1. Introduction
Shear-driven instabilities associated with internal waves and double diffusion are the primary source of diapycnal mixing in the stratified ocean interior (Schmitt 1994; Timmermans et al. 2003; Radko 2013; MacKinnon et al. 2017; de Lavergne et al. 2019). Tides and wind are the primary energy sources for the oceanic internal wave field (Chaigneau et al. 2008; Whalen et al. 2012; MacKinnon et al. 2017; de Lavergne et al. 2019). In a statically stable water column, where both temperature and salinity either increase or decrease with depth, double diffusion occurs due to approximately 100-times-faster molecular diffusion of heat than the salt (Zhang et al. 1998; Radko 2013). Salt fingering and diffusive convection are the two forms of oceanic double diffusion. When warm and salty water overlies cold and fresh water, the water column is conducive for the formation of the salt fingering form of double diffusion. Whereas the diffusive convection form of double diffusion occurs in the water column when colder and fresher water overlies warmer and saltier water.
Past studies have shown that much of the interior World Ocean is conducive for the formation of double-diffusive mixing (Zenk 1970; Tait and Howe 1971; Zodiatis and Gasparini 1996; Schmitt et al. 1987; Padman and Dillon 1987; Schmitt 1994; Schmitt et al. 2005; Rudels et al. 1999; You 2002; Timmermans et al. 2003; Sirevaag and Fer 2012; Lee et al. 2014; Fernández-Castro et al. 2015; Walesby et al. 2015; Nagai et al. 2015; Bebieva and Timmermans 2016, 2019; Guthrie et al. 2017; Taillandier et al. 2020). Based on the monthly climatology of temperature and salinity data, You (2002) showed that approximately 44% of the World Ocean is conducive for double-diffusion processes.
A well-defined staircase-like structure consisting of homogenous well-mixed temperature and salinity “layers” separated by thin “interfaces” with a strong vertical gradient of temperature and salinity is the typical characteristic of the water column where active double-diffusive processes exist (Tait and Howe 1971; Zodiatis and Gasparini 1996; Schmitt et al. 2005; Sirevaag and Fer 2012; Scheifele et al. 2014; Bebieva and Timmermans 2016; Shibley et al. 2017; Shibley and Timmermans 2019; Taillandier et al. 2020). However, such staircases are expected to exist only when shear-driven turbulence is weak (Padman and Dillon 1987; Inoue et al. 2007; Radko 2013) because strong turbulence can erode the staircases more rapidly than double diffusion can create them (Ruddick 1985). Nevertheless, numerical experiments and observations have shown that double-diffusion instability can coexist with shear-driven turbulence (Linden 1974; St. Laurent and Schmitt 1999; Smyth and Kimura 2011; Bebieva and Timmermans 2016). Based on the Tracer Release Experiment data in the North Atlantic, St. Laurent and Schmitt (1999) have shown the coexistence of double-diffusion and turbulent mixing regimes without a well-defined salt finger staircase. Based on the measurements from vertically rising microstructure profiler in the Seychelles–Chagos Thermocline Ridge region in the Indian Ocean, Walesby et al. (2015) demonstrated the existence of diffusive convection form of double diffusion with a weak staircase in the upper 20 m of the water column.
In oceanic regions where very weak shear-driven mixing exists, double diffusion provides a vital source of energy for vertical fluxes of heat, salt, nutrients, and dissolved substance (Sirevaag and Fer 2012; Lee et al. 2014; Fernández-Castro et al. 2015; Bebieva and Timmermans 2016; Taillandier et al. 2020). Hence, in these regions, double-diffusion processes play a critical role in determining the physical, biological, and chemical state of the ocean (Ruddick and Gargett 2003). Hence, improved knowledge of double-diffusive mixing will facilitate better representation of these processes in the ocean component of coupled ocean–atmosphere models used for seasonal and climate time-scale predictions and in coupled physical–biogeochemical models used for the simulation of ecosystem state, potentially leading to better simulations of the physical and biogeochemical state of the ocean.
The hydrography and circulation of the Arabian Sea (AS), a semi-enclosed basin in the northern Indian Ocean, is primarily modulated by the seasonally reversing low-level atmospheric circulation (Lee et al. 2000). Moreover, the substantial evaporation over precipitation in the northern region of the AS, and nearby marginal seas, the Persian Gulf and the Red Sea, leads to the formation of different water masses (Rochford 1964; Shenoi et al. 1993; Shetye et al. 1994; Kumar and Prasad 1999). Based on the location of the formation and its temperature, salinity, and density characteristics, the primary water masses identified in the upper 1000 m of AS are the Arabian Sea High Salinity Water (ASHSW; σθ, 22.8–25 kg m−3; θ, 24°–28°C; S, 35.3–36.7) between the surface and 100 m, Persian Gulf Water (PGW; σθ, 26.2–26.8 kg m−3; θ, 13°–19°C; S, 35.1–37.9) between 200 and 400 m and the Red Sea Water (RSW; σθ, 27.0–27.4 kg m−3; θ, 9°–11°C; S, 35.1–35.7) between 300 and 800 m (Rochford 1964; Shenoi et al. 1993; Kumar and Prasad 1999). Besides, the presence of Bay of Bengal low-salinity water with salinity 33–34 was also reported in the southeastern AS (SEAS) (Shenoi et al. 2005; Kurian and Vinayachandran 2006). These water masses lead to the formation of a rich structure of thermohaline interleaving layers with alternating layers of warm saline water and cold fresh water in the AS (Centurioni et al. 2017). Also, the AS is one of the most biologically productive oceanic regions in the World Ocean and hosts one of the most intense perennial oxygen minimum zone (Madhupratap et al. 1996; Wojtasiewicz et al. 2018).
As demonstrated by Whalen et al. (2012), the interior of the eastern AS (EAS) is one of the places where weak shear-driven mixing persists. Hence, in the EAS, double diffusion may be a dominant process for vertical fluxes of heat, and its importance needs to be studied. Despite the potentially significant contributions of double diffusion on vertical mixing, no systematic measurements to quantify the importance of double-diffusive processes have been made in the EAS. This paper describes the first measurements of temperature and shear microstructure in the EAS using a time series at 18.4°N, 67.4°E and along a few tracks in the EAS during winter and spring (Fig. 1). The study further describes the nature and characteristics of double diffusion there and its spatial distribution.
Monthly average of (a) SMAP sea surface salinity, (b) MW IR OI SST (°C) and ASCAT wind vectors (m s−1), and (c) OSCAR surface current vectors (m s−1) during (left) winter (January 2019) and (right) spring (May 2019). The black contour in (a) is drawn to represent the core of ASHSW having salinity 36. In (a) cruise track is marked as a thin white line. The black open circles in (a) represent the microstructure stations, and the green closed circle represents the time series station at 18.4°N, 67.4°E. For convenience, the cruise transects during winter 2019 are divided into five segments (W1, gray; W2, green; W3, light blue; W4, purple; and W5, yellow). The cruise transect during spring 2019 (S1; dark blue) is marked in (a). The shading in (d) represents the climatology (1979–2018) of TropFlux net surface heat flux (W m−2) during (left) January and (right) May.
Citation: Journal of Physical Oceanography 52, 6; 10.1175/JPO-D-21-0186.1
Specifically, we address the following questions relevant for small-scale mixing in the thermocline of EAS:
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What form of double diffusion dominates in the EAS?
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What are the properties of staircases in the double-diffusion regime?
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What is the background level of shear-driven turbulence and the relative importance of double diffusion?
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How accurate are the parameterizations of double-diffusive fluxes?
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What is the overall vertical heat flux due to double diffusion, and what are its plausible implications for the ocean general circulation models used to simulate thermohaline structure in the EAS?
The manuscript is organized as follows: A brief description of observational campaigns in the EAS during the winter and spring 2019 and the details of microstructure data processing and the estimation of thermal variance dissipation rates (χ) and turbulent kinetic energy dissipation rates (ε) are summarized in section 2. The results are discussed in section 3. The implication of these results for understanding the source of a bias in the ocean model simulation in the thermocline region of EAS is discussed in section 4. A summary is given in section 5.
