, Boulder, Colorado.
Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JPO-D-19-0114.s1.
OSCAR is a diagnostic estimate of near-surface velocity at 5-day frequency that ignores local acceleration and nonlinearities but accounts for geostrophic, thermal wind, and Ekman currents.
DT all-sat-merged Global Ocean Gridded SSALTO/DUACS sea surface height L4 product and derived variables (dataset-duacs-rep-global-merged-allsat-phy-l4-v3).
Recent observations and model simulations describe a second pathway as a persistent subsurface inflow of salty water during the NE monsoon that exists as a superposition of frequent salty intrusion events that average out to a region of broad northward flow of high salinity water west of 85°E (Wijesekera et al. 2015; Jensen et al. 2016).
We choose 152 m to avoid any uncertainties associated with interpolating over the gap in ADCP coverage.
From 0.95() to 1.05().
Global Ship-based Hydrographic Investigations Program.