1. Introduction

The southern Bay of Bengal acts as a critical link between the low-salinity northern part of the bay, and the high-salinity water of the Arabian Sea. Freshwater input from rivers and rainfall must be exchanged with high-salinity waters of the Arabian Sea to the south and west in order to maintain basin-scale mixing. Recent studies (e.g., Schott and McCreary 2001; Bhat et al. 2001; Webster et al. 2002; Rao et al. 2011; Wijesekera et al. 2016a; Vinayachandran et al. 2018) have highlighted the influence of oceanic–atmospheric coupling within the Bay of Bengal (BoB) on the onset and intensity of the Indian Ocean monsoon (IOM). Understanding the exchange of water masses and the associated heat and salinity fluxes that are driving factors for upper-ocean heat content and mixed layer structure of the BoB is of utmost importance to understand and predict the IOM. Subsurface mixing is likely to play an important role in sea surface temperature (SST) and salinity variability within the BoB. Quantification of mixing in the BoB is therefore critical for the understanding of water-mass exchange, and vertical transfer of heat and salinity between subsurface and surface waters. Forcing from the monsoon, coupled with energetic mesoscale and submesoscale features, complicates the regional circulation, and as a consequence, the mechanisms that drive turbulent mixing and water-mass exchange between the BoB and the Arabian Sea are poorly understood. Furthermore, details of how mixing processes regulate and influence air–sea interactions in the southern BoB are not well defined.

Within the BoB, the seasonal reversal of the winds due to the monsoonal cycle (Kumar et al. 2012) is the dominant seasonal feature that defines the large-scale circulation. From May through September, strong southwesterly winds impart wind stress-curl forces, spinning up the Southwest Monsoon Current (SMC), also known as the Summer Monsoon Current. During this time, a semistationary mesoscale cyclonic eddy known as the Sri Lanka dome (SLD) (Vinayachandran and Yamagata 1998; Lozovatsky et al. 2016; Cullen and Shroyer 2019) is formed to the east of Sri Lanka. October through November is a transitional period leading into the northeast monsoon during the months of December–February, while March and April are again transitional periods, marked by low winds.

The large-scale dynamics, forced by the IOM, generate a rich field of mesoscale and submesoscale motions, which, in turn, provide the mechanisms for turbulent mixing. Recent observations revealed the formation and propagation of eddies and Rossby waves in the southern BoB, and their interactions with the SMC (Wijesekera et al. 2016b; Webber et al. 2018; Pirro et al. 2020a,b). Wijesekera et al. (2016b) noted that a cyclonic and anticyclonic eddy pair influenced the location and strength of the SMC during the summer of 2014. Webber et al. (2018) reported that the variability in SMC strength and position is driven by the combination of local forcing (wind stress curl over the Sri Lanka dome) and remote equatorial forcing (Kelvin and Rossby wave propagation). Pirro et al. (2020a) reported an anticyclonic eddy southeast of Sri Lanka in July 2018 with surface velocities up to ~1 m s⁻¹, a size in the meridional direction of ~200 km, and penetration approximately to the depth of the thermocline (~150 m).

The complex and multiscale spatial–temporal geography of upper-ocean mixing in the Bay of Bengal has been the focus of several studies. Warner et al. (2016) observed heightened subsurface turbulence during the southwest monsoon, and during the passage of a storm. Cherian et al. (2020) found turbulent mixing below the mixed layer to be relatively weak throughout much of the year, with elevated signals during the southwest monsoon, and bursts of turbulence due to low-frequency current shear between October and January. Thakur et al. (2019) found a similar pattern of intermittent mixing in yearlong records to the north, which show variability in turbulence observed at diurnal, semidiurnal, and shorter time scales below the mixed layer. Microstructure surveys conducted off the east coast of Sri Lanka revealed relatively weak subsurface dissipation rates (Jinadasa et al. 2016); however, Lozovatsky et al. (2019) found locally elevated turbulence at the periphery of the SLD. A modeling study by Jensen et al. (2016, 2020) found that both the propagation of internal tides and stirring from the local eddy field may be significant mechanisms for mixing in the BoB, and recent mooring observations of hydrographic and current data suggest that interactions between semidiurnal tides and eddies in the southern BoB are likely to enhance turbulent mixing in the thermocline (Wijesekera et al. 2019).