2. Data and methods
a. Observational campaign
The datasets used for this study were collected during two cruises in the EAS on board research vessels Sagar Nidhi (SN) and Sagar Kanya (SK) during winter 2019 (SN-137; 4 January–5 February 2019) and spring 2019 (SK-358; 1–29 May 2019) (Fig. 1a; Table 1). The cruises were organized as part of the Ministry of Earth Sciences (MoES) Indian National Centre for Ocean Information Services (INCOIS) project on Ocean Modeling, Data Assimilation and Process Specific Observations (O-MASCOT) designed to investigate the variability of small-scale mixing processes in the north Indian Ocean. During these cruises, the microstructure of turbulence-scale velocity shear, temperature, and conductivity profiles was collected in the upper 400 m of the water column in the EAS using a Rockland Scientific vertical microstructure profiler (VMP-250).
Summary of microstructure observations used in this study.
The VMP-250 is a free-fall profiler originally designed to operate within the upper 500 m of the water column, though the instrument used to collect data presented here was upgraded to a 1000 m depth rating. The approximate weight of the instrument in the air (water) is around 11 kg (3 kg), and the overall length is 1.6 m, and it records data internally. The approximate descent rate of VMP-250 during the cast was around 0.8 m s−1. The VMP-250 was equipped with two airfoil shear probes, a fast response thermistor (FP07), and a fast microconductivity probe (SBE7). Besides, VMP-250 was also equipped with standard conductivity–temperature, pressure, fluorescence, and turbidity sensors from JFE Advantech. The microstructure salinity (salinity is given in practical salinity scale), fluorescence, and turbidity data were not considered further in this study; hence, they are not discussed further. The sampling rate of microstructure shear and the temperature is 512 Hz, and the JFE Advantech conductivity–temperature sensor is 64 Hz. Data collection using VMP-250 was carried out from the ship’s starboard side while the ship was freely drifting toward the port side.
The VMP data collected during these two cruises consist of time series measurements at 3-h intervals for a few days at 18.4°N, 67.4°E and spot measurements along the transects in the EAS (Figs. 1a,b). Four to six successive profiles were collected every 3-h interval at the time series station and at stations along the transect to obtain statistically better representative mean values of turbulent parameters. Time series measurements of 8 days duration (10–17 January 2019) and 16 days duration (8–23 May 2019) were made during winter 2019 and spring 2019, respectively. A total of 472 and 649 VMP profiles were collected at the time series stations during winter and spring 2019 cruises, respectively. Note that the time series measurements during winter 2019 and spring 2019 were carried out in the core (∼36.8) of ASHSW (Fig. 1a).
During the winter 2019 cruise, 179 VMP profiles were collected from 40 stations (Fig. 1a) along the transect in the EAS and SEAS. The transect was planned in such a way that it covers the core (∼36.8) and periphery (∼36) of ASHSW (leg W1–W3) and relatively low saline (∼34) Bay of Bengal water (leg W4–W5) in the SEAS (Fig. 1a). The leg W1 and W3 traversed from the periphery of ASHSW (∼36) to the core of ASHSW (∼36.8), while the leg W2 traversed from the core of ASHSW to its periphery (∼36) (Fig. 1a). The leg W4 is primarily located in the salinity frontal regions in the SEAS, where the low-salinity Bay of Bengal water (∼34) meets the ASHSW (∼36; Fig. 1a). In the salinity frontal region in the SEAS (leg W4), a high spatial resolution VMP survey was carried out at 11 VMP stations with a close spacing of ∼22 km between them (Fig. 1). The survey along leg W5 was located in the lower saline Bay of Bengal water (>33.5). The transect made in spring 2019 was shorter than that in the previous winter; it covered six stations yielding 25 VMP profiles. The VMP profiles at stations along transects were made in the local morning and night hours (at 0530 and 1730 UTC).
b. Estimation of turbulent kinetic energy dissipation rate (ε)
c. Buoyancy Reynolds number (Reb)
As described in the previous section, double diffusion can exist under both turbulent and nonturbulent regimes. The turbulent or nonturbulent nature of the water column is examined through buoyancy Reynolds number (Reb) (Gregg 1988; Inoue et al. 2007). The Reb is defined as the ratio of the destabilizing effect of turbulence to the stabilizing effect of stratification and viscosity, and it provides information on the ability of stratification to suppress the turbulence.
d. Estimation of diapycnal diffusivity (Kρ)
The Osborn (1980) turbulence model assumes a balance between the production of turbulence kinetic energy, its rate of dissipation, and work against buoyancy in a steady state. The
It is worth pointing out here that, in shear-driven turbulence, the water column’s density stratification decreases due to mixing, and it is represented as a positive value of Kρ. However, in pure double-diffusion conditions, Kρ values are negative, and it represents a reduction in the potential energy and intensification of the density stratification of the water column (Thorpe 2005). It is worth pointing out that, in the present study, the Kρ values based on entire data points below the mixed layer are presented, irrespective of whether mechanical turbulence and double diffusion dominate in the data segment. Since Kρ values are negative in the double-diffusion regime, the estimation of Kρ based on the entire data points using Osborn (1980) turbulence model represents its extreme upper bound. It is explicitly noted when Kρ is calculated based only on the data points that are not favorable for double diffusion.
e. Estimation of thermal variance dissipation rates (χ)
We followed the methods described by Bluteau et al. (2017) to estimate χ from temperature microstructure. This method uses the background ε to estimate χ. In the low-energy environments (ε ≤ 5 × 10−8 W kg−1), χ is estimated through the integration of temperature gradient spectra in the viscous–diffusive subrange. On the other hand, in the energetic environments (ε > 5 × 10−8 W kg−1), χ is estimated by fitting Kraichnan’s model spectra in the inertial–convective subrange of the temperature gradient spectra (Bluteau et al. 2017). The estimation obtained through these two approaches is combined to get the complete profile of χ.
A value of 4.1 × 10−3 s is prescribed for τ0 and 1 m s−1 for u0 (Vachon and Lueck 1984; Bluteau et al. 2017). Note that the respective value of w (∼0.8 m s−1) in each data segment is used in the expression 6. The approximate value of τ with respect to the profiling speed (w ∼ 0.8 m s−1) of the instrument used in the study is around 4.6 × 10−3 s. However, it is worth pointing out that the estimation of χ is sensitive to the exact choice of values for τ0, and these aspects are discussed in appendix C.
f. Estimation of thermal diffusivity (KT)
g. Double-diffusion diagnostics: Turner angle (Tu)
The advantage of the Tu is that it has a finite range between −180° and 180°. The summary of the physical meaning of the classical definition of Tu is presented in Table 2. Tu between |180°| and |90°| indicates that the water column is statically unstable, and the values between −45° and 45° are considered as doubly stable. The Tu values between 45° and 90° (Rρ > 1) indicate that warm saline water lies over cold fresh water where the water column is conducive for salt fingers. Following Bebieva and Timmermans (2016), the Tu value between 72°–90° (1 < Rρ < 2) and 45°–72° (Rρ > 2) are used to characterize the existence of strong and weak salt finger regime, respectively. Tu values between −45° and −90° (0 < Rρ < 1) indicate the existence of cool fresh water over warm and salty water, making the region of the water column conducive for diffusive convection. Similar to the salt finger regime, the diffusive convection is considered as strong when Tu values are between −90° and −51° (0.1 < Rρ < 1) and weak when their values are between −51° and −45° (0 < Rρ < 0.1) (Bebieva and Timmermans 2016).
The physical meaning of the Tu values and its corresponding Rρ values.
h. Double-diffusion diagnostics: Dissipation ratio (Γεχ)
Gregg et al. (2018) described this term as an alternate form of
Note that, in expression (10), Γεχ→∞, when the magnitude of vertical temperature gradient becomes very weak (∂T/∂z → 0). Considering these characteristics, St. Laurent and Schmitt (1999) discarded the Γεχ estimation from their analysis in the Tu regimes −45° to 0°. As suggested by St. Laurent and Schmitt (1999), we discarded the Γεχ values in the Tu regime −45° to 0°.
i. Double-diffusion diagnostics: Staircases
A staircase-like structure is a common feature of salt fingering and diffusive convection (Melling et al. 1984; Schmitt 1994; Kelley et al. 2003; Sirevaag and Fer 2012; Scheifele et al. 2014; Bebieva and Timmermans 2016; Guthrie et al. 2017; Fine et al. 2018; Shibley and Timmermans 2019; Taillandier et al. 2020), particularly in conditions of weak background turbulence. The staircase structure may be absent when double-diffusion instability coexists with sufficiently strong turbulence (St. Laurent and Schmitt 1999; Bebieva and Timmermans 2016; Guthrie et al. 2017). A well organized and persistent occurrence of staircase structure may further support the occurrence of double-diffusive instability in the thermocline region of the AS.
