1. Introduction

The Madden–Julian oscillation (MJO) is a subseasonal tropical convective disturbance with far-reaching impacts on global weather and climate systems (Zhang 2013). Despite its importance and because of its complexity, MJO prediction is poor and its behaviors are not clear. Large-scale models, both coupled and atmosphere only, have demonstrated low skill at predicting the MJO (DeMott et al. 2015). DeMott et al. (2015) attributed two common threads to the unsatisfying quality of general circulation model (GCM) experiments in simulating the MJO: poor simulation of the upper ocean’s response to the MJO and large systematic errors in tropical sea surface temperature (SST). Coupled GCMs with better representation of the upper ocean’s response have generally delivered improved MJO simulations (Seo et al. 2014; Ham et al. 2014). This suggests that the MJO is a coupled atmosphere–ocean process. Hence, both air–sea interactions (Sobel et al. 2008) and internal ocean processes (Moum et al. 2016) play fundamental roles in the evolution and propagation of the MJO.

While the atmospheric structure of the MJO and MJO forcing to the ocean is at least roughly established from satellite observations and various reanalysis products, the ocean’s responses to that forcing and ocean feedbacks to the MJO are poorly known (DeMott et al. 2015). This is largely due to the paucity of observations linking oceanic responses and feedbacks to the MJO. This problem is particularly acute in the western Indian Ocean, the region where the MJO typically originates, because of piracy.

Recent observations in both atmosphere and ocean during the Dynamics of the Madden–Julian Oscillation (DYNAMO) experiment, which took place between October 2011 and March 2012, targeted the initiation and evolution of the MJO in the equatorial Indian Ocean (Yoneyama et al. 2013; Moum et al. 2014). Moum et al. (2014) gave an overview of atmospheric and oceanic features attributed to pulses of the MJO observed from a geostationary ship at 0°, 80.5°E during DYNAMO. A significant cooling of SST was evident following MJO pulses, and the cooling was due nearly equally to surface and subsurface vertical heat fluxes. The approximate equality of surface and subsurface cooling was supported by a large-eddy simulation study that focused on the mixed layer temperature response during the first 24 h of the active phase (Hoecker-Martínez et al. 2016). In that study, subsurface turbulent fluxes explained 1/4–1/3 of the net cooling. McPhaden and Foltz (2013) argued that entrainment cooling, albeit indirectly estimated, accounted for a significant cooling in the mixed layer when barrier layers were absent. Chi et al. (2014), employing data from DYNAMO moorings at 0°, 78.5°E and 2°S, 78.5°E that do not include turbulence measurements, argued that the surface mixed layer heat budget during active MJOs was primarily driven by surface heat flux and, to a lesser degree, by advection and by other unspecified fluxes (including turbulence). Here, we use direct turbulence measurements to show the details of the upper-ocean cooling by pulses of two particular MJOs. Surface and subsurface contributions to cooling were roughly equal.

The MJO also affects sea surface salinity (SSS) variability in the tropical Indian Ocean. Recent studies have demonstrated that 1) precipitation and evaporation and 2) advection of salty water from the Arabian Sea are equally important in forcing MJO-driven SSS changes (Grunseich et al. 2011; Shinoda et al. 2013; Drushka et al. 2014; Li et al. 2015). In our observations, the Arabian Sea Water (ASW) lay near 50-m depth and impacted near-surface salinity only after vigorous upward mixing.

Previous studies of the dynamic response of the tropical Indian Ocean to the MJO have been centered around the generation of the near-surface equatorial jet and equatorial waves (Shinoda et al. 2013; Jensen et al. 2015). Using a regional coupled model, Shinoda et al. (2013) demonstrated that MJO westerly winds accelerated the upper ocean eastward across the entire zonal extent of the equatorial Indian Ocean. While general characteristics of the equatorial jet have been simulated reasonably well, fundamental differences between model results and observations remain. Jensen et al. (2015) noted that the modeled equatorial jet was substantially weaker and thinner than observed. The thinner shear layer of the simulated jet may be due to the weaker mixing prescribed in the model. Our observations reveal the importance of turbulence in transmitting momentum vertically from the surface to the ocean interior.

Here, we discuss thermal, freshwater, and dynamic responses of the upper ocean to two MJO pulses observed in October–early December 2011, extending the preliminary results of Moum et al. (2014). The focus is the role of subsurface turbulent mixing in governing these responses, which we argue has been underestimated in previous studies and may not be adequately represented in model parameterizations.

The rest of the paper is organized as follows: Specifications of data used in this study are given in section 2. An overview of surface forcing, hydrographic, and acoustic components of the data, illustrating oceanic responses to pulses of the MJO, is discussed in section 3. Section 4 describes mean and variations of subsurface turbulence. An assessment of the contribution of subsurface mixing to control thermal, saline, and dynamic responses is presented in sections 5, 6, and 7, respectively. A discussion (section 8) and conclusions (section 9) follow.

2. Data

The research vessel (R/V) Roger Revelle was stationed at 0°, 80.5°E over two cruise legs, on 5–28 October and 11 November–2 December 2011, to measure oceanic and atmospheric processes in connection with studies of the MJO. Primary data sources for this study were meteorological flux measurements (De Szoeke et al. 2015), hull-mounted acoustic Doppler current profiler (ADCP), and Chameleon microstructure profiler. These two cruise periods coincided with suppressed, disturbed, and active phases of two MJO pulses (Moum et al. 2014).

Hourly averages of surface heat fluxes, zonal u, and meridional υ velocity from the 150-kHz ADCP (4-m resolution) and of 6957 turbulence profiles in the upper 250 m are analyzed. Moum et al. (1995) have documented procedures to quantify the microscale shear and thereby estimate the turbulent kinetic energy (TKE) dissipation rate ε from the measurements. Since the Chameleon microstructure profiler was launched from the aft of the ship, measurements of ε near the surface were impacted by ship wakes. Considering the ship wake–induced contamination, ε values at depths shallower than a cutoff depth (z_min) of 7 m, chosen based on Smyth et al. (1996a), are not used in this study. Pujiana et al. (2015) reported that nighttime aggregations of fish swimming against the background flow beneath the geostationary ship induced biases to the shipboard acoustic and turbulence data obtained through these cruise legs. The bias has been minimized for our present analysis using methods described in the appendix.