The question arises: given the relative intermittency of elevated turbulent mixing in the southern BoB, what are the key mechanisms behind the subsurface mixing necessary to balance the freshwater input associated with the monsoon? It has been suggested that the southern BoB is a region where enhanced mixing occurs (Vinayachandran et al. 2013); however, it remains unknown how the mesoscale eddy field influences mixing. The aim of the work presented here is to understand the mechanisms of water-mass exchange between the BoB and the Arabian Sea through the context of yearlong, subsurface dissipation estimates from moorings. We focus on a period of mooring deployment from July of 2018 through May of 2019. Long-term measurements of turbulent kinetic energy (TKE) dissipation rates (ε) and temperature variance dissipation rates (χ_T) provide insight into the intermittent nature of mixing at the base of the thermocline in the BoB. Velocity and hydrographic data from two subsurface moorings, each equipped with fast thermistors and microstructure shear probes, are used to quantify ε and χ_T, and to investigate the role of monsoon-driven mesoscale dynamics on mixing. We observe significantly enhanced turbulence during the passage of a subsurface-intensified anticyclonic eddy. During this time, background shear and strain appear to lead to the increased turbulent vertical heat flux.

Yearlong records of turbulence help to bridge the gap between ship-based microstructure surveys, which are typically limited in duration, and studies that focus on larger-scale dynamics through the use of remote sensing, modeling, and mooring arrays. This work attempts to frame the small-scale turbulent dissipation within a larger framework of mesoscale motions in the BoB. Turbulent dissipation rates along with velocity and hydrographic fields were collected as a part of the U.S. Naval Research Laboratory (NRL) research initiative, Role of Indian Ocean on Monsoon Intraseasonal Oscillations (RIO-MISO), which was conducted in collaboration with another research initiative, Oceanic Control of Monsoon Intraseasonal Oscillations in the Tropical Indian Ocean and the Bay of Bengal (MISO-BOB), sponsored by the U.S. Office of Naval Research (ONR). Together, this work is aimed at furthering the understanding of the role of the ocean in modulating the propagation of the monsoon intraseasonal oscillations in the BoB. The observational program includes long-term mooring observations, shipboard oceanic and atmospheric measurements, and autonomous vehicle measurements. Here, we focus on turbulent mixing in the thermocline, below the mixed layer, at semidiurnal to seasonal time scales, exploring how the upper ocean/thermocline influences MISO cycles and monsoon development.

The paper is organized as follows. The moorings and data, as well as the methodology used for our turbulence measurements, are described in section 2. In section 3, background flow conditions such as the SMC, Rossby waves, and eddies are described. In section 3, we also highlight current variability on time scales such as tidal, inertial, and subseasonal, which are identified from wavelet and conventional spectral methods. In section 4, we present shear and temperature microstructure measurements, along with estimates of diffusivity based on finescale parameterizations. Additionally, we use temperature and salinity measurements in conjunction with the microstructure data to estimate turbulent heat and salinity fluxes. Conclusions are presented in section 5.

2. Instrumentation, observations, and methods

As a component of the MISO-BOB campaign, five subsurface moorings were deployed in the Bay of Bengal from July 2018 to June 2019. The spatial layout of the moorings is shown in Fig. 1. These moorings were designed to collect both current and hydrographic data. For the purpose of this study, we focus on two of these moorings, N1 and N5 (Fig. 1), because in addition to the temperature, conductivity, and current velocity instruments, these moorings were equipped with instrumentation to collect both shear- and temperature-based turbulent microstructure observations. Horizontal currents were measured using 300-kHz acoustic Doppler current profilers (ADCPs) for the upper water column, and 75-kHz ADCPs to extend coverage at depth. ADCP locations and details for N1 and N5 can be found in Table 1. The ADCPs provided high-quality velocity data; however, a portion of the upper-water-column velocity data between 115 m and the sea surface was lost at N5 after 14 February 2019 due to instrument failure. For calculations in this paper, hourly velocity data were interpolated to an 8-m grid between depths of 30 and 1200 m.

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Locations of moorings overlaid with SSH anomaly and geostrophic velocities from AVISO products (https://www.aviso.altimetry.fr/en/data/products.html). Moorings N1 and N5, the focus of this study, are contained within the black ellipse.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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Table 1.

Summary of ADCP instruments on moorings N1 and N5. An instrument depth is given in meters. Up is for upward-looking and down is for downward-looking ADCP.