The definitions of various properties of the staircase, such as “layer thickness (H),” “interface thickness (h)” between two “layers,” and temperature gradient (ΔT) in the double-diffusion regime, are presented in the Fig. 2d.
Sample temperature profiles (°C) to show the existence of the staircase in the double-diffusion region in the EAS on (a) 16 Jan,(b) 28 Jan, (c) 9 May, and (d) 9 May 2019. The red profiles represent the zoomed version portions of blue profiles. The plots in (a), (c), and (d) represent the salt finger form of double diffusion, and the plot in (b) represents the diffusive convection form of double diffusion. The properties of the staircase, such as layer thickness (H; m), interface thickness (h; m) between two layers, and temperature gradient (ΔT; °C) between two layers are marked in (d).
Citation: Journal of Physical Oceanography 52, 6; 10.1175/JPO-D-21-0186.1
We followed the methods proposed by Walesby et al. (2015) and Sirevaag and Fer (2012) to identify the staircase structures in temperature profiles. For this purpose, the individual temperature profiles were gridded into 0.1 m vertical resolution, and the background temperature gradient was estimated from this data by taking a 2.5 m running mean (Walesby et al. 2015). A layer is defined as the portion of the temperature profile, where at least four adjacent temperature gradient values are smaller than the background gradient, and the smallest value of these gradients should be less than the background gradient by at least 0.02°C m−1 (twice the accuracy of the temperature sensor) (Sirevaag and Fer 2012). Hence, we restricted ourselves to the minimum layer thickness of 40 cm and ignored the smaller layers. The interface was defined as the portion next to the layer, which has a temperature gradient between the adjacent data points greater than background gradients, and the maximum value of these gradients should be greater than the background gradient by a value of 0.02°C m−1.
j. Double-diffusion parameterizations
Double-diffusive structures span scales of a centimeter to a few meters, far smaller than the resolution of ocean general circulation models. The impact of double diffusion on large-scale dynamics is thus incorporated in the ocean models through parameterization schemes (Large et al. 1994; Radko and Smith 2012). The double-diffusion parameterization scheme’s basic approaches are to develop an empirical formula based on the relationship between vertical heat diffusivity (KT) associated with the double-diffusion and large-scale parameters such as the density ratio (Rρ). Previous studies have developed various parameterization schemes based on laboratory experiments, theories, and limited datasets (Large et al. 1994; Radko and Smith 2012). Tuning of these parameterization schemes in the models requires comparison with microstructure observations under a range of conditions in different oceanic basins. Hence we use the microstructure measurements to document the performance of the existing double-diffusive parameterization schemes in the EAS.
In this study, the performance of the Schmitt (1981); Large et al. (1994), Zhang et al. (1998), and Radko and Smith (2012) salt finger parameterizations and the Fedorov (1988) and Kelley (1984) diffusive convection parameterization are evaluated. Large et al. (1994) and Fedorov (1988) are part of the widely used K-profile parameterization (KPP) scheme. The details of these schemes are summarized in appendix A.
k. Estimation of vertical heat flux due to double diffusion
Note that these flux laws have been extensively used in the literature to estimate the vertical heat flux due to double diffusion. However, the direct comparisons with microstructure-based estimates showed mixed agreements (Sirevaag and Fer 2012; Lee et al. 2014; Scheifele et al. 2014; Fine et al. 2018). Past studies have shown that the flux law overestimates the vertical heat flux than the estimation based on microstructure measurements (Schmitt et al. 1987; Lueck 1987; Kelley et al. 2003; Fine et al. 2018; Sirevaag and Fer 2012) both in the salt finger and diffusive convection regime. For instance, the study by Lueck (1987) and Kelley et al. (2003) shows that vertical heat fluxes calculated using flux law overestimate compared to the microstructure-based estimate in the salt finger regime by two orders and a factor of 30, respectively. Similarly, in the diffusive convection regime, Fine et al. (2018) and Sirevaag and Fer (2012) reported that the flux law overestimated the microstructure based estimate by a factor of 4 and an order of magnitude, respectively.
However, the study by Guthrie et al. (2015) revisited the validity of flux laws, using a high-quality, well-resolved microstructure dataset and concluded that laboratory flux laws of diffusive convection agree well with microstructure based estimate. Hence, in this study, flux law proposed by Schmitt [1979, Eq. (11)] and Kelley [1990, Eq. (12)] are used to estimate heat flux associated with salt fingering and diffusive convection, respectively.
l. Uncertainties and error estimates
The total errors associated with the average of each estimated parameter consists of statistical uncertainty associated with a finite amount of data and error associated with instrumentation and assumption applied in the algorithm while deriving the parameters. Following Hummels et al. (2013) and St Laurent and Schmitt (1999), we presented only the error bar associated with the statistical uncertainty along with the average value of each variable and did not include the uncertainties due to measurement errors and assumption. The statistical uncertainty is presented as the standard error of the mean, and it is estimated through bootstrap methods (Thomson and Emery 2014). The primary advantage of the bootstrap method is that it does not require knowledge of the underlying data distribution, and it can be applied to small data samples to estimate the uncertainties (Thomson and Emery 2014). The statistical error estimates of parameters that consist of multiple variables (Kρ, KT, and Γεχ) is estimated by combining their uncertainties based on standard error propagation as summarized in appendix B (St Laurent and Schmitt 1999; Hummels et al. 2013).
The uncertainties associated with instrumentation error and assumption applied in the algorithm while deriving the turbulence parameters are summarized in appendix C. The combined effect of these uncertainties estimated through propagation error is presented in Table C1.
m. Mixed layer depth, isothermal layer depth, and barrier layer thickness
The depth where the density is equal to the sea surface density (at 1 m) plus 0.2 kg m−3 is defined as the mixed layer depth (Kara et al. 2000). The depth where the temperature is 0.8°C lower than sea surface temperature (SST) is defined as isothermal layer depth, and the difference between the depths of the isothermal layer and mixed layer is defined as the barrier layer thickness (Kara et al. 2000).
Note that we have mainly concentrated in the region below the ocean surface boundary layer (or mixed layer) since these parts of the ocean are continuously interacting with the overlying atmosphere, and turbulent mixing processes in this region is primarily driven by wind and buoyancy flux due to net surface heat flux at the sea surface (Foltz 2019).
n. Satellite and reanalysis data
Optimal interpolated (OI) microwave and infrared (MW_IR) SST product (OI-SST) at 9 km resolution (Gentemann et al. 2008), Soil Moisture Active Passive (SMAP) sensor derived sea surface salinity at 0.25° resolution (Meissner et al. 2019), Advanced Scatterometer (ASCAT) (Ricciardulli and Wentz 2016) wind vectors at 0.25° spatial resolution, and Ocean Surface Current Analysis Real-Time (OSCAR) surface currents (Bonjean and Lagerloef 2002) at 0.3° spatial resolution were used to depict the prevailing near-surface atmospheric and oceanographic condition in the EAS during January and May 2019. Besides, the climatology of net surface heat flux from TropFlux available at 1° spatial resolution (Kumar et al. 2012) was also used.
3. Results and discussion
a. Vertical structure of temperature and salinity
The depth–time section of near-surface temperature and salinity during winter and spring at the time series station shows the existence of warm high saline water over cold low saline water (Figs. 3a,b and 4a,b). Due to higher wind speed and net surface heat loss from the ocean, the mixed layer is deeper and cooler (∼70 m and ∼26°C) during winter than in spring (∼30 m and ∼30°C) (Figs. 1, 3, and 4). The near-surface salinity during winter is lower (∼36.6) than that in spring (∼36.8). The depth of 23°C isotherm, a proxy for thermocline depth, is also deeper during spring (∼150 m) than that in winter (∼100 m). Overall, the vertical thermohaline structure in transects showed similar characteristics as observed at the time series stations in the respective season, except in the SEAS (Figs. 3a,b and 4a,b).
The depth–time section of (a) temperature (°C), (b) salinity, (c) Tu (°), (d) log(Reb), (e) log10(ε) (W kg−1), and (f) log10 (χ) (K2 s−1) at the time series station (18.4°N, 67.4°E) in the EAS during (left) winter 2019 and (right) spring 2019. The cyan lines represent the mixed layer depth (m). The blue line in (a) is the depth of 23°C isotherms (m). The dashed contour in the (a)–(c) represents the isopycnals 24–26 kg m−3 in every 1 kg m−3.