Hourly averages of surface and subsurface data measured between August 2011 and August 2012 at the nearby mooring at 0°, 80.5°E, part of the Research Moored Array for African–Asian–Australian Monsoon Analysis and Prediction (RAMA) mooring array (McPhaden et al. 2009), are also examined. Surface data include standard meteorological parameters such as solar radiation and precipitation, while subsurface data consist of current velocities, temperature, salinity, and mixing at some select depths from the mooring. Moored temperature microstructure sensors, χpods, mounted on the RAMA mooring at 24-, 34-, 59-, and 75-m depths, measured temperature at 10 Hz and its time derivative at 120 Hz. The reader is referred to Moum and Nash (2009) for further details regarding χpod analysis procedures. These long-term moored datasets provide not only a general overview of the background state of hydrography, flow, and mixing but also independent quantitative assessments of the shipboard measurements, though without the fine vertical resolution afforded by shipboard profiling.

In addition to the shipboard and moored data, satellite, reanalysis, and Argo float data are also examined. The satellite data are the gridded outgoing longwave radiation (OLR) from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) satellite and High-Resolution Sea Surface Temperature (GHRSST) product (Donlon et al. 2009). The OLR data have spatial resolution 0.25° × 0.25° and sampling interval Δt of 1 day, while the spatial and temporal resolutions of the SST data are 0.01° × 0.01° and daily, respectively. To fill in surface flux data while the Revelle was off station, we employ TropFlux reanalysis products (Praveen Kumar et al. 2012) consisting of shortwave, latent, longwave, sensible, and net surface heat fluxes with daily time resolution and spatial resolution 1° × 1°. The surface heat flux is the sum of shortwave, latent, longwave, and sensible heat fluxes. TropFlux has been evaluated at this location and during this period by De Szoeke et al. (2015) in comparison to shipboard data obtained during our experiment.

3. Overview

In this section, we briefly describe the evolution of the two MJO pulses observed during the periods 5–28 October and 11 November–2 December 2011 when the ship was on station at 0°, 80.5°E. The observational gap between 28 October and 10 November represents a side trip to Phuket for reprovisioning and restaffing. Ancillary data from the nearby RAMA mooring (see section 2) was used to fill this gap.

a. Surface forcing

We observed two MJO pulses at 0°, 80.5°E, each composed of suppressed, disturbed, and active phases. The phases are defined using low-pass filtered (5 day) surface wind stress τ⁰ and . The suppressed phase is defined by low-passed < 0 W m⁻², ending with the start of daytime rainfall. The active phase is defined by low-passed > 0 W m⁻² and τ⁰ > 0.025 N m⁻² with predominantly westerly wind bursts. The disturbed phase represents the intervening period between the suppressed and active phases, a transition from shallow to deep atmospheric convection, marked by increased cloudiness and more frequent daytime rainfall (Thompson 2016). The suppressed and disturbed phases together are henceforth defined as the calm phase. Time series figures are shaded to indicate suppressed (red), disturbed (green), and active (blue) phases.

The surface forcing is summarized in Figs. 1 and 2, and the average values for each of the three phases of the two MJOs are contrasted in Table 1. The first MJO pulse (labeled MJO 1) was not fully captured in our observations as the ship left the station on 28 October, thereby missing the final few days of the active phase (Fig. 2). Observations of the second, stronger pulse (MJO 2) partially covered the suppressed phase (3–17 November) but fully documented the disturbed (17–23 November) and active (23 November–1 December) phases (Figs. 1, 2a).

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Time–longitude plots of (a) OLR, (b) , (c) zonal surface wind stress , and (d) sea level anomalies averaged across 3°N–3°S, illustrating eastward propagation of two pulses of the MJO over the Indian Ocean in October–early December 2011. A complete cycle of the first pulse passed over the observational site at 0°, 80.5°E over the course of 6 Oct–1 Nov 2011, while the second pulse occurred between 3 Nov and 1 Dec 2011. Colored bars on the y axis mark the suppressed (red), disturbed (green), and active (blue) phases of each MJO pulse. Positive indicates westerly (eastward) zonal winds. Slanted dashed lines in (a) indicate the speed at which the MJO convective pulses propagate eastward.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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Hourly averages of (a) OLR, (b) τ⁰, (c) , (d) T, (e) P (blue) and E (red) rates, (f) S, and (e) N² data at 0°, 80.5°E observed over the period of two MJO pulses during 6 Oct–2 Dec 2011. The data, except the OLR, observed between 6 and 28 Oct and 11 Nov–2 Dec are from the R/V Revelle, while those observed between 28 Oct and 11 Nov are from the nearby RAMA mooring. For each MJO pulse, shaded areas in (a) mark the suppressed (red), disturbed (green), and active (blue) phases. Thick black contours in (d) and (g) indicate the ML base, while thin gray contours in (d) and (g) represent the RL base. Blue contours in (d) and (g) mark the isothermal layer base.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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Table 1.

The , τ⁰, and cumulative rainfall measured at the ship and averaged separately over suppressed, disturbed, and active phases of the two MJOs observed at 0°, 80.5°E in boreal autumn 2011.

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The suppressed phases were characterized by strong surface heating, relatively weak winds, and little rainfall (Table 1; Fig. 2). During the disturbed phases, winds were also weak, but surface heating was reduced because of increased precipitation and clouds. During the active phases, winds and precipitation both increased and there was a net cooling of the sea surface by the atmosphere. SST increased during the suppressed phases, decreased during the active phases, and was roughly constant during the disturbed phases (Fig. 3c). Relative to MJO 1, MJO 2 was preceded by stronger surface heating and weaker winds. The active phase of MJO 2 was marked by stronger winds and cooling.

Two westerly wind bursts, separated by 1.5 days, dominated the active phase of MJO 2 (Fig. 1c). These have been attributed to the passage of sequential, convectively coupled, atmospheric Kelvin waves formed at 40°–50°E and propagating eastward with a phase speed of 8.6 m s⁻¹, and enveloped by the MJO convective clouds that traversed eastward at a slower speed of 5 m s⁻¹ (Fig. 1a; Moum et al. 2014; Baranowski et al. 2016).

b. Thermal and haline responses

For this discussion it is useful to imagine the upper ocean divided into three layers, as shown in Figs. 2d and 2g. The uppermost is the surface mixed layer (ML), in which turbulence is strong and stratification is weak (Brunt–Väisäla frequency N indicates the stratification strength). This layer interacts most directly with the atmosphere. Temperature T and salinity S respond rapidly to changes in surface forcing and feed back to the atmosphere on longer time scales. The ML base, denoted z = −h(t), is conventionally defined by a density increase of 0.01 kg m⁻³ above the surface value. The lowest layer is the pycnocline, in which stratification is strong and turbulence is weak. The uppermost boundary of the pycnocline is denoted z = −H(t) and is defined by an isopycnal. In the present analyses, we use σ_θ = 22.1 kg m⁻³ for the first leg of our observation period (6–28 October) and σ_θ = 22.9 kg m⁻³ for the second leg (11 November–2 December), adjusting the definition to account for large-scale changes between the two periods. The lower extent of the pycnocline is not important here. Between these layers, that is, in −H < z < −h, lies the remnant layer (RL), a moderately stratified, weakly turbulent blend of ML and pycnocline waters. The definition of RL used here follows that implemented by Brainerd and Gregg (1993).