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A combination of instruments was used to measure temperature (T), conductivity (C), and pressure (P). SBE37 (T, C, P), SBE39 (T, P), SBE56 (T), Vemco (T), and RBR solo [dissolved oxygen (DO)] sensors were installed at approximately 5 m intervals between the top of the moorings and a depth of ~ 130 m, at 10-m intervals to 230 m, and at larger intervals in deeper water (Table 1). Two MicroMoors (Fig. 2), for measuring shear microstructure and high-frequency temperature, were located on moorings N1 and N5 in the thermocline, below the mixed layer at approximately 105 and 145 m, respectively. The MicroMoor is a 4.5-m-long instrument platform, with a weight of 282 kg and a net positive buoyancy of 166 kg (e.g., https://rocklandscientific.com/products/moored-systems/nemo/). The MicroMoor was attached to the mooring line via a swivel and bridle on both the top and bottom. The bridle acts as a pivot and permits the MicroMoor to remain level during mooring blowdown. The MicroMoor carries three main instrument systems; first, a Rockland Scientific (RSI) MicroRider turbulence sensor package located in the nose section of the float and consists of two air-foil shear probes, and two FP07 fast thermistors. Velocity-shear and acceleration measurements were taken continuously at 512 Hz for 10 min every hour. Temperature pressure, tilt, and yaw sensors along with a magnetometer recorded instrument orientation at 256 Hz. Reference temperature and conductivity were measured via a tail-mounted Sea-Bird Electronics (SBE) 3 temperature sensor and SBE 4 conductivity cell. Third, an electromagnetic current meter mounted on the tail of the instrument provided horizontal current velocity. Due to issues relating to vehicle pitch, ADCP velocities were used in the computation of horizontal wavenumbers in this paper. All these datasets, excluding the ADCP velocities, were recorded inside the MicroRider. Further details of the MicroMoor float are given in Lueck et al. (2015). The shear probes are used to determine the TKE dissipation rate ε, while the high-frequency temperature time series are used to compute the horizontal temperature gradient. Temperature gradient spectra are then integrated in order to determine the temperature variance dissipation rate χ_T.

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Diagram of the MicroMoor float. Arrows show the position of the MicroRider (microstructure package described in the text), battery pack, and secondary SBE temperature/salinity sensors. In the photo, the MicroRider is protected by a tubular cover with a burn wire released within a day of deployment. Illustration provided by Rockland Scientific Inc.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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a. Microstructure processing

Velocity shear and temperature measurements were processed using software provided by Rockland Scientific (Lueck 2016). We provide a brief overview of this processing here. A comprehensive explanation of the data processing algorithms and procedures are available in RSI’s Technical Note 028 (Lueck 2016). We estimate the variance from the measured shear and temperature gradient spectra record in half-overlapping 8-s segments. Each of these is further subdivided into three half-overlapping 4-s subsegments, which are detrended, cosine windowed, and transformed into shear power spectra using a fast Fourier transform (FFT). Each set of the three spectra is averaged to create a single shear or temperature gradient power spectra. Coherent acceleration signals are removed from the shear spectra using the Goodman et al. (2006) algorithm. This spectral processing was chosen to best eliminate the effects of an apparent 10-s vertical oscillation observed on the MicroMoor platform. Both shear and temperature-gradient frequency spectra are transformed into wavenumber (k) space using current velocities from the ADCP instrument for each 10-min MicroMoor data segment and assuming Taylor’s frozen-field hypothesis is k = ω/U, where ω is the frequency and U is the flow speed relative to the sensor. Because of ballasting issues of the MicroMoor, the float tilted upward during the low velocity flow; hence, our calculation of TKE dissipation rates were limited to periods with the current velocity above 0.15 ms⁻¹, and an instrument pitch angle of less than 15°. Shear spectra are fitted to Nasmyth spectra (e.g., Nasmyth 1970; Wolk et al. 2002) and integrated, providing an estimate of the TKE dissipation rate ε:

$\epsilon ={\displaystyle \frac{15}{2}}\hspace{0.17em}\nu {\displaystyle {\int }_0^{\infty }\mathrm{\Psi }\left(k\right)\hspace{0.17em}dk},$(1)

where Ψ(k) is the wavenumber spectrum of horizontal shear (Lueck 2016; Osborn 1974) and ν is the kinematic viscosity of seawater. In practice, an upper integration limit is necessary to exclude electronic noise which dominates the spectra at large wavenumbers. A third-order polynomial was fit to the shear spectra in order to determine the location of the spectral minimum, an indicator for the onset of noise domination (Lueck 2016). Conversely, high-frequency gradient spectra are integrated to provide an estimate of the rate of temperature variance dissipation χ_T:

${\chi }_T=6D{\displaystyle {\int }_0^{\infty }{\varphi }_{Tx}\left(k\right)\hspace{0.17em}dk},$(2)

where ϕ_Tx is the temperature gradient wavenumber spectra (Dillon and Caldwell 1980; Moum and Nash 2009) and D is the thermal diffusivity. To better resolve temperature microstructure, we limit our estimates of χ_T to periods where the current magnitude is below 0.25 m s⁻¹. Temperature gradient spectra are integrated between 0.5 and 10 Hz. Temperature gradient spectra are also iteratively fit to the theoretical Batchelor spectrum (Batchelor 1959). We find both methods of determining χ_T produced similar results and, for the purposes of this paper, only present estimates based on the iterative fits to the theoretical Batchelor spectrum. We then estimate eddy diffusivity using χ_T and ε, respectively:

$K_T={\displaystyle \frac{{\chi }_T}{2T_z^2}},$(3)

$K_{\rho }={\displaystyle \frac{\mathrm{\Gamma }\epsilon }{N^2}}$(4)

(Osborn and Cox 1972; Osborn 1980), where T_z is the local vertical temperature gradient determined from the temperature sensors on the mooring line, the mixing efficiency of Γ= 0.2 (Gregg et al. 2018), and N is the buoyancy frequency calculated using CTDs on the mooring line. Sample temperature-gradient and shear spectra are shown in Figs. 3 and 4. In the top two panels of Fig. 3, observed temperature spectra are overlaid with the theoretical Batchelor fit (black curve) (e.g., Dillon and Caldwell 1980). The upper-left panel shows a temperature gradient spectrum from a period of low turbulence, and the right shows spectrum during a more energetic period. The portion of the observed spectra highlighted in magenta represents the area to be fit to determine χ_T. In the bottom panel, both spectra are shown in nondimensional form, as in Dillon and Caldwell (1980), where q = 3.9, and k_b = (εν⁻¹D⁻²)^1/4 is the Batchelor wavenumber. In Fig. 4, shear spectra are overlaid with Nasmyth curves (e.g., Nasmyth 1970; Wolk et al. 2002). The thick blue curves show the denoised shear spectra, while the black lines show Nasmyth spectra. The panels on the left depict spectra taken from a time of relatively weak turbulent mixing, while the right panels show spectra during periods of stronger turbulence.

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Examples of temperature gradient wavenumber spectrum (orange and green lines) from a thermistor attached to the MicroMoor/MicroRider package. (a) The spectrum depicts a period of relatively weak turbulence. (b) The spectrum depicts a period of strong turbulence. The thin black lines are the fitted theoretical Batchelor spectrum. (c) Both spectra in nondimensional form, along with spectra averaged over the 10-min period from which each example in (a) and (b) was taken. The χ_T estimates are in units of °C² s⁻¹, and TKE dissipation rates ${\epsilon }_{{\chi }_T}$ derived from χ_T are in W kg⁻¹.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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The wavenumber spectra of two orthogonal components of the shear from the MicroMoor/MicroRider package during a period of (left) low and (right) high turbulence. Clean shear spectra are shown with blue lines. The dotted blue lines are the spectra prior to coherent-noise removal. The thin green and red lines show the spectra of acceleration used to remove noise. The dimensional Nasmyth spectra are depicted by solid black lines for the estimated rate of TKE dissipation (W kg⁻¹) listed above each plot.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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3. Background flow characteristics

Figures 5 and 6 show AVISO sea surface height (SSH) and velocity and temperature at moorings N1 and N5, respectively, during the mooring deployment period. Both N1 and N5 exhibit a host of strong dynamical features. At N1, during August, the SMC penetrates to a depth of 150 m. As the southwest monsoon spins down, both moorings exhibit periodic low-frequency flow reversals. These reversals occur on time scales of 20–40 days, and are consistent with the signature of westward-propagating Rossby waves and eddies (Vinayachandran and Yamagata 1998; Chen et al. 2017). The passage of these eddies/Rossby waves appears as a vertical banding in the meridional and zonal components of the current velocity in Figs. 5 and 6 with periods ranging from a few weeks to a month. Two eddy-like surface features appear in the signals at N1 and N5 during summer. One is a large anticyclonic eddy to the southeast of Sri Lanka, which is expressed as a positive SSH anomaly (SSHa) at N1, and the other is an adjacent cyclonic eddy, referred to as the Sri Lanka dome, to the east of Sri Lanka, which can be seen by the negative SSH anomalies at N5. During the period from September through October, the eddy at N1 exhibits a subsurface-intensified velocity core with the highest velocity (~0.7 m s⁻¹) occurring at a depth of ~200 m. The Sri Lanka dome is constricted between eastern Sri Lanka and the central BoB, and appears to move northward during the encroachment of the anticyclonic eddy. A Hovmöller diagram for AVISO SSHa (Fig. 7) clearly shows the westward propagation of the low-frequency features apparent in the velocity sections (Figs. 5 and 6). Westward-propagating features during July and August are noted in Pirro et al. (2020a), and are consistent with topographically trapped Rossby waves; however, their occurrence is somewhat earlier than the signals described in this paper, which appear during September and November.