Citation: Journal of Physical Oceanography 52, 6; 10.1175/JPO-D-21-0186.1
Vertical distribution of (a) temperature (°C), (b) salinity, (c) Tu (°), (d) log(Reb), (e) log10(ε) (W kg−1), and (f) log10 (χ) (K2 s−1) from the cruise transects in the EAS during (left) winter 2019 and (right) spring 2019. The cyan filled circles represent the mixed layer depth (m), and white circles in (a) represent isothermal layer depth (m); the region between cyan and white filled circles represents the barrier layer. The color bar above the figure represents different segments of the cruise transects during winter 2019 (W1, gray; W2, green; W3, light blue; W4, purple; and W5, yellow) and spring 2019 (S1, dark blue). Note that, due to salinity stratification, the barrier layer of thickness ∼50–60 m is apparent in the SEAS (transects W4 and W5) between the depth ∼30 m (mixed layer depth; cyan filled circles) and ILD (∼85 m; white filled circles). Note that the color bar for salinity in (b) is different from Fig. 3b.
Citation: Journal of Physical Oceanography 52, 6; 10.1175/JPO-D-21-0186.1
Past studies have shown that the formation of surface layer haline stratification in the SEAS is due to the intrusion of low saline Bay of Bengal water brought there by the East India Coastal current and winter monsoon currents during winter (Kurian and Vinayachandran 2006) (Figs. 1a,c). The existence of low saline Bay of Bengal water (<33.5) over the ASHSW (>36) in the SEAS is apparent during winter 2019 (Figs. 4b and 5c; between the cast numbers 25–40). The strong saline stratification in the near-surface layer in the SEAS leads to the formation of the barrier layer and temperature inversions (with magnitude >1°C) (Shankar et al. 2004; Kurian and Vinayachandran 2006). The barrier layer and temperature inversions start appearing during late November, peak during January, and disappear by March (Shankar et al. 2004; Kurian and Vinayachandran 2006). Consistent with the earlier studies, the observations in the SEAS during winter 2019 showed a barrier layer of thickness 50 m and temperature inversion of magnitude 0.75–1.2°C (Fig. 4a; between the cast numbers 25–40; in the cruise transect W4–W5).
Potential temperature–salinity (θ–S) diagram for (a),(b) time series station at 18.4°N, 67.4°E and (c),(d) cruise transects in the EAS during (a),(c) winter 2019 and (b),(d) spring 2019. The color bars in (a) and (b) represent temporal evolution and in (c) and (d) represent latitudinal variations.
Citation: Journal of Physical Oceanography 52, 6; 10.1175/JPO-D-21-0186.1
The existence of interleaving layers in the vertical profile of temperature and salinity is conspicuous in the observations from the time series station and transects during winter and spring 2019 (Figs. 3a,b and 4a,b). The signature of interleaving layers of salinity, with approximately 0.4 changes in salinity between the isopycnals at 25–26 kg m−3 and 0.25 between the isopycnals at 26.5–27 kg m−3, is apparent in the θ–S diagram (Figs. 5a,b). Past studies had suggested that the vertical structure of temperature and salinity in the thermocline region in the EAS are conducive for double-diffusion instability (You 2002; Azizpour et al. 2017). Hence, we document the nature and characteristics of double diffusion in these layers of the EAS in the succeeding sections.
b. Turner angle
The depth–time section of Tu at time series stations shows that a significant number of data points exist in double-diffusion-favorable conditions (45° < Tu < 90° and −90° < Tu < –45°) (Figs. 3c and 4c). The salt finger favorable condition (45° < Tu < 90°) is apparent between 100 and 200 m (σɵ ∼ 25–26 kg m−3) and around 300 m (σɵ ∼ 26.5 kg m−3) during spring 2019 and between 100 and 150 m (σɵ ∼ 25–26 kg m−3) and 300–350 m (σɵ ∼ 26.5 kg m−3) depth during winter 2019 (Fig. 3). The existence of diffusive convection favorable condition (−90° < Tu < –45°) is evident around 100 m depth (σɵ ∼ 23–24 kg m−3) during winter 2019 and between 200 and 300 m (σɵ ∼ 26–27 kg m−3) depth during spring 2019 (Figs. 3c and 4c). As evident in the time series station, the salt finger favorable conditions are apparent in the measurements from the transects in the EAS during winter 2019 and spring 2019 (Fig. 4). Conditions favorable for diffusive convection are evident in the barrier layer region of the SEAS during winter 2019 (Fig. 4). The coexistence of halocline due to the intrusion of Bay of Bengal low saline water into the SEAS and the existence of moderately strong temperature inversion (1°C) is conducive for the formation of diffusive convection conditions in the barrier layer region of SEAS during winter 2019 (Fig. 4).
A quantitative analysis of bin averaged data below the mixed layer as a function of Tu and Reb during winter 2019, and spring 2019 suggests that approximately 70% of the data points are favorable for the occurrence of the salt finger (45° < Tu < 90°) and only 2% are favorable for diffusive convection (−45° < Tu < −90°) (Figs. 6a,b). Moreover, approximately 80% of the data in the diffusive convection favorable condition exist in a strong regime (−51° < Tu < −90°), and roughly 66%–70% of the data in salt finger favorable condition indicate moderately strong to strong regimes (55° < Tu < 70°) (Fig. 6). Though relatively scarce, based on the entire data, 45% of the data points are favorable for diffusive convection in the barrier layer region of the SEAS during winter 2019 (Fig. 6c).
Distribution of data samples as a function of Turner angle (Tu; x axis; every 5°) and log(Reb) (y axis; 25 bins between 100 and 102) during (a) winter 2019 and (b) spring 2019. (c) As in (a) and (b), but for the measurements from the barrier layer region of SEAS during winter 2019. (d)–(f) The percentage of data points that exist in each 5° Turner angle bin during winter 2019, spring 2019, and the barrier layer region of the SEAS during winter 2019, respectively. The black vertical lines demarcate salt finger favorable (45° < Tu < 90°), diffusive convection favorable (−90° < Tu < –45°), and double stable (−45° < Tu < 45°) regimes in the water column. The brown horizontal line in the (a)–(c) represents Reb = 20. The dotted vertical lines in the salt finger (Tu = 72°, Rρ = 2) and diffusive convection (Tu = −51°, Rρ = 0.1) regime demarcate strong and weak regime. The Rρ values (top of the x axis) corresponding to the Tu values (bottom of the x axis) are also presented.
Citation: Journal of Physical Oceanography 52, 6; 10.1175/JPO-D-21-0186.1
The Turner angle data thus indicates that the moderately strong salt finger is possible in most of the water column below the mixed layer in the EAS, interspersed with strong diffusive convection favorable thin layers.
c. The double-diffusion staircases
The vertical profiles of temperature obtained from the field campaign in the EAS at four different depth segments are presented in Fig. 2 to illustrate the existence of staircase structure in the double-diffusion regime. Figure 2 depicts the existence of a well-defined staircase-like structure in both salt finger and diffusive convection regime in the EAS.
Staircases are common in the data (Figs. 2 and 7). About 90% of the profiles have greater than 35 staircase structures. The number of staircases is slightly higher during spring 2019 (∼50 steps per profile) than those in winter 2019 (∼40 steps per profile) (Fig. 7a). The well-defined staircases are present in all temperature profiles, and they occupy approximately 20% of the 400 m of the water column below the mixed layer. The frequency distribution of various properties of the staircase in the salt finger regime in the EAS, such as layer thickness (H), interface thickness (h), temperature gradient (ΔT), and salinity gradient (ΔS) at the interface is presented in Fig. 7. The individual values of H(h) in the steps reach as high as 2.5 m (1.8 m), with an average value of 1.1 m (0.9 m) (Figs. 7a,b). The histogram of H during winter 2019 and spring 2019 shows that around 50% of layer thickness has a value between 0.8 and 1.2 m, and 30% of them have values below 0.8 m (Fig. 7b). Similarly, 70% of interface thickness has a value below 0.8 m during winter and spring 2019 (Fig. 7c). This analysis suggests that a sharp interface separates a well-defined layer thickness in most staircase structures in the EAS. The mean temperature gradient across the interface is around 0.12°C during winter 2019 and spring 2019, and it reaches as high as 0.4°C in both seasons (Fig. 7d). Besides, 45% of the temperature gradient at the interface has a value greater than 0.1°C (Fig. 7d). The magnitude of ΔS across the interface is small (0.01) compared to ΔT, and the magnitude of ΔS during spring 2019 (0.02) is slightly higher than that during winter 2019 (0.01) (Figs. 7d,e). Further, approximately 50% of ΔS values were higher than 0.01 (Fig. 7e).