An influx of salty water (S > 35.5 psu) from the Arabian Sea (ASW; Schott and McCreary 2001) in early November affected a significant change in the salinity profile between first and second legs. In November, the upper ocean was both saltier and more strongly stratified than in October, with freshwater overlying a subsurface salinity maximum that varied from 50- to 80-m depth (Figs. 2f,g, 3d,e). This change had some influence on the nature of diurnally varying ML heat content as described below.

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Hourly averages of (a) τ⁰, (b) , (c) T, (d) S, and (e) N² at 0°, 80.5°E during two MJO pulses between 6 Oct and 2 Dec 2011. The T, S, and N² time series demonstrate averages across the surface ML (red) and the RL (blue). Black curve in (c) indicates SST. The data measured between 6 and 28 Oct and 11 Nov and 2 Dec are from the R/V Revelle, while those observed between 28 Oct and 11 Nov are from a nearby RAMA mooring.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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During the suppressed phases, diurnal variations in SST ranged from 0.5°C to more than 2.5°C (Fig. 3c). The greater variations during the suppressed phase of MJO 2 were associated with slightly greater heating rates, weaker winds, and the significantly shallower ML in part caused by the greater stratification brought by the changes in salinity. The deeper ML in Figs. 2d and 2g during MJO 1 acted to distribute diurnal surface heating over a greater volume and hence to reduce diurnal variations in both SST and ML temperature.

The imbalance between daytime and nighttime during the suppressed and disturbed phases increased ML temperature by 0.48°C during MJO 1 and by 0.75°C during MJO 2 (Figs. 3b,c). RL temperature increased 0.57°C during MJO 1 and 0.38°C during MJO 2 (Fig. 3c). The increase was smaller during MJO 2 because of the isolated events cooling the RL on 12 and 16–17 November 2011, possibly associated with an oceanic Rossby wave (Seiki et al. 2013).

Over the course of the suppressed and disturbed phases, ML salinity increased by 0.1 psu during MJO 1 and by 0.2 psu during MJO 2 (Figs. 2f, 3d). Average salinity in the surface ML was fresher than in the RL by 0.2 psu.

During the active phases, net heat loss through the surface reduced ML temperature by 0.3°C during MJO 1 and 1.1°C during MJO 2 (Fig. 3c). RL temperature decreased by 0.2°C during MJO 1 and 0.8 °C during MJO 2 (Fig. 3c). Although precipitation P exceeded evaporation E during the active phase, ML salinity increased by 0.06 psu for MJO 1 and by 0.27 psu for MJO 2 (Fig. 3d). Meanwhile, RL salinity increased 0.07 psu for MJO 1 and decreased 0.12 psu for MJO 2 (Fig. 3d).

Because of the strong salinity stratification, an isothermal layer (IL) extended below the ML base throughout the MJO phases. The IL base is identified by a temperature difference equivalent to 0.01 kg m⁻³ of density decrease from the surface (with the salinity fixed at its surface value). The barrier layer, the difference between the IL and ML bases, was as thick as 30 m during the suppressed and disturbed phases (Fig. 2d). The barrier layer was reduced during the active phase, except for a brief period during the second wind burst when it was 40 m thick.

c. Dynamic response

The dominant dynamic response during the observation period was the generation of an eastward Yoshida–Wyrtki jet during the active phase of MJO 2. The wind bursts accelerated the current to 1.5 m s⁻¹ in a near-surface jet underlain by strong vertical shear Sh (Figs. 4a,b,d). The core of the jet was roughly symmetric about the equator, constrained between latitude 2°N–2°S, and carried an eastward transport of 24 Sv (1 Sv ≡ 10⁶ m³ s⁻¹) within the upper 100 m (Moum et al. 2014). The upper-layer acceleration in response to the MJO 1 active phase was less pronounced (Fig. 4b) than in MJO 2, consistent with weaker wind stress τ⁰.

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Hourly averages of (a) (blue) and meridional wind stress (red), (b) u, (c) υ, and (d) Sh² at 0°, 80.5°E during two MJO pulses between 6 Oct and 2 Dec 2011. Thick black contours mark the ML base, while thin gray contours indicate the RL base. Cyan contours in (b) and (d) mark the base of the Yoshida–Wyrtki jet. Positive values in (b) denote eastward u, and positive values in (c) indicate northward υ.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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Westerly wind-forced Kelvin waves might also contribute to the observed upper layer u variations along the equatorial Indian Ocean, which are typically evident in the near-equator sea level anomalies (Shinoda et al. 2013). Anomalies in the sea level η, averaged across 3°N–3°S, traversed eastward across the basin on roughly a monthly basis with phase speeds matching those of low baroclinic mode Kelvin waves in the equatorial Indian Ocean during our observations (Fig. 1d; also see Iskandar and McPhaden 2011). Eastward currents attributed to downwelling Kelvin waves (i.e., positive η anomalies, orange-red in Fig. 1d) might partly accelerate eastward currents during the active phases of both MJO pulses, while the westward current associated with upwelling Kelvin waves (negative η anomalies, blue in Fig. 1d) opposes eastward currents during the calm phase of MJO 2 (Figs. 1d, 4b).

Current measurements captured a 5-day oscillation, evident particularly in υ within the upper 75 m during the suppressed phase of MJO 2 (Fig. 4c). This signal included strong Sh² at depths between 40 and 60 m on 13–15 November 2011 (Fig. 4d) and coincided with a pair of cooling events between 11 and 18 November 2011 (Fig. 3c). The oscillation may represent a Yanai wave train, possibly resulting from a series of wind bursts occurring through 1–9 November 2011 (Fig. 4a). Nagura et al. (2014) and Smyth et al. (2015) reported Yanai waves with similar properties, although at a longer time scale, generated by winds in the western Indian Ocean. In addition to the Yoshida–Wyrtki jet and equatorial waves, the upper-layer horizontal currents responded to diurnal and semidiurnal tidal forcing (Figs. 4b,c).

