1. Introduction
Many processes in the ocean surface boundary layer (OSBL) vary with the diurnal cycle of solar heating and nighttime cooling. The most frequently studied is that of sea surface temperature (SST), which is most pronounced under conditions of low winds and high solar insolation (e.g., Ward 2006). The diurnal variability of SST can be several degrees Celsius and has been shown to affect air–sea fluxes on climatological time scales in subtropical regions (Bernie et al. 2005; Kawai and Wada 2007; Clayson and Bogdanoff 2013). In addition to SST, diurnal variability has been observed in sea surface salinity (Drushka et al. 2014; Asher et al. 2014), momentum and shear (Weller and Plueddemann 1996; Plueddemann and Weller 1999; Cronin and Kessler 2009; Weller et al. 2014), and biogeochemical tracers such as dissolved oxygen and chlorophyll (Nicholson et al. 2015). In comparison, the diurnal variability of turbulence has received far less attention, although it is a key physical component the OSBL.
Diurnal restratification has been observed to reduce the dissipation rate of turbulent kinetic energy (ε; see section 3c for definition) below the restratification layer, leaving behind a remnant layer that is isolated from the surface wind stress (Brainerd and Gregg 1993; Caldwell et al. 1997; Callaghan et al. 2014). Restratification limits the vertical diffusion of the surface wind stress and thus causes the momentum flux to be focused to a shallower layer, causing it to slide with minimal friction (Kudryavtsev and Soloviev 1990). The magnitude of the diurnal jet is typically O(10) cm s−1 and extends to a depth of a few meters (Price et al. 1986; Woods and Strass 1986). Kelvin–Helmholtz (KH) instabilities have been observed to form from the enhanced shear due to the diurnal jet and may be a source of active turbulence (Woods 1968; Soloviev and Lukas 2014).
While there exist many studies that have investigated the response of ε to a destabilizing buoyancy flux (Shay and Gregg 1986; Lombardo and Gregg 1989) and below the diurnal jet (Lombardo and Gregg 1989; Brainerd and Gregg 1993; Caldwell et al. 1997), there have been no studies that the authors are aware of that have investigated the variability of ε within the diurnal jet. If shear instabilities are common, as suggested by Woods (1968), this would provide a source of turbulent kinetic energy (TKE), which would enhance air–sea transfer of moderately soluble gases, such as CO2 and O2 (Lamont and Scott 1970; Jähne and Haußecker 1998; McGillis et al. 2004; Zappa et al. 2007), relative to wind-based parameterizations. Experiments by Khoo and Sonin (1992) demonstrated an appreciable increase in the mass transfer of CO2 due to an increase in turbulence on the water side with zero interfacial shear or wave motion. As diurnal cycles of SST occur predominantly in low and midlatitudes, regions with a positive δpCO2 (the partial pressure of the CO2 in the air minus the partial pressure of CO2 in the water) and hence a source of CO2 to the atmosphere (Takahashi et al. 2009), enhanced turbulence associated with the diurnal jet would act to increase outgassing in these regions.
The diurnal jet in the ocean is analogous to that of the nocturnal jet in the atmosphere, also known as the low-level jet, as both consist of inertial rotations due to a diurnally varying buoyancy flux. However, there are a few key differences that could have large consequences for the dynamics. The nocturnal jet in the atmosphere is generated above the frictional stress layer during nocturnal cooling of the surface layer. This leads to an inertial oscillation generated due to frictional decoupling of the geostrophic forcing (Gill 1982). This mechanism suggests that the low-level jet only requires a nocturnal inversion to occur and will be independent of the wind and the nocturnal boundary layer depth. The diurnal jet in the ocean, on the other hand, is different in that it exists within the stress layer. Therefore, it is expected that the diurnal jet should exist as a wind-driven current that will rotate with the local inertial frequency (Price et al. 1986) and not as a free inertial oscillation (Gill 1982), although inertial oscillations could theoretically be generated from the diurnal variability in the OSBL thickness (D’Asaro 1985).
The motivation for this paper is to investigate the turbulent dynamics within the diurnal jet. What is the effect of the diurnal on the near-surface turbulence? Does the increase in shear due to the diurnal jet increase production of turbulent kinetic energy or does gravity limit the vertical diffusion of the Reynolds stress? Is the diurnal jet susceptible to shear instability? This paper will attempt to address some of these questions with regards to the diurnal increase in stratification and the diurnal jet.
The outline for the paper is as follows: Section 2 provides an overview of the diurnal processes in the OSBL. Data and methods are presented in section 3. Section 4 shows the diurnal variability of temperature and velocity over the duration of the experiment. The diurnal structure of the observations was investigated using a composite day, which is calculated from phase averaging the forcing and ocean response as a function of the local time of day in section 5. An investigation of the relevant depth scale along with comparisons of previous results is shown in section 6. Section 7 presents statistics of the Richardson number, and section 8 investigates the large values of ε near the surface. A summary and discussion of the results are presented in section 9.
2. Overview of diurnal evolution of ε
The diurnal evolution of ε in the OSBL is primarily controlled by the varying surface buoyancy flux of solar heating during the day and surface cooling during the night (Price et al. 1986). The convective cycle during the night has been well described by similarity theory (Shay and Gregg 1986; Lombardo and Gregg 