Frequency distribution (%) of staircase statistics during (left) winter 2019 and (right) spring 2019 in the salt finger regime. (a) The number of steps per profile, (b) layer thickness (H; m) (c) interface thickness (h; m) between two layers, and (d) temperature gradient (ΔT; °C), and (e) salinity (ΔS) gradient across the interface. The blue dot in each panel represents the mean of each parameter. Note that we considered only those staircases with a layer thickness of more than 0.4 m; hence, in (b) the minimum value is restricted to 0.4 m.
Citation: Journal of Physical Oceanography 52, 6; 10.1175/JPO-D-21-0186.1
A 2D histogram between ΔT and ΔS is examined to understand their relationship at the interface (Figs. 8a,b). The magnitude of ΔT increased with ΔS, suggesting that at the interface, where higher values of ΔT exists, the ΔS values also will be higher, and this characteristic is pronounced in the strong salt finger regime (2.5 < Rρ) (Figs. 8a,b). On the other hand, in the weak salt finger regime (5 > Rρ), the magnitude of ΔT shows a much wider range compared to ΔS (Figs. 8a,b).
2D histogram (%) between (a),(b) ΔT (°C) and ΔS and (c),(d) ΔT (°C) and h (m) at the staircase interface during (a),(c) winter 2019 and (b),(d) spring 2019. In (a) and (b), Rρ is estimated at the individual interface thickness and its average value in each ΔT–ΔS bin is contoured. The approximate value of Tu corresponds to the Rρ value of 2.5 (5) is 68°(56°).
Citation: Journal of Physical Oceanography 52, 6; 10.1175/JPO-D-21-0186.1
Similarly, a 2D histogram between ΔT and h, depicts the absence of a one-to-one relationship between them (Figs. 8c,d). Further, it is apparent from Figs. 8c and 8d that, majority of the interface has a thickness between 0.5 and 1 m and ΔT magnitude between 0.05° and 0.1°C. However, above the mean value of h (0.9), the percentage of occurrence of higher ΔT values decreases with increasing h (Figs. 8c,d). These characteristics suggest that the diffuse interface tends to hold a small magnitude of ΔT.
Thus, the staircases are common in the EAS, though intermittent in the regions favorable for double diffusion. These staircase characteristics are consistent with the importance of double-diffusion processes in the EAS.
d. Shear mixing rate
The depth–time sections of the Reb at the time series station and along the transects are examined to understand the nature of the shear mixing rate in the EAS during winter 2019 and spring 2019 (Figs. 3d and 4d). In general, the Reb values are less than 20, and ε is approximately 10−9 W kg−1 below the mixed layer, compared to elevated turbulence in the mixed layer (ε > 10−7 W kg−1 and Reb > 400) (Figs. 3d,e and 4d,e). The data also showed that the values of χ are between 10−7 and 10−8 K2 s−1 in the thermocline region of EAS (Figs. 3f and 4f). Approximately 80%–88% of Reb values are less than 20, and 11%–17% of Reb values are within 20–100 below the mixed layer. Moreover, in the salt finger favorable conditions, Reb values are less than 20 for 86%–90% of the data points, and approximately 10%–13% of them fall between 20 and 100 (Figs. 6a,b). Similarly, 70%–90% Reb values are less than 20 in the diffusive convection regime (Figs. 6a–c). This characteristic of the vertical distribution of Reb value suggests that the mechanical or shear-driven turbulence is very weak in the water column below the mixed layer in the EAS during winter 2019 and spring 2019.
To corroborate the existence of weak shear-driven mixing rates in the EAS, the Kρ based on all the data points below the mixed layer was estimated (Figs. 9a,c). The frequency distribution of Kρ below the mixed layer depth shows that the values are primarily distributed between 3 × 10−7 and 8 × 10−6 m2 s−1; of these, 75% of them are less than 3 × 10−6 m2 s−1 (Figs. 9a,c). The mean value of Kρ based on all the data points below the mixed layer in the EAS is 5.4 × 10−6 ± 1.1 × 10−6 m2 s−1 during winter 2019 and 2.3 × 10−6 ± 4.5 × 10−7 m2 s−1 during spring 2019 (Fig. 9). Note that mean values of Kρ, based on the data only in the double stable regime (−45° < Tu < 45°) does not show a significant difference (6.5 × 10−6 ± 2.2 × 10−6 m2 s−1 during winter 2019 and 2.0 × 10−6 ± 2.1 × 10−8 m2 s−1 in spring 2019) with respect to the estimation based on all the data points below the mixed layer. The mean value of Kρ reported here are approximately one order of magnitude smaller than its typical values in the thermocline region [O(10−5)] of the global ocean (Gregg 1987, 1998; Ledwell et al. 1998; Waterhouse et al. 2014; Fernández-Castro et al. 2014; Lee et al. 2014). This feature is also consistent with earlier studies that reported low internal wave energy during winter and spring in the thermocline in the open-ocean region of the EAS (Fig. 2a of Whalen et al. 2012; Figs. 2a and 2c of Chaigneau et al. 2008). For example, using strain information from Argo float profiles, an earlier study showed that the annual mean of ε is ∼ O(10−9) W kg−1, and Kρ is approximately 5 × 10−6 m2 s−1 in the EAS between 250 and 500 m of the water column (Figs. 2a and 3a of Whalen et al. 2012).
Frequency distribution (%) of Kρ (m2 s−1; red) and KT (m2 s−1; blue) during (a) winter 2019 and (c) spring 2019. The red and blue dots in (a) and (c) represent the mean values of Kρ and KT, respectively. The mean profile of Kρ (m2 s−1; red) and KT (m2 s−1; blue) below the mixed layer in a 10 m bin during (b) winter 2019 and (d) spring 2019. In (b) and (d), shading represents the uncertainty of mean estimated based on standard error propagation as described in appendix B.
Citation: Journal of Physical Oceanography 52, 6; 10.1175/JPO-D-21-0186.1
The data thus indicate that shear-driven mixing rates are small where the contribution of Kρ is not more than 5.4 × 10−6 m2 s−1. These characteristics suggest that double diffusion is a significant source for diapycnal mixing in the thermocline of EAS.
e. Dissipation ratio (Γεχ)
The distribution of Γεχ as a function of Tu and Reb during winter 2019 and spring 2019 are presented in Fig. 10. It is apparent from Fig. 10 that the values of Γεχ are higher compared to
Distribution of dissipation ratio (Γεχ) as a function of Turner angle (Tu; x axis; every 5°) and log(Reb) (y axis; 25 bins between 100 and 102) during (a) winter 2019 and (b) spring 2019 for the time series and along the transects. The brown horizontal lines in the (a) and (b) represent Reb = 20. The variation of mean Γεχ with respect to Tu during (c) winter 2019 and (d) spring 2019 is marked as a black line. The blue and green horizontal lines in (c) and (d) represent the values 0.2 (
Citation: Journal of Physical Oceanography 52, 6; 10.1175/JPO-D-21-0186.1
Note that the estimated values of Γεχ in the EAS are comparable to other oceanic basins (Oakey 1988; Schmitt et al. 2005; Inoue et al. 2007; 2008; Ishizu et al. 2013; Nakano et al. 2014; Nakano and Yoshida 2019; Nagai et al. 2015). The analysis also indicates that higher values of Γεχ in the diffusive convection regimes compared to salt finger favorable conditions is consistent with past studies (Oakey 1982; Schmitt et al. 2005; Inoue et al. 2007, 2008; Ishizu et al. 2013; Nakano et al. 2014; Nakano and Yoshida 2019; Nagai et al. 2015) (Fig. 10). This particular characteristic is attributed to significant dissipation of thermal variance (χ) due to an unstable temperature profile in the diffusive convection case and relatively small dissipation of thermal variance (χ) due to stable temperature profile in the salt finger regime (Oakey 1982; Schmitt et al. 2005; Inoue et al. 2007, 2008; Ishizu et al. 2013; Nakano et al. 2014; Nakano and Yoshida 2019; Nagai et al. 2015).