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Time series of AVISO sea surface-height anomaly (SSHa), depth profiles of current zonal (U) and meridional (V) velocities, and temperature as a function of depth and time at N1.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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As in Fig. 5, but for N5.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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SSH anomaly from AVISO at the approximate latitude of N1 and N5 plotted along the longitude range (82°–91°E). Dotted white lines represent propagation speeds of 0.45 ms⁻¹ during February–March 2019 at 82°–87°E (top line) and 0.12 m s⁻¹ during September–November 2018 at 82°–87°E (bottom line). Vertical dashed lines indicate the longitudes of N1 (right line) and N5 (left line).

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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To further illustrate variability over time, a continuous wavelet transform (Torrence and Compo 1998) was performed at N1 for currents and temperature at a depth of 116 m. Figure 8 shows kinetic energy (top panel), and temperature variance wavelet spectra. The intermittent nature of high-frequency motions throughout the year can clearly be seen, where increases in kinetic energy (KE) appear in “burst” events. Although dominant persistent features can be seen at semidiurnal and near-inertial periods for KE and at semidiurnal periods for temperature variance, there is considerable variation over time. During periods of increased variance at these frequency bands, elevated variance appears to extend to higher frequencies, filling out the internal–gravity wave spectrum between f and N.

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The wavelet variance spectra of (top) velocity and (bottom) temperature at a depth of 116 m at N1. In both subplots, the horizontal black lines indicate (from top to bottom) semidiurnal, diurnal, inertial, and spring–neap periods.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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During September–October, a subsurface intensified energetic anticyclonic eddy is observed at N1. The eddy is visible as a positive SSHa on 3 October 2018 (Figs. 1 and 5, top panel). High-frequency KE appears to be elevated during this time; however, the strongest high-frequency temperature variance appears to occur somewhat earlier during September. The mixed layer depth is 80–100 m during September and October, then decreases in depth during October, reaching a minimum depth at the beginning of November of around 50 m. The deepening of the thermocline during the anticyclonic eddy may explain the decreased high-frequency temperature variance seen during this time, as variations in temperature may be underresolved if the instrument is located within the transition to the mixed layer.

High-frequency motions such as near-inertial oscillations and semidiurnal and diurnal tides can be seen intermittently at both N1 (Fig. 8) and N5 (not shown). At these frequencies, there is a high degree of temporal variability in velocity. Figure 10 shows area-preserving frequency–depth rotary spectra of the velocity at N1, taken about one month apart. During the period of 15 September–29 October 2018, variance in the anticyclonic eddy is elevated at both diurnal and semidiurnal frequencies, and the entire internal–gravity wave spectrum is elevated approximately to a depth of 100 m. Additionally, the semidiurnal band is elevated to about a depth of 500 m. Semidiurnal energy is higher at depths below 200 m in the clockwise component than in the counterclockwise component. A low-frequency subsurface maximum corresponding to the depth of the eddy can clearly be seen around 200 m at frequencies below f, from 0.03 to 0.1 cpd. In contrast, roughly one month later (15 November–29 December 2018, Fig. 9), the velocity spectra show weaker energetics at diurnal frequencies, and elevated variance in the semidiurnal band to a depth of 400 m. During both periods, the clockwise velocity spectra have near-surface elevated peaks around f, indicating downward-propagating near-inertial motions.

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Variance preserving depth–frequency rotary spectra of velocity at N1. (top two panels) Clockwise (CW) and counterclockwise (CCW) spectra during the occurrence of an energetic, anticyclonic eddy, and (bottom two panels) the CW and CCW spectra for the period after the passage of the eddy, taken one month later. The vertical black lines (from left to right) indicate spring–neap, inertial, diurnal (K₁, O₁), and semidiurnal (M₂, S₂) periods.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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4. Observations of turbulent mixing

Estimates of long-term turbulence are presented in three ways. First, we present 10-min averages, taken at hourly intervals of the turbulent temperature variance dissipation rates and turbulent kinetic energy dissipation rates, from the MicroMoor instrumentation located on N1 and N5 (Figs. 10 and 11, respectively). Next, we present estimates of diffusivity calculated using a finescale parameterization at N1 and N5 (Figs. 14 and 16) down to 500 m. Last, we present long-term estimates of diffusivity using the MicroMoor-derived χ_T and ε values according to Eqs. (3) and (4). We then compare diffusivity estimates made from finescale parameterizations to the microstructure diffusivity estimates (Figs. 15 and 17).