4. Upper-ocean mixing

a. Turbulence evolution

During the suppressed and disturbed phases, convectively driven mixing dominated ML turbulence. Aided by stronger winds and weaker stratification, convection penetrated deeper during MJO 1 than MJO 2. Strong turbulence is characterized here by large nighttime values of ε (Figs. 5a,b). Averaged over a 5-m depth range including the ML base, ε showed the diurnal cycle of nighttime peaks and daytime minima during the calm phase (Fig. 5c; red curve), emphasized by a comparison of daytime- (1000–1600 local time) and nighttime-averaged (2200–0400 local time) profiles of ε during the suppressed and disturbed phases of MJO 1 and 2 (Fig. 6a).

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Hourly averages of (a) , (b) ε, (c) ε averaged over −h − 5 m < z < −h (red) and −H − 5 m < z < −H (blue), and (d) Ri at 0°, 80.5°E during two MJO pulses in 6 Oct–2 Dec 2011. The ε data are from shipboard Chameleon microstructure profiler. Black, gray, and green contours in (b) and the cyan contour in (b) mark the ML base, the RL base, L_MO, and the base of the Yoshida–Wyrtki jet, respectively.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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(a) Averaged daytime (orange; 1000–1600 local time/0400–1000 UTC) and nighttime (black; 2200–0400 local/1600–2200 UTC) profiles of ε over the suppressed and disturbed phases (calm phases) of MJO 1 and 2 pulses observed at 0°, 80.5°E between 6 Oct and 2 Dec 2011. (b) Normalized ε profile when h/(−L_MO) > 1 averaged over the calm phases of the MJO pulses. Vertical dashed line marks = 0.64. (c) Profiles of ε averaged over the course of two cruise legs (black) and calm (red) and active (cyan) MJO phases. Black, red, and cyan rectangles show time-averaged ε through two cruise legs, calm phases, and active phases, respectively, obtained from the moored χpods deployed at the nearby RAMA mooring. Color-coded thin curves in all panels indicate the 95% bootstrap confidence limits for the profiles.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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While mixing driven by the diurnal jet (Moulin et al. 2017) can trigger turbulence below the ML in oceanographic stratified shear flows (Smyth et al. 2013) and elsewhere, it does not do so here, at least not during prewind burst MJO phases, nor does there appear to be significant shear-generated daytime turbulence to the depths of the nighttime ML.

Convective mixing, induced by surface buoyancy loss to the atmosphere , appears as the dominant TKE source driving the diurnal variation of ε in the ML. The normalized nighttime ε, (Fig. 6b), decayed with depth and was near 0.64, a typical value for convective mixed layers (e.g., Shay and Gregg 1986), over much of the layer. Wind-driven mixing and other physical processes such as surface wave breaking likely explained > 1 near the surface (Anis and Moum 1994). The Monin–Obukhov length, , where κ is von Kármán’s constant and ρ is seawater density, was on average 6 times smaller than the ML thickness during the MJO calm phases (Fig. 5c), further confirming that TKE production within the ML during the calm phases was primarily derived from convection.

Deep turbulence occurred at the RL base but appeared uncoupled from surface forcing (Figs. 5b,c). Unlike near-surface turbulence, it did not exhibit consistent nighttime maxima and daytime minima. Shear-driven mixing likely accounted for the deep turbulence as it was observed at depths where the gradient Richardson number Ri = N²/Sh² was low (Fig. 5d). Note that enhanced ε and low Ri were also identifiable within the RL on 11–17 November during the calm phase of MJO 2 (Figs. 5b,d).

Surface-forced mixing extended to the pycnocline depth over the course of the MJO active phase. This was particularly evident through the active phase of MJO 2, during which low Ri and large ε were observed at the upper pycnocline in response to the passage of the Yoshida–Wyrtki jet (Figs. 5b,d). Turbulence often took the form of rapid bursts of a few hours duration extending downward from the ML base, similar to “deep cycle” turbulence observed in the eastern equatorial Pacific (e.g., Moum et al. 1989; Smyth et al. 2013; Pham et al. 2017; Smyth et al. 2017).

Sheared currents and consequent strong mixing continued past the active phase. During the wind burst, the mean value of L_MO was 22 m, or 60% of the ML thickness, indicating that both wind stress and buoyancy contributed to producing turbulence within the ML. The mean value of ε measured during the active phase of MJO 2 in the ML was 1.1 × 10⁻⁶ m² s⁻³, about 2 times larger than in the RL (Fig. 5c). Moreover vertical structure of time-averaged ε indicates that mixing in the uppermost 100 m during the active phase was 1.5 × 10⁻⁶ m² s⁻³ on average, a factor of 5–6 greater than that during the calm phase (Fig. 6c).

The foregoing results, obtained from ship-based microstructure measurements, are in agreement with those collected from sensors attached to the nearby RAMA mooring. Cruise-averaged values of ε computed from shear probes on Chameleon agreed with those calculated from values inferred from measurements by fast thermistors on moored χpod sensors at the χpod depths (Fig. 6c).

b. Turbulence fluxes

The observed values of ε, Sh², and N² are employed to estimate turbulent mass diffusivity K_ρ and turbulent eddy viscosity K_m, assuming a balance between creation and dissipation in the turbulent kinetic energy equation as follows (e.g., Smyth et al. 1996a,b):

View Expanded

where P_τ is the rate of TKE production by turbulent Reynolds stress interacting with the mean vertical shear; J_b denotes the creation of TKE by the turbulent buoyancy flux.

The turbulent diffusivity and eddy viscosity are approximated as

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respectively, where the flux coefficient Γ (sometimes called the mixing efficiency) is approximated as 0.2 (Osborn 1980; Moum 1996). Turbulent thermal diffusivity K_T and saline diffusivity K_S are assumed to be equal to K_ρ.

The terms K_ρ and K_m were largest close to the surface and generally decayed with depth (Figs. 7a,b). The average value of K_ρ in the upper 100 m during the active phases was 4 × 10⁻² m² s⁻¹, roughly 6 times greater than during the calm phase. The mean values of K_m in the upper 100 m during the active and calm phases were 4.6 × 10⁻³ and 1.3 × 10⁻³ m² s⁻¹, respectively.

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Time-averaged estimates of (a) K_ρ and (b) K_m at 0°, 80.5°E through the cruise legs (black), active phases (cyan), and calm phases (red) of two MJO pulses measured between 6 Oct and 2 Dec 2011. Gray curves denote the 95% bootstrap confidence limits for the cruise-averaged estimates.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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The zonal component of the turbulent flux of momentum, or Reynolds stress, is given by

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The turbulent heat J_q and salt J_s fluxes are computed as

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where ρC_p is the volumetric heat capacity, and ∂u/∂z, ∂T/∂z, and ∂S/∂z are vertical derivatives of zonal current, temperature, and salinity, respectively.