In the salt finger regime, Γεχ values show good agreement with
However, higher values of Γεχ (1–3) are observed between Tu values 0°–45° (double stable regime), which is higher than the constant value of 0.2 for
One plausible explanation or higher values of Γεχ in a double stable regime might be associated with the presence of thermohaline intrusion in the water column of the EAS (Figs. 5 and 3b). As suggested by previous studies, the lateral gradient of temperature associated with thermohaline intrusion can lead to the relatively higher value of χ (Joyce 1977; Ruddick et al. 2010), which in turn leads to higher values of Γεχ. Nakano (2016) suggested that the higher values of Γεχ in the double stable regime may be associated with turbulence damped by viscosity. Note that, in the present study, around 99% (80%) Reb values below the mixed layer depth are smaller than 100 (20). Hence, we speculate that the higher Γεχ values than
Thus, it emerges that the dissipation ratio in the double-diffusion-favorable regime in the EAS is qualitatively inconsistent with
f. Comparison of double-diffusion parameterization schemes in the EAS
In this section, the performance of various ocean general circulation model double-diffusion parameterization schemes ability to capture KT calculated from observed χ in the EAS is examined. For this purpose, the KT evolution with respect to Tu from the observation and double-diffusive parameterization schemes are compared (Fig. 11). In the salt finger regime, we evaluated the performance of Schmitt (1981), Large et al. (1994), Zhang et al. (1998), and Radko and Smith (2012) (Fig. 11). Similarly, Fedorov (1988) and Kelley (1984) diffusive convection parameterization schemes performance was also evaluated (Fig. 11).
Comparison of vertical heat diffusivity (KT; m2s−1) calculated from observed χ [Osborn and Cox (1972), thin black lines] and different parameterizations used in OGCMs (thick lines) in (a) diffusive convection [Kelley (1984), thick dark green line; Fedorov (1988), thick cyan line; legends are labeled in the bottom left] and (b) salt finger [Radko and Smith (2012), thick red line; Large et al. (1994), thick green line; Zhang et al. (1998), thick yellow line; Schmitt (1981), thick blue line; legends are labeled in the bottom right] regimes as a function of Turner Angle (Tu; °) during (top) winter 2019 and (bottom) spring 2019. The black line represents the median of observed KT in every 2° of Tu bin. The shading represents the distribution of the mean value of observed Kρ in each Turner angle (Tu; x axis; every 5°) and log(KT) (y axis; 3 bins between every factor of 10) bins. The dotted line in the salt finger and diffusive convection regime demarcates strong and weak double-diffusion conditions. The Rρ values (top x axis) corresponding to the Tu values (bottom x axis) are also presented. The thin pink line represents KTRρ estimated using N2,
Citation: Journal of Physical Oceanography 52, 6; 10.1175/JPO-D-21-0186.1
The frequency distribution of KT in EAS below the mixed layer depth shows that the bulk of the KT values (∼95%) are distributed between 3 × 10−7 and 1 × 10−4 m2 s−1 (Figs. 9a,b) and the mean KT is an order of magnitude higher than Kρ in the EAS during winter 2019 (6.9 × 10−5± 2.4 × 10−5 m2 s−1) and spring 2019 (1.9 × 10−5± 1.0 × 10−6 m2 s−1) (Figs. 9c,d).
In the diffusive convective regime, observed KT shows nearly constant values between −45° and −75° (Fig. 11a). Both the Kelley (1984) and Fedorov (1988) schemes showed good agreement with observation in diffusive convection regime between −90° and −70°. However, Kelley (1984) outperformed the Fedorov (1988) scheme in the observations in diffusive convection regime between −70° and −45° (Fig. 11a).
In the salt finger regime (45° < Tu < 90°), observed KT values progressively decreased from Turner angle value of 90° (strong salt finger regime) and reached a minimum value close to 60° and subsequently did not show significant variations (Fig. 11b). It is apparent from Fig. 11b (thick red and thin black lines) that the Radko and Smith (2012) scheme outperformed all other parameterization schemes in the salt finger regime. The evolution of median KT values estimated using the Radko and Smith (2012) scheme with respect to Turner angle showed good agreement with the observation with a correlation coefficient of 0.8 during winter 2019 and spring 2019 (Figs. 11b; compare thick red and thin black line). The better performance of the Radko and Smith (2012) salt finger scheme reported here is consistent with a similar study in the western pacific (Nagai et al. 2015).
Thus based on the microstructure measurements from the EAS, it may be concluded that Radko and Smith (2012) parameterization scheme for salt finger and Kelley (1984) scheme in the diffusive convection regime performs better compared to other double-diffusion schemes.
g. Vertical heat flux due to double-diffusion instability
The frequency distribution of vertical heat flux estimated using flux law under the salt finger (FSF-Schmit), and the diffusive convection (FDC-Kelley) regime during winter 2019 and spring 2019 and their mean values are presented in Fig. 12. The mean heat flux due to salt finger during winter 2019 and spring 2019 shows comparable magnitude with a slightly higher magnitude in the latter case (∼−3.1 ± 0.03 W m−2) than former (∼−2.8 ± 0.1 W m−2) (Figs. 12a,b). During winter 2019 (spring 2019), the mean vertical heat flux due to diffusive convection is 8.3 ± 0.4 W m−2 (5.3 ± 0.2 W m−2), respectively (figure not shown). For the sake of comparison, the magnitude of heat flux (FKT) estimated using the expression ρcpKT〈∂T/∂z〉 in the staircase region shows a reasonably good agreement with an estimation based on flux law in the salt finger (−2.2 ± 0.16 W m−2 in winter 2019 and −2.7 ± 0.1 W m−2 in spring 2019) and diffusive convection (9.2 ± 0.3 W m−2 in winter 2019 and 20.61 ± 2.08 W m−2 in spring 2019) regime (Fig. S1 in the online supplemental material).
Frequency distribution (%) of heat flux (W m−2) estimated using flux law in the salt finger (FSF-Schmit) regimes in the EAS during (a) winter 2019 and (b) spring 2019 and (c) diffusive convection (FDC-Kelley) regimes in the barrier layer region of SEAS during winter 2019. The negative [in (a) and (b)] and positive values [in (c)] indicates the downward and upward heat flux due to salt fingering and diffusive convective regimes, respectively. The error bar represents the uncertainty of the mean estimated based on standard error propagation as described in appendix B.
Citation: Journal of Physical Oceanography 52, 6; 10.1175/JPO-D-21-0186.1
Note that the existence of diffusive convection is very sporadic in the EAS, and it occupies approximately 2%–3% of the water column only compared to predominated salt finger regimes (∼70%). Though downward heat flux due to salt finger favorable conditions dominated in the water column in the EAS, the upward heat flux due to thin layers of diffusive convection between the salt finger regime leads to divergence of heat flux. The weighted sum of heat flux associated with these two processes leads to a net downward heat flux of magnitude −2.5 W m−2. The diffusive convection between the salt finger regime indicates the presence of thermohaline intrusion in the water column, and its existence is apparent in the EAS (Figs. 3–5). As demonstrated by past studies, the thermohaline intrusion can effectively transport heat laterally (Rudels et al. 2009; Ruddick et al. 2010; Fine et al. 2018). However, the present dataset is insufficient to quantify the lateral heat flux due to thermohaline intrusion in the EAS.
In the barrier layer region of the SEAS, approximately 45% of the data points fell under diffusive convection regimes during winter 2019, and the mean of vertical heat flux due to diffusive convection in this region are 4.7 ± 0.7 W m−2 (Fig. 12c). It is worth pointing out that the mean of heat flux values due to diffusive convection in the SEAS during winter 2019 is slightly lower than the overall data points. Note that the heat flux magnitude due to diffusive convection in the SEAS is much higher than (∼−0.1 to −0.36 W m−2) the estimation based on flux law in the Arctic (Padman and Dillon 1987; Guthrie et al. 2015; Bebieva and Timmermans 2016). However, the studies by Polyakov et al. (2012) and Fine et al. (2018) reported a comparable magnitude of heat flux (−8 to −13 W m−2) due to diffusive convection in the SEAS. As demonstrated in these previous studies, the difference in the heat flux is primarily attributed to the magnitude of ΔT, such as in the high heat flux case ΔT values are significant (0.3°–0.4°C; Polyakov et al. 2012; Fine et al. 2018) than the low heat flux situations (0.01°–0.03°C; Padman and Dillon 1987; Guthrie et al. 2015; Bebieva and Timmermans 2016). Consistent with the higher diffusive convection heat flux cases (Polyakov et al. 2012; Fine et al. 2018), the magnitude of ΔT in the SEAS is around ∼0.1°C.
In summary, the analysis show ∼−2.5 W m−2 downward heat flux in the thermocline region due to salt finger and diffusive convection in the EAS and upward heat flux of 5 W m−2 in the barrier layer region of SEAS is occurring in association with diffusive convection. The schematic diagram (Fig. 13) describes the vertical heat flux associated with the double diffusion in the thermocline region in the EAS and diffusive convection in the barrier layer region of SEAS.