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Time series of (top) the temperature variance dissipation rate χ_T (°C² s⁻¹) and (bottom) the turbulent kinetic energy dissipation rate ε (W kg⁻¹) at mooring N1. The red and blue markers represent 10-min averages of χ_T and ε, respectively, estimated for each individual thermistor and shear probe contained on the MicroMoor. The darker color dots represent a moving 3-day average of χ_T.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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As in Fig. 10, but for N5. Due to probe failures, only estimates from one thermistor and one shear probe are shown.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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b. Comparison with mixing estimates from finescale dissipation models

Finescale estimates are made from shear and strain based on internal-wave statistics as described earlier in the manuscript [Eqs. (5)–(8)]. Because our estimates of the strain field are based on temperature, care must be taken to examine the relative contributions of salinity to density. In regions where salinity dominates, density may cause inaccuracies in our finescale strain estimates based on temperature. Because of this, we first present an analysis of the Turner angle (Ruddick 1983) at the depth of the MicroMoors at both N1 and N5 (Fig. 12). The Turner angle provides a way for estimating the relative contributions of temperature and salinity on density. If the Turner angle is near 45°, the salinity contribution to density is negligible. For a Turner angle between 0° and 45° and between 45° and 90°, the salinity contribution increases, but temperature still dominates. Results for both N1 and N5 indicate that the use of temperature to estimate strain is valid for most of the deployment; however, from April through the end of the deployment, the Turner angle at N5 reaches 90°, indicating the dominance of salinity on the density. During this time, the use of isotherms as a proxy for isopycnals may lead to errors in our finescale estimates.

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Turner angle (Tu) computed at the depth of the MicroMoors for moorings (top) N1 and (bottom) N5. Hourly averages are shown in blue, and daily averages are in red. Horizontal dashed lines represent Tu = 45°, and Tu = 90°, respectively.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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Figures 13 and 14 show the finescale-derived diffusivity for the upper 500 m of the water column, along with the strain ratio and shear utilized for the diffusivity estimates. At both moorings, the diffusivity is typically at or below our estimated noise floor of ~10⁻⁶ m² s⁻¹; however, there are several periods indicating elevated dissipation between 100 and 400 m. At N1, the subsurface shear is elevated for the duration of the SMC (July–September), and the diffusivity is not elevated above background levels until increased straining due to the background eddy field in October when turbulent mixing becomes strongest at the depth of the MicroMoor. It should be noted that there are several other events of similar magnitude that occur at other depths that do not seem to be associated with the presence of an eddy. For the purpose of this paper, we choose to focus on the vicinity of the MicroMoors, because at those locations, we have microstructure data to compare with our finescale estimates. To examine the relative contributions of strain and shear to mixing, we compare the frequency spectra of the layer averaged shear (Figs. 15a,c) and strain (Figs. 15b,d) at N1. These averages were calculated from shear and strain estimates between 120 and 140 m that were close to the depth of the MicroMoor. The top two subplots (Figs. 15a,b) represent shear and strain spectra taken during a period of increased mixing, that is between 15 September and 29 October 2018. Subplots in Figs. 15c and 15d show spectra evaluated between 15 November and 29 December 2018, which was a time of relative quiescence. We note a broadband increase in both shear and strain during the period of increased mixing. Total shear and strain variance increased by 49% and 43%, respectively, when integrated across all frequencies during the period of the increased mixing. When viewed as individual frequency bands, there was 135% increase in strain variance and an 85% increase in shear variance at subinertial frequencies. Subinertial strain accounted for 9% of the total variance during the quiescent time period, and 35% of the total variance during the passage of the eddy. Additionally, there was a 73% increase in shear variance between 0.8f and 1.2f, and during both time periods this near-inertial frequency band contained ~10% of the total shear variance. Wijesekera et al. (2019) examined both shear and strain variance in a similar area between December 2013 and August 2015. During anticyclonic eddies, Wijesekera et al. (2019) found shear variance to be elevated by between 50% or by a factor of 2, and during cyclonic eddies, strain variance was found to be elevated by over a factor of 2, particularly in the semidiurnal band. Although we found slightly more enhancement of strain during an anticyclonic eddy, these results reinforce the idea that strain, shear, and subsequent turbulent mixing are highly influenced by the background eddy field in the southern BoB. Figure 16 compares diffusivities calculated using shear and temperature microstructure, with diffusivities estimated from finescale parameterizations averaged over a 40-m window surrounding the depth of the MicroMoor. Although the finescale parameterizations appear to underestimate the magnitude of turbulent mixing, both microstructure measurements and finescale estimates show that intermittent ~30-day events such as the one observed in October dominate the yearly mixing budget. Measurements at N1 suggest that for most of the year, turbulence is relatively weak, resulting in diapycnal diffusivities near those of molecular diffusion. Our shear based estimates of diffusivity are made only at high relative flow velocities and thus likely represent an overestimate of total mixing. Conversely, our temperature microstructure based diffusivity estimates likely represent an underestimate. However, if we use both estimates together to estimate the average diffusivity over the whole record, the 11-month average is ~10⁻⁴ m² s⁻¹, indicating the importance of relatively infrequent eddy events and their interactions with finescale motions to drive the mixing within the BoB.