The average value of τ_x was negligible at the top of the pycnocline and increased above this depth (Fig. 8c). A least squares exponential fit to τ_x within the upper 100 m indicated that the scale depth of the stress divergence was 45 m, and the intercept of the fit at the surface was about the same as the average value of zonal wind stress . Exponential depth dependence was also apparent in the time-averaged vertical structure of τ_x during the calm and active phases.

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Time-averaged estimates of (a) J_q, (b) J_s, and (c) τ_x at 0°, 80.5°E through the cruise legs (black), active phases (cyan), and calm phases (red) of two MJO pulses measured between 6 Oct and 2 Dec 2011. Gray curves denote the 95% bootstrap confidence limits for the cruise-averaged estimates. Black, red, and cyan circles indicate surface fluxes during the cruise legs, calm phases, and active phases, respectively. The surface heat flux is given as −( − shortwave radiation). Black box in (a) indicates the average depth of the ML base. Color-coded dashed curves in (c) show exponential fits to the subsurface τ_x values.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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Turbulent heat flux J_q was usually downward (J_q < 0) on average (Fig. 8a). The cruise-averaged value of J_q at the average ML base (18 m) was −48 W m⁻², while that at the average RL base at 67 m was −33 W m⁻². Heat transfer across the upper ocean was intensified during the MJO active phases. Although subsurface turbulence generally cooled the surface ML, it occasionally warmed the ML following heavy precipitation events. Rainwater cooled the sea surface and hence reversed ∂T/∂z, which consequently led to upward turbulent heat flux warming the surface ML. The turbulent salt flux J_s was generally upward across the upper ocean during all MJO phases (Fig. 8b), consistent with the negative vertical salinity gradient ∂S/∂z < 0 because of to the salinity maximum near the RL base (Fig. 2f).

Colored circles at z = 0 in Fig. 8 show the surface fluxes averaged over the same periods as subsurface fluxes. The subsurface fluxes of heat and momentum at least roughly asymptote to surface values. The salt flux profile does not, and it is not clear to us why this is the case since the salinity signal is significant and easily measurable. While the precise near-surface vertical structures of the fluxes are not clear from these observations, this agreement (at least in the case of heat and momentum) indicates that our estimates are at least roughly dynamically consistent with the surface flux matching condition.

5. Heat transfers

To further assess the role of turbulent mixing, a vertically integrated heat equation is employed to examine the heat budget in the ML and the RL. The ML extends from the surface to z = −h(t), so that the net ML heating is described by

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The fraction of the solar heat flux that penetrates to z = −h, denoted I^−h, is estimated from radiation profiles obtained during the experiment (C. Ohlmann 2017, personal communication). The term here does not represent turbulent heat flux exactly at the ML base but rather an estimate averaged over −h − 5 m < z < −h. This average permits the estimates of when ML is shallower than z_min = 7 m, as is typically observed during the suppressed phase of the MJO, and accommodates the region where direct entrainment by turbulence takes place (Smyth et al. 1996a). The residual R includes unresolved processes (e.g., horizontal advection) as well as observational errors.

The RL extends from z = −h(t) to z = −H(t), and the corresponding heat evolution equation is

View Expanded

where I^−H is the radiative heat flux at the RL base, and the remaining terms are as defined in (7).

In the following two subsections we discuss our estimates of these terms during MJO 1 and MJO 2, including the cumulative estimates that are obtained by integrating (7) and (8) in time using the trapezoidal rule.

a. MJO 1

1) Surface mixed layer

Through most of the suppressed phase of MJO 1, the surface ML was warmed by the surface heat flux minus the fraction of the solar flux that penetrated the ML base and cooled from below by (Figs. 9a,b). The excess of accumulated over accounted for 76% of the net heating, 32 MJ m⁻² or 46 W m⁻² on average, in the ML (Figs. 9b, 12a). Because of substantially reduced surface warming, the ML warming during the suppressed phase subsequently turned to cooling at an average rate of −14 W m⁻² in the disturbed phase (Figs. 9b, 12a). The residual heat flux contributed to warming the ML throughout the calm phase, and advection likely predominantly controlled the residual. Advective heat flux into the ML, − inferred from averaged ML velocities and spatial gradients of satellite-derived SST centered at 0°, 80.5°E, exhibited a net ML warming of 13 W m⁻², on average, during the calm phase (Fig. 9b). This advective heat flux accounted for roughly 50% of the average residual-driven net warming in the ML (Fig. 12a).

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The cumulative heat budget in the ML and RL during MJO 1. (a) τ⁰. Time-integrated (i.e., accumulated) heating rate and heat fluxes into the (b) ML and (c) RL. Orange curve indicates net heating rate, red curve denotes accumulated surface net heat flux; blue and cyan curves illustrate accumulated turbulent heat flux across the ML and RL bases, respectively; magenta and green curves denote accumulated penetrating radiation at the base of ML and RL, respectively; and dashed line represents residual. A 1.25 cpd low-pass filter is applied to smooth the net heating rate and heat fluxes. Gray diamonds in (b) show time-integrated advective heat flux into the ML inferred from daily averages of shipboard current velocities and spatial gradient of satellite-derived SST. The spatial gradient of SST is computed using centered differences around 0°, 80.5°E using a 0.25° separation.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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During the active phase, the ML lost heat at an average rate of 147 W m⁻² (Figs. 9b, 12a). The heat loss was partly due to , with an average cooling rate of 67 W m⁻², while the mean was −30 W m⁻² (Fig. 12a). These two dominant factors accounted for 45% and 20% of the net cooling, respectively, and the rest of the cooling was due to the residual. Advection appeared to cool the ML (Fig. 9b), though its average heat, −5 W m⁻², only accounted for a tenth of the average residual heat flux (Fig. 12a). Note that the average magnitudes of and were comparable during the active phase.

2) Remnant layer

The RL, in general, warmed over the calm phase of MJO 1 (Fig. 9c). During the suppressed and disturbed phases, the residual term was the dominant heat source. A significant contribution was added by −I^−h, due both to the sunny weather and the shallowness of the overlying ML, and by (Figs. 9c, 12a), though this was counteracted by , which transferred heat to the ocean interior.