Schematic diagram explaining the vertical heat flux associated with the salt finger and diffusive convection in the thermocline in the EAS during winter and spring and diffusive convection in the barrier layer region of the SEAS during winter. The numbers in the parentheses represent the percentage of area occupied by salt finger and diffusive convection forms of double diffusion below the mixed layer. In addition to salt finger and diffusive convection, the presence of thermohaline intrusion in the water column can effectively transport heat laterally, though its contribution is not quantified in the present study. NHF: net surface heat.
Citation: Journal of Physical Oceanography 52, 6; 10.1175/JPO-D-21-0186.1
4. Plausible impact of double-diffusion-induced heat flux in the AS
Past studies have reported that ocean models in the Coordinated Ocean-Ice Reference Experiments (CORE-II) and Coupled Model Intercomparison Project Phase 5 (CMIP-5) showed apparent warm bias in the thermocline region of the AS (Shikha and Valsala 2018; Rahaman et al. 2020). These studies have depicted the maximum magnitude of these biases in temperature (∼3°C) located between 100 and 400 m of the water column in the thermocline region (Figs. 1 and 2 in Shikha and Valsala 2018 and Fig. 20a of Rahaman et al. 2020). Besides, these studies also suggested that the warm bias in the ocean model leads to the false representation of stratification in the water column, which potentially impacts large-scale ocean dynamics through faster propagation of planetary wave than observed (Shikha and Valsala 2018). As demonstrated by Shikha and Valsala (2018), the higher planetary wave speed in the ocean model can significantly impact the simulation of the life cycle and seasonality of interannual climate signals in the tropical Indian Ocean. Our analysis shows that the existence of weak mechanical-driven turbulence in the thermocline region of the EAS. The present study also highlights that the vertical fluxes of heat in the thermocline region (∼100–400 m) in the EAS is primarily determined by the salt finger form of double diffusion, which may not be captured by the mixing parameterization schemes which are commonly used in the ocean models.
When compared, the vertical heat flux associated with the salt finger (−3 W m−2) is 40 times smaller than the net surface heat flux at the air–sea interface during winter 2019 (∼−120 W m−2) and spring 2019 (∼120 W m−2) (Fig. 1c). However, as demonstrated by Merryfield et al. (1999), the incorporation of salt finger induced mixing in the ocean model effectively diffused the higher values of temperature downward. Hence, the false representation of the downward heat flux due to the salt finger in the ocean models might be a plausible explanation of a warm bias in the thermocline region of the EAS. Note that most ocean models have been using KPP-based salt finger parameterization schemes (Large et al. 1994). However, the present study suggests that the salt finger parameterization developed by Radko and Smith (2012) shows a better agreement with the observation than Large et al. (1994). Hence, ocean model sensitivity studies using different salt finger parameterizations may provide more insight toward understanding the source of the warm bias in the thermocline region in the EAS.
The present study also depicts the upward heat flux (∼5 W m−2) due to diffusive convection in the barrier layer region of the SEAS during winter 2019 (Figs. 13 and 12c). The climatology of TropFlux net surface heat flux shows approximately 20 W m−2 heat gain by the ocean during January in the SEAS (Fig. 1c). Hence, the magnitude of upward heat flux due to double diffusion (5 W m−2) from the barrier layer during winter 2019 is about 25% of the climatological net surface heat flux in the SEAS in winter. These characteristics suggest that the heat flux due to double diffusion plays an important role in determining the winter SST in the SEAS. This result has significant importance as the past studies have shown that the high SST in the SEAS during spring plays a vital role to determine the monsoon onset through the formation of monsoon onset vortex (Rao and Sivakumar 1999; Shenoi et al. 1999; Masson et al. 2005). Durand et al. (2004) had suggested that the vertical advection of heat trapped in the temperature inversions are important in determining the SST in the SEAS during presummer. In contrast to Durand et al. (2004) and Kurian and Vinayachandran (2006) suggested that the role of the entrainment process due to the deepening of the mixed layer is very weak during winter in the SEAS due to feeble wind forcing. They further argued that the evolution of SST in the SEAS is primarily determined by the net surface heat flux rather than the entrainment of warm barrier layer water to the mixed layer (Fig. 8 of Kurian and Vinayachandran 2006). However, the present study suggests that the upward heat flux due to the diffusive convection in the barrier layer region is also helping the determination of SST during winter in the SEAS.
5. Summary and conclusions
Microstructure temperature and shear measurements in the upper 400 m of the eastern Arabian Sea (EAS) collected during the two cruises in winter 2019 (4 January–5 February 2019) and spring 2019 (1–29 May 2019) are utilized to document the nature and characteristics of double-diffusive mixing in this region.
The analysis based on Tu suggests that approximately 70% and 2% of samples are conducive for salt finger and diffusive convection conditions, respectively. About 80% of the diffusive convection conditions are strong (−51° < Tu < −90°), and roughly 70% of the salt finger conditions are moderately strong (55° < Tu < 70°). The barrier region of the SEAS is thus a hotspot for diffusive convection, with approximately 45% of the data points favor diffusive convection. Thermohaline staircases are common in regions favorable for double diffusion with 90% of all profiles having more than 35 steps.
Our analysis shows that the mean Kρ estimated using Osborn (1980) turbulence model with a constant value for mixing coefficient (0.2) is not more than 5.4 × 10−6 m2 s−1, and 80% of the Reb values are less than 20 during winter and spring of 2019. This is consistent with the earlier studies indicating that the thermocline of the EAS is a region of low internal wave energy (Whalen et al. 2012; Chaigneau et al. 2008). We conclude that shear-driven mixing rates are weak and double diffusion is a significant source for diapycnal mixing in the thermocline region of EAS during winter and spring.
The values of Γεχ are much higher than the
Various parameterizations of double diffusion used in ocean general circulation models were compared with the microstructure measurements of KT in EAS. Radko and Smith (2012) and Kelley (1984) formulations showed the best agreement with the observation for the salt fingering and diffusive convection regimes, respectively.
The weighted sum of heat flux associated with salt fingering and diffusive convection in the thermocline during winter and spring is estimated as net downward heat flux of magnitude −2.5 W m−2. Upward heat flux from the barrier layer to the mixed layer due to diffusive convection during winter is approximately 5 W m−2. This is approximately 25% of the climatological net surface heat flux (∼20 W m−2) in the SEAS during winter.
The present study indicates the existence of very weak mechanical-driven turbulence in the EAS thermocline. This suggests that the double diffusion may act as a vital process responsible for the vertical transfer of heat, salt, nutrients, and dissolved oxygen in these layers. The impact of double diffusion on the biogeochemistry of the EAS is a subject for future work.
Acknowledgments.
The encouragement provided by Director, INCOIS, is gratefully acknowledged. The authors thank three anonymous reviewers and the Editor Dr. Ilker Fer for their constructive comments and suggestions which greatly helped to improve the manuscript. We express sincere gratitude to MoES-Joint Scientific and Technical Advisory Committee (JSTAC), The Vessel Management Cells (VMC) at NIOT, and NCPOR for providing Sagar Nidhi and Sagar Kanya to carry out the observations. We also thank the captain, crew, and all scientists of the two voyages for their contributions in data collection. This work is carried out as part of Ashin’s Ph.D. work. TropFlux data are available at https://incois.gov.in/tropflux/data_access.jsp. We thank EUMETSAT for providing the ASCAT SZR L1B data files used in this study. C-2015 ASCAT data are produced by Remote Sensing Systems under the sponsorship of NASA Ocean Vector Winds Science Team. SMAP salinity data are produced by Remote Sensing Systems under the sponsorship of NASA Ocean Salinity Science Team. Microwave OI SST data are produced by Remote Sensing Systems under the sponsorship of National Oceanographic Partnership Program (NOPP) and the NASA Earth Science Physical Oceanography Program. Data are available at www.remss.com. OI-SST, ASCAT, and SMAP data are available at www.remss.com. This is INCOIS contribution 453.