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Finescale (top) eddy diffusivity, (middle) strain ratios, and (bottom) shear calculated at N1. The black lines are 5-day low-passed isotherms drawn approximately every 50 m.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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As in Fig. 13, but for N5.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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Variance preserving (a),(c) shear and (b),(d) strain spectra at N1 averaged between 120 and 140 m. (top) The spectra calculated from shear and strain estimates during the passage of an anticyclonic eddy (15 Sep–29 Oct 2018). (bottom) Shear and strain spectra calculated for a period of low eddy activity (15 Nov–29 Dec 2018). The vertical black lines (from left to right) indicate spring–neap, inertial, diurnal (K₁, O₁), and semidiurnal (M₂, S₂) periods, and in (c) and (d) the first harmonic semidiurnal overtide are also shown.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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Low-frequency background variability shown with (top) the 20° isotherm and (bottom) long-term estimates of diffusivity using the MicroMoor microstructure data derived χ_T and ε values at N1 along with diffusivity estimates calculated from the finescale parameterization shown as black dots. Estimated diffusivities lower than molecular diffusion are not shown.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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At N5, as at N1, turbulence appears to be intermittent, with prolonged periods of quiescence punctuated by large mixing events. At N5 (Fig. 11), values of temperature variance dissipation are largely below χ_T = 10⁻⁹ °C² s⁻¹ with elevated peaks during July, September–October (possibly corresponding to the anticyclonic eddy during September and October, Figs. 6 and 7), and in January (associated with a low-frequency downwelling event or anticyclonic eddy, Figs. 6 and 7). During periods of isotherm upcropping, the subsurface strain field at N5 becomes elevated (middle panel in Fig. 14). At these times high-turbulence levels are observed at the MicroMoor depth. During the event in October, the energetic anticyclonic eddy propagated west into the region of N5, which coincided with the northward movement of the SLD. Figure 17 (as in Fig. 16 but for N5) shows diffusivity estimates from both shear and temperature microstructure, along with diffusivity estimated from finescale parameterizations at the depth of the MicroMoor. In this case, finescale parameterizations appear to overestimate the magnitude of turbulent mixing; however, all diffusivity estimates agree in that both microstructure measurements and finescale estimates show that a few isolated events, within the upper 200 m, dominate the mixing over the course of the deployment.

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As in Fig. 16, but for N5.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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c. Estimates of vertical turbulent heat and salinity flux

Using our microstructure estimates of diffusivity, we follow the methodology of Cherian et al. (2020) to examine the relative importance of turbulent mixing to the seasonal cycle of heat and salt fluxes. Heat flux $J_q^t$ and salt flux $J_s^t$ are estimated from our dissipation time series using

$J_q^t=-{\rho }_0{c}_p{K}_T{T}_z,$(9)

$J_s^t=-{\rho }_0{K}_s{S}_z,$(10)

where c_p is the heat capacity of seawater, K_T and K_s are the eddy diffusivities for temperature and salinity, T_z is the local vertical temperature gradient, and S_z is the local vertical salinity gradient, and ρ₀ is the density seawater. As in Cherian et al. (2020), we made the assumption that turbulence mixes all scalars at the same rate so that the turbulent diffusivities of both temperature and salinity are equal, and that K_T = K_ρ. This allows us to use both shear and temperature microstructure to estimate long-term salinity and heat flux at both N1 and N5.