In the active phase, a net heat loss of −4.7 MJ m⁻², equivalent to −12 W m⁻² on average, was observed largely because of the residual heat flux (Figs. 9c, 12a). Warming from above via both −I^−h and was smaller than the residual, while the cooling effect of was relatively small and insufficient to explain the heat loss registered in the RL during the active phase.

b. MJO 2

1) Surface mixed layer

During the suppressed phase of MJO 2, the net heating rate in the surface ML was mainly controlled by vertical processes. The cumulative downward exceeded that of downward by 15 MJ m⁻², 36 W m⁻² on average, and the ML heated at the rate 39 W m⁻² (Figs. 10a,b, 12b). Because of the reduced surface warming, the ML registered cooling at an average rate of −11 W m⁻² in the disturbed phase (Figs. 10b, 12b).

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As in Fig. 9, but for the suppressed and disturbed phases of MJO 2.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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In the active phase of MJO 2, the net surface heat flux mostly drew heat from the ocean during two discrete wind bursts (Figs. 11a,b). The heat loss was small during the intervening period. Like , responded to the wind bursts (Fig. 11b). Turbulence transferred heat across the ML base at an average rate of −79 W m⁻² (Fig. 12b, rightmost frame). The downward continued to cool the ML even after the wind bursts ceased and net surface warming resumed (Fig. 11b).

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As in Fig. 9, but for the active phase of MJO 2.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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Average magnitudes (W m⁻²) of the cumulative heat budget terms during various phases of (top) MJO 1 and (bottom) MJO 2. The top half of each represents the surface ML, while the bottom half of each represents the RL.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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Surface and subsurface turbulent heat fluxes appeared as the main mechanisms explaining the net cooling of the ML during most of the active phase of MJO 2 (Fig. 11b). A cumulative heat loss of −142 MJ m⁻², equivalent to −205 W m⁻² on average, was observed in the surface ML (Figs. 11b, 12b). Of this heat loss, entrainment cooling accounted for 38%, while cooling through the surface explained 37%. Thus, a net cooling of 1.1°C measured in the ML during the active phase was predominantly, in similar proportions, caused by surface forcing and subsurface turbulence. The residual heat flux, accounting for 25% of the net cooling, was likely caused by advection (Fig. 11b).

2) Remnant layer

The water column registered a net heat loss of −163 W m⁻² during the suppressed phase, and the heat loss was driven by the residual heat flux (Figs. 10c, 12b). Over the disturbed phase, the RL turned warmer, again because of the residual (Figs. 10c, 12b). Downward J_q across the ML and RL bases were small.

Like the surface ML, the RL cooled during the wind bursts within the active phase of MJO 2. Vertical divergence of J_q exerted a smaller contribution than the residual heat flux. The cumulative heat loss observed in the RL during the active phase was −138 MJ m⁻², equivalent to −200 W m⁻² on average, resulting in a cooling of the RL of 0.8°C (Figs. 11c, 12b, 3c). The downward J_q was strong but equally so at the top and bottom of the layer so that its net effect on the RL temperature was small. Instead, the residual, which may represent advection by Yanai waves as described by Smyth et al. (2015), was dominant.

6. Salt/freshwater transfers

Precipitation, evaporation, and advection have been suggested as the main processes controlling MJO-induced SSS variations (Drushka et al. 2012, 2014; Li et al. 2015), while horizontal advection of salty ASW eastward along the equator is the primary cause of increased upper-ocean (ML + RL, in our nomenclature) salinity during the October–November monsoon transition period (Wyrtki et al. 1971; Jensen 2001; Grunseich et al. 2011). Our observations support this conclusion approximately but suggest a secondary effect from precipitation while also allowing us to distinguish between advection into the ML, advection into the RL, and turbulent transfer between the two. Our observations of upper-ocean salinity showed an overall increasing trend over the various MJO phases, except in the RL during the active phases of the MJO. Note that the salinity maximum (S > 35.5 psu) attributed to the ASW lay below the RL throughout MJO 1 and the suppressed phase of MJO 2 but rose into the RL, particularly between 30 and 60 m, during the disturbed phase (Fig. 2f). In this section, we assess the causes of those trends via salt budgets for the ML and RL.

For the surface ML, the vertically integrated salt equation is expressed as

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where is equivalent surface salt flux, S₀ is surface salinity, and the residual R consists of advective effects as well as errors in our estimates of other terms. For the salt budget in the RL, (9) becomes

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The equivalent freshwater budget for each layer can be obtained through dividing (9) and (10) by the average value of salinity (multiplied by −1) across each respective layer.

a. MJO 1

1) Surface mixed layer

The surface ML exhibited an overall increase in salt content (or freshwater loss) over MJO 1, with acting as the main driver for the increase continuously throughout all phases of the MJO. A net salt gain of 3 psu m⁻¹, equivalent to a freshwater loss of 87 mm, was accumulated during the suppressed phase, over which excess E over P and almost equally contributed to the salt gain [Figs. 13a,b, 16a (below)]. The ML registered a net salt loss of −2.3 psu m⁻¹ during the disturbed phase, although increased fivefold (Figs. 13b, 16a). Substantial residual salt flux, together with increased rainfall, offset to account for the ML freshening during the disturbed phase. Aided by and to a lesser degree R, the ML accumulated a net salt input of 2.3 psu m⁻¹ despite increased rainfall during the active phase (Figs. 13b, 16a). Vertical divergence between upward across the ML base and upward (or downward freshwater flux) through the surface accounted for the net salt input.

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The cumulative salt budget in the ML and RL during MJO 1. (a) τ⁰. Time-integrated salinity trend and salt fluxes into the (b) ML and (c) RL. Orange curve indicates integrated salinity trend; red curve denotes integrated surface salt flux; blue and cyan curves illustrate integrated turbulent salt flux across the ML and RL bases, respectively; and dashed line is residual. A 1.25 cpd low-pass filter is applied to smooth the salinity trend and salt fluxes.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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2) Remnant layer

Like the ML, the RL exhibited a net salt gain over MJO 1. Within the RL the offset between R and dictated the salt gain, while was relatively small. The layer accumulated a net salt gain of 19.9 psu m⁻¹ over the suppressed and disturbed phases combined, of which 19.2 psu m⁻¹ was attributed to the excess of the residual over upward (downward freshwater flux; Figs. 13c, 16a). The net salt gain turned into salt loss during the active phase, through which the accumulated salt loss in the RL was −2 psu m⁻¹, driven mainly by upward turbulent salt flux into ML (Figs. 13c, 16a).

b. MJO 2

1) Surface mixed layer

The surface ML, in general, continued to become more salty through MJO 2. A net salt input of 1.5 psu m⁻¹ was observed during the suppressed phase, with similar contributions from downward , upward , and R [Figs. 14a,b, 16b (below)]. During the disturbed phase, increased precipitation was insufficient to balance R and to yield a net salt gain of 0.4 psu m⁻¹ (Figs. 14b, 16b). The trend of ML salt gain continued during the active phase despite a net freshwater gain of 104.3 mm (Fig. 15b) at the surface. The total salt input in the ML was 9.1 psu m⁻¹, equivalent to 257 mm of freshwater loss on average, and it was mainly because of the vertical divergence between and (Figs. 15b, 16b).