APPENDIX A
Double-Diffusion Parameterization Schemes
Past studies have developed parameterization schemes to estimate vertical heat diffusivity (KT) due to double diffusion in the ocean general circulation model. These parameterization schemes are based on a functional dependence of KT on Rρ. Below the summary of those double-diffusion parameterization schemes used in the present study for the comparison of KT to VMP observation is presented.
a. Salt finger parameterization
b. Diffusive convection parameterization
APPENDIX B
Statistical Error
APPENDIX C
Uncertainties in Turbulence Parameters
Past studies demonstrated that prescribing the correct value of τ0 in the frequency response function (expression 5 and (B6)) is still a challenging problem (Gregg 1999; Hummels 2012). In association with uncertainty in estimating H(f), χ is usually reported for slower profiling speeds and/or lower dissipation rates (Gregg 1999). However, it is worth pointing out that approximately 99% of the ε vales below the mixed layer during winter 2019 and spring 2019 in the EAS are less than 5 × 10−8 W kg−1 (Fig. S2), suggesting prevailing low dissipation rates in the depth regime of interest in the study region. We assessed the sensitivity of χ estimates based on τ0 value of 3 × 10−3 s (τ ∼ 3.4 × 10−3 s) and 5 × 10−3 s (τ ∼ 5.6 × 10−3 s), instead of the default value of 4.1 × 10−3 s. Our analysis shows that 99% of χ estimation based on the τ0 value of 4.1 × 10−3 s is within a factor of 1.5 with respect to the estimation based on the values 3 × 10−3 s and 5 × 10−3 s for τ0 (Figs. S3 and S4).
A frequency histogram of χ depicts that roughly 99% of the estimation of χ is higher than 5 × 10−11 K2 s−1 (Fig. S5). The frequency spectra of temperature gradient computed from the thermistor for different values of χ during winter 2019, and spring 2019 are compared with the frequency spectrum of the noise in the gradient of temperature fluctuations (Fig. S6). For that purpose, we followed the method proposed by Lueck (2019) and used their default values for the noise model to derive the temperature gradient noise spectrum. In general, amplitudes of the frequency spectrum of the noise and temperature gradient computed from the thermistor show a comparable magnitude when noise is started to dominate in the data (Fig. S6). For higher values of χ (∼1 × 10−7 K2 s−1), the noise-dominated portions persist above 90 Hz (Fig. S6). The noise-dominated portions shift to lower frequencies with respect to reduction in the magnitude of χ, and for low values of χ (∼5 × 10−11 K2 s−1), noise-dominated portions are apparent from 40 Hz (Fig. S6). It is apparent from the figure that even in the lower values of χ, the signal is well above the noise, and χ obtained by integration is not affected by the noise-dominated part of the spectra.
Note that, while deriving ε and χ, local isotropy is assumed. However, such an assumption of isotropy is valid only in turbulent conditions and may not be applicable in a double-diffusion regime with low Reb values (Reb < 100). As demonstrated by previous studies, the isotropy assumption may be reasonable in the layers but not in the interfaces in the staircase structure associated with double-diffusion processes (Stillinger et al. 1983; Gregg and Sanford 1987; Hamilton et al. 1989; McDougall and Ruddick 1992; Guthrie et al. 2015). The assumption of isotropy in the interfaces leads to the overestimation of ε and χ values across the entire staircases (Gregg and Sanford 1987; Hamilton et al. 1989; McDougall and Ruddick 1992; Caplan 2008; Guthrie et al. 2015; Gregg et al. 2018). For instance, based on microstructure measurement collected as part of the Caribbean Sheets and Layers Transect (C-SALT) field program in the western tropical North Atlantic, Gregg and Sanford (1987) showed that isotropic assumption in the interfaces in a salt finger regime slightly overestimated the ε value when it was estimated across interfaces and layers (1.9 × 10−10 W kg−1) compared to the estimation based on the data in the layers alone (1.4 × 10−10 W kg−1). Gregg and Sanford (1987) further demonstrated that χ estimated over entire staircase structures (2.4 × 10−8 K2 s−1) is 4 times higher than the estimation only at the layers (5.7 × 10−9 K2 s−l), while the estimation only at the interface (1.1 × 10 −7 K2 s−l) reaches as large as a factor of 20 compared to layers. These results suggested that the estimation of ε and χ in the staircase are dominated by values in the layers rather than in the interfaces (McDougall and Ruddick 1992). Similarly, based on the microstructure measurements from a slowly moving profiler in the diffusive staircases regimes in the arctic ocean, Guthrie et al. (2015) have reported that χ estimates in the interfaces (6 × 10−9 K2 s−1) are 20 times larger than that in the layers (3 × 10−10 K2 s−1). However, Guthrie et al. (2015) showed that the difference in the value of ε in the layer (3 × 10−10 W kg−1) and interface (5 × 10−10 W kg−1) is relatively smaller compared to χ.
Note that in the present study, ε and χ are estimated at a vertical resolution of ∼3 m. However, the mean layer thickness at the staircase structure is around 1.1 m (please refer to section 3d). Hence, the vertical resolution of our data is insufficient to estimate the turbulent parameters only at the layer region. Nevertheless, the interface’s impact on our default estimation of χ and ε in the staircases in the dataset used in this study is evaluated. For that purpose, following Gregg and Sanford (1987), we identified two data segments where both layer and interface exist, and the estimation of turbulent parameters in the layer region is compared with estimation where both layer and interface prevail (Fig. S7). Consistent with the previous result of Gregg and Sanford (1987), the χ estimated in the layer region alone (1.2 × 10−8 K2 s−1 in layer 1 and 8.6 × 10−9 K2 s−1in layer 2) is approximately 5–9 times lower than the estimation in the segment that covers both layer and interface (5.8 × 10−8 K2 s−1 in segment 1 and 7.8 × 10−8 K2 s−1 in segment 2) (Fig. S7). Similarly, ε estimated in the layer region alone (1.0 × 10−9 W kg−1 in layer 1 and 2.0 × 10−10 W kg−1 in layer 2) is approximately 4.5 times lower than the estimation in the segment, where both layer and interface prevail (1.0 × 10−9 W kg−1 in segment 1 and 9.0 × 10−10 W kg−1 in segment 2) (Fig. S7). However, we have ignored those possible errors here.
Note that in the low energetic double-diffusion active region, spectral shapes may not follow turbulence forms. To demonstrate how good our estimation of χ and ε in this low-energy environment (ε ≤ 5 × 10−8 W kg−1), wavenumber spectra of microstructure temperature gradient (shear) along with Kraichnan spectrum (Nasmyth spectrum) during winter 2019 and spring 2019 are presented in Fig. S3. It is apparent that temperature gradient spectra (shear spectra) show good agreement with the Kraichnan spectrum (Nasmyth spectrum) (Figs. S3 and S7). Hence, the above analysis also indicates that spectral shapes of microstructure temperature gradient and shear follow turbulence forms in the depth regime of interest in the study.
The drop speed of the VMP, which we used in the study, is approximately 0.8 m s−1. In the energetic environments (ε > 5 × 10−8 W kg−1), χ is estimated by fitting Kraichnan’s model spectra in the inertial–convective subrange of the temperature gradient spectra. For large ε (>5 × 10−8 W kg−1), the inertial subrange appears in higher wavenumbers (Fig. 1 of Bluteau et al. 2017), which is not resolvable by the instrument used in the study. Hence, very few data points are only available for the spectrum fitting in the energetic environment. On the other hand, in the low-energy environments (ε ≤ 5 × 10−8 W kg−1), χ is estimated by integrating temperature gradient spectra in the viscous–diffusive subrange. The frequency histogram of ε below the mixed layer during winter 2019 and spring 2019 shows that majority (∼99%) of data points below the mixed layer during the study period in the EAS is falling under this low energetic environment regime (Fig. S2). Note that we restricted our analysis below the mixed layer in this study, and hence, our estimation of χ is mainly estimated through the integration of temperature gradient spectra in the viscous–diffusive subrange.
We assume that these uncertainties are entirely independent of one another, and the total uncertainty in the estimation of ε and χ is calculated through the root sum square of the magnitude of these uncertainties. Based on this approach, the maximum expected uncertainty of ε and χ is approximately a factor of 4.5 and 9, respectively. The combined effect of the maximum value of the expected uncertainty of each parameter on Kρ, KT, and Γεχ are estimated using propagation error (Table C1). In the present study, discussions are based on the average value of turbulence parameters (e.g., Figs. 9–11). Note that in most cases, the uncertainties associated with the individual estimation of a parameter are much smaller than the maximum value of the uncertainty (e.g., Fig. S4). Based on these assumptions on uncertainty distribution, approximate 68% and 99% confidence limits of uncertainty ranges of average values of Kρ, KT, and Γεχ are estimated using a Monte Carlo approach (Table C1; supplemental material S1). It is apparent from Table C1 that uncertainty is reduced to 40% or less with respect to its expected maximum value when averaging.
The summary of uncertainty associated with the estimation of turbulent parameters. All values are in factors (e.g., factor of ∼4).
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