Figures 18 and 19 show hourly averaged salt flux (top panels), heat flux (middle panels), and the cumulative sum of salt and heat flux (bottom panels) derived from shear and temperature microstructure. At N1, the highest values of both salt and heat flux occur during the anticyclonic eddy in October. At this time, about 10% of the data exceeds 5 × 10⁻⁵ psu m s⁻¹, and the 10-min averages of the salinity flux values reach ~10⁻¹ psu m s⁻¹. The monthly average of the salinity flux over the course of this event is ~5 × 10⁻⁶ psu m s⁻¹. During this time, 10% of 10-min averages of the heat flux exceed 5 W m⁻², while maximum heat flux values exceed 100 W m⁻², and daily averages peak above 20 W m⁻². These values appear to be larger than those reported in Cherian et al. (2020) by about a factor of 2. For both salinity and heat, the time period during September–October is responsible for over 90% of the total fluxes observed during the mooring deployment. At N5, the highest values of both salt and heat flux occur during the transition from negative to positive SSH anomaly in January. This transition of SSH anomaly may indicate that the mooring is located near the edge of a cyclonic eddy (or remnants of the SLD) during this time period. Over this period, instantaneous salinity flux values reach ~10⁻³ psu m s⁻¹, while the monthly average of the salinity flux over the course of the January mixing event is ~5 × 10⁻⁷ psu m s⁻¹, about a factor of 10 smaller than the values seen at N1. The same is true for the cumulative flux values displayed in the bottom panels of Figs. 18 and 19. At N5, instantaneous heat flux values exceed 100 W m⁻², and daily averages reach 10 W m⁻² during the strongest mixing. Similarly to N1, the bulk of the total flux for both salinity and heat occurs in a few short isolated events.

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Long-term estimates of the (top) salt flux and (middle) heat flux at mooring N1. (bottom) The cumulative sum of the heat flux (dashed red line) and salt flux (solid blue line). The largest markers (top two panels) show fluxes derived diffusivities obtained from temperature based microstructure, while smaller colored markers outlined in black are overlaid showing shear-based diffusivity estimates when available. In the top two plots, the MicroMoor depth is plotted on the y axis to provide reference to the background conditions.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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As in Fig. 18, but for N5.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0280.1

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5. Conclusions

Long-term observations of turbulence in the thermocline at two locations in the southern BoB were made using both moored microstructure measurements and finescale parameterizations of strain and shear. These observations span the period of July 2018–June 2019. The locations of these moorings allow for insight into subsurface mixing during the annual cycle of the Indian Ocean monsoon. At times, the microstructure and finescale estimates of turbulence show similar broad patterns and magnitudes, and at other times both estimates disagree by orders of magnitude. Furthermore, the data presented in this paper revealed a pattern of turbulent mixing linked to both the background eddy field, and high-frequency motions. At N1 (8°N, 85.75°E), we observed the passage of an anticyclonic eddy, which contained a particularly energetic subsurface flow to a depth of 200 m during October 2018. During this period, we also observed increases in high-frequency KE which coincided with heightened-turbulence levels. We found that at the depth of the MicroMoor, the bulk of the turbulent mixing during the yearlong record occurred at that time. At N5 (8°N, 83.75°E), the low-frequency field was dominated by alternating cyclonic and anticyclonic motions as the SLD moved from south to the north. Times of elevated turbulence appeared to coincide with transitions between these background flow regimes. Our main inferences are as follows:

1. Throughout much of the year, diffusivity in the southern BoB was low, i.e., K_ρ ~10⁻⁶ m² s⁻¹ or below, both within the SMC and SLD. This finding agrees with the bulk of previous studies (Cherian et al. 2020; St. Laurent and Merrifield 2017). However, during the period of the mooring deployment, several significant mixing events were observed that are associated with much-higher diffusivity values above ~10⁻³ m² s⁻¹, resulting in overall yearly averaged diffusivities near ~10⁻⁴ m² s⁻¹.

2. Lozovatsky et al. (2019) reported weak diffusivities (<10⁻⁵ m² s⁻¹) within the interior of the SLD but numerous patches of turbulence with diffusivities above ~10⁻⁵ m² s⁻¹ at the dome’s periphery. This is consistent with our findings, especially at N5. During periods of transition from positive to negative SSH anomaly, the edge of the SLD was collocated with the mooring. At these times, we observed elevated eddy diffusivities between ~10⁻⁵ and ~10⁻³ m² s⁻¹.

3. The increase and deepening of strain and shear fields that correspond with elevated turbulence during the passages of mesoscale eddies suggests that the low-frequency modification of the background field is a key ingredient for the generation of enhanced subsurface turbulence in the southern BoB. Intensification of both strain and horizontal shears generated by mesoscale eddies such as the SLD could lead to elevated turbulence and mixing compared to areas of low mesoscale activity as shown by the dramatic increase in low-frequency strain during the passage of an anticyclone eddy, along with the overall broadband increase in both strain and shear variance during that time. Furthermore, near-inertial, diurnal, and semidiurnal kinetic energies were elevated during times of increased turbulent mixing within the anticyclonic eddy. This suggests that dynamic interactions between the internal–gravity wave field and the eddy are crucial contributors to turbulent mixing.