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As in Fig. 13, but for the suppressed and disturbed phases of MJO 2.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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As in Fig. 13, but for the active phase of MJO 2.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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Values of the cumulative salt budget terms (psu m⁻¹) during various phases of (top) MJO 1 and (bottom) MJO 2. The top half of each represents the surface ML, while the bottom half of each represents the RL.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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2) Remnant layer

In the RL, the residual salt flux was dominant, bringing salt in during all three MJO phases. The offset between the amount of salt brought into the RL by the residual and the amount of salt exported upward into the ML by turbulence explained the increase of RL salt content that registered a net salt input of 10.6 psu m⁻¹ during the calm phases (Fig. 16b). The layer between 30 and 60 m exhibited temperature and salinity characteristics of the ASW during the disturbed phase (Fig. 17). In contrast to the calm phase, the active phase RL revealed a net salt loss of −6.4 psu m⁻¹, which was driven chiefly by the upward (Figs. 15c, 16b).

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T–S scatter from Argo profilers deployed within a region bounded by latitude of 5°N–5°S and longitude of <70 °E in the Indian Ocean during October–November 2011 (gray filled circle) and from the R/V Revelle between 30 and 60 m during 18–25 Nov 2011 (black open circle). ASW, AAIW, and RSPGIW stand for Arabian Sea Water, Antarctic Intermediate Water, and Red Sea Persian Gulf Intermediate Water, respectively. The ASW, AAIW, and RSPGIW temperature (salinity) range between 27° and 29°C (35.5–35.8 psu), 3° and 5°C (34.3–34.5 psu), and 5° and 14°C (34.8–35.4 psu), respectively (Schott and McCreary 2001). Solid curves denote σ_θ.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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7. Momentum transfers

We now investigate relative contribution of wind stress and subsurface turbulence in accelerating the upper ocean, particularly during the active phase of the MJO. As discussed in section 3, the genesis of the Yoshida–Wyrtki jet during the active phase of MJO 2 is the most pronounced dynamic response documented at our station (Figs. 4a,b). Here, we examine the contribution of subsurface turbulence to the jet’s evolution. The contribution of subsurface turbulence is assessed through analyses of zonal momentum terms using a conservation equation integrated between the surface and the base of the Yoshida–Wyrtki jet layer −h_J(t):

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where is the vertically averaged zonal current, and τ_x is the zonal Reynolds stress. The superscripts 0 and J specify evaluation at the surface and the base of the jet, respectively. The jet thickness h_J(t) is inferred from the depth of maximum Sh², demarcating the Yoshida–Wyrtki jet from the less intense eastward current underneath. The first two terms on the right-hand side of (11) express turbulent momentum flux at the top and bottom of the jet layer, respectively. The residual R contains terms that we cannot estimate (the zonal pressure gradient, the zonal divergence of mean zonal momentum, the upwelling of zonal momentum, and the mesoscale eddy flux) plus observational errors. Diurnal and semidiurnal variations were filtered out by applying a low-pass filter with a cutoff frequency of 1.25 cycles per day. A linear extrapolation was employed to estimate zonal current magnitudes between the surface and the shallowest ADCP depth bin at 12 m.

The zonal current, vertically averaged between the surface and z = −h_J, accelerated eastward from about 0.3 m s⁻¹ at prewind bursts to 1–1.3 m s⁻¹ during the wind bursts (Figs. 18a,b). The jet accelerated eastward rapidly following each passage of two wind bursts, while it slowed in the intervening period. The eastward acceleration was a response to enhanced eastward (Figs. 18b,c). The , in contrast, counteracted to slow down the eastward jet in the near-surface layer by transferring eastward momentum downward to the deeper region (Fig. 18c). The resulted in westward acceleration averaging −2.4 × 10⁻⁶ m s⁻² over the active phase, roughly 2/3 the average magnitude of the contribution from (Fig. 19).

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(a) . (b) Low-passed u averaged over −h_J < z < 0 for uniform u within the upper 12 m (gray) and for linearly extrapolated u within the upper 12 m (orange). (c) Low-passed Reynolds stress at the surface (red) and at −h_J (cyan), zonal acceleration averaged between −h_J < z < 0 for uniform u in the upper 12 m (gray) and for linearly extrapolated u in the upper 12 m (orange); z = −h_J is the base of the Yoshida–Wyrtki jet layer. Orange (gray) dashed line indicates residual for the uniform (linearly extrapolated) u in the upper 12-m case. The cutoff frequency of the low-pass filter is 1.25 cycle day⁻¹.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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Average magnitudes (m s⁻²) of the cumulative budget terms in the Yoshida–Wyrtki jet layer during the active phase of MJO 2.

Citation: Journal of Physical Oceanography 48, 1; 10.1175/JPO-D-17-0146.1

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Despite its tendency to drive the surface layer eastward, surface wind stress was not enough to overcome subsurface turbulence to explain the observed eastward acceleration during the MJO active phase. The average magnitude of acceleration caused by the vertical divergence of τ_x was smaller than the observed mean eastward acceleration by 0.9 × 10⁻⁶ m s⁻² (Fig. 19).

This momentum budget is not sensitive to the extrapolation of u through the uppermost 12 m (Figs. 18b,c). For example, if we replace the linear extrapolation with a uniform value, the zonal acceleration within the Wyrtki jet layer is reduced by only about 5%.

8. Discussion

We have described ocean mixing observed during various phases of the MJO convective systems in October–early December 2011 in the equatorial Indian Ocean. Our observations indicate that turbulent mixing was critical to vertical redistributions of heat, salt, and momentum particularly over the course of the MJO active phases, most specifically during westerly wind bursts. During the MJO active phase, the average magnitude of K_ρ across the ML base was 0.8–1 × 10⁻² m² s⁻¹, a three order of magnitude increase in diffusivity relative to that during the MJO calm phase. Strong mixing during the wind bursts was not confined to the ML but extended to the RL. Convection was an important source of turbulence production in the ML, as indicated by average values of h > 2L_MO and . Shear-driven mixing at the base of the Yoshida–Wyrtki jet likely accounts for strong turbulence in the RL.

Turbulence accounted for 20%–40% of the average cooling of the surface ML during the active phases of the MJO, roughly the same as the heat loss induced by surface cooling. Chi et al. (2014) estimated the turbulent heat flux as a budget residual based on data from the DYNAMO mooring at 0°, 78°E. They found that was insignificant during the active phase of MJO 1 and > during the active phase of MJO 2. Our more direct estimates of the same ratios are 0.8 and 1.0. Moreover, our observed estimate during the wind burst period of MJO 2 was smaller than the simulated magnitude reported by Hoecker-Martínez et al. (2016). Their modeled heat flux, averaged over a 24-h period after the outset of the wind burst, varied in the range of −300 ± 100 W m⁻², about twice the observed heat flux. The discrepancy is exacerbated because the model ML is overly shallow, so its base coincides with strong mixing near the surface.

Upper-ocean salinity at the station generally increased over the course of two pulses of the MJO in October–early December 2011 within the ML. The offset between and generally controlled ML salt content throughout MJO phases. The dominant role of turbulence to entrain salty ASW across the ML base was particularly evident during the active phase of the MJO 2, when the ML registered a net salt gain despite substantial freshwater input from heavy rainfall. During this period, mixing entrained salty ASW from the pycnocline into the ML. The importance of salt entrainment, relative to rain-induced surface freshwater input, is consistent with the simulation result of Hoecker-Martínez et al. (2016). Our salt flux estimate compares reasonably well with their simulated flux, ranging around 3–5 × 10⁻⁵ psu m s⁻¹, on average, over 24 h after the onset of the wind burst. Our results signify the importance of subsurface turbulence in governing SSS under MJO convective systems and contrast with previous studies linking the surface salinity response mainly to precipitation and evaporation (Grunseich et al. 2011; Guan et al. 2014; Drushka et al. 2014; Li et al. 2015).

Within the RL, an increase in salt content was generally observed through October–November 2011, except during the active phase of MJO 2 when the amount of turbulence-diffused freshwater input exceeded that of advectively driven salt input into the layer. The salt input into the RL likely originates from the Arabian Sea, advected eastward by the monsoon transition–driven eastward current along the equator (Wyrtki et al. 1971; Grunseich et al. 2011).

The formation of the Yoshida–Wyrtki jet dominated the dynamic response of the upper ocean to MJO westerly wind bursts. The 1–1.5 m s⁻¹ eastward equatorial jet was evident across the upper 100 m at our station during MJO 2. The jet was present, though weaker, during the less energetic MJO 1 pulse. The genesis of the jet during the MJO 2 pulse was primarily controlled by wind stress and turbulence at the base of the jet. The stress acted to accelerate the jet eastward, while decelerated the jet. Vertical stress divergence between surface wind stress and subsurface turbulence accounted for 60% of observed eastward acceleration on average. This result provides a new insight into the role of subsurface turbulence in regulating the eastward equatorial jet, which we reckon has been underrepresented in previous studies. The canonical view of the eastward equatorial jet dynamic in the Indian Ocean has argued that the jet’s genesis primarily reflects a balance between two source terms, westerly winds and eastward advection of u, and two sink terms, westward pressure gradient and meridional advection of u (Nagura and McPhaden 2008, 2014). Our observations indicate that the role of the westward pressure gradient to decelerate the equatorial jet at our station is relatively less important than subsurface turbulence within the time scale of MJO wind bursts, about 5 days. This likely becomes more influential for time scales >5 days once the basinwide zonal pressure gradient is set up following the eastward propagation of the MJO westerly winds.

The underrepresentation of ocean mixing might also be a factor contributing to notable discrepancies between observations and numerical experiment results. Using a coupled ocean–atmosphere general circulation model, Jensen et al. (2015) attempted to simulate the ocean’s response to MJO 2 wind bursts and found a significantly shallower eastward jet. Their model shear layer, marking the base of the jet, was as deep as 50 m at the end of the wind bursts, while the observed shear layer extended to 100 m. Given the model and observed winds are consistent, it appears that mixing prescribed in the model was not sufficiently effective to transfer momentum downward from the surface to the ocean interior. The average value of the model eddy viscosity at the ML base during the active phase varied between (0.5–5) × 10⁻⁴ m² s⁻¹, approximately an order of magnitude smaller than our observations suggest.

9. Conclusions

From a suite of atmospheric boundary layer and upper-ocean measurements during 6–28 October and 11 November–2 December 2011, we evaluated the role of subsurface turbulence in governing the ocean’s response to two pulses of the MJO at the central equatorial Indian Ocean.

The cumulative effect of the MJO calm phases (the period of intense solar heating, infrequent precipitation, and calm winds preceding the active phase) on the surface ML was an increase in temperature and salinity by 0.5°–0.75°C and by 0.1–0.2 psu, respectively. During the MJO active phases, marked by net surface cooling, strong winds, and heavy rainfall, ML temperature decreased by 0.3°–1.1°C, while salinity continued to increase despite heavy rainfall. The largest temperature and salinity changes occurred during the stronger MJO 2. As in the ML, RL temperature increased during calm phases and cooled during active phases. The RL became saltier throughout the calm phases but rapidly freshened during the active phases as vigorous turbulence exchanged fresh near-surface water with the underlying, saltier ASW.

The most pronounced dynamic response to the MJO was the formation of the Yoshida–Wyrtki jet during the wind bursts of the MJO 2 active phase, accelerating the depth-averaged eastward current from 0.3 to 1.5 m s⁻¹.

Based on our observations, the primary roles of subsurface turbulence in vertically redistributing heat, salt, and momentum during various phases of the MJO pulses are as follows:

1. In the surface ML, surface heat flux is the main driver of warming during the calm phase. During the active phase, both surface and subsurface turbulent heat fluxes across the ML base are equally important, , in cooling the ML. Following wind bursts, turbulence continues to cool the mixed layer even after surface warming resumes. Vertical divergence of J_q is relatively unimportant to heat content variability in the RL.

2. ML salinity increases during the MJO pulses because of the excess of turbulent salt flux across the ML base, entraining salty ASW from the pycnocline upward, over the net freshwater input at the surface. On average, the turbulent salt flux is about 2 times the effective flux at the surface. In the RL, the residual salt flux counteracts the freshening effect of .

3. The acceleration of the eastward Yoshida–Wyrtki jet during MJO westerly wind bursts is due to the excess of surface wind stress over turbulence stress at the jet’s base. Here, the westward turbulent stress was about 65% of the eastward MJO wind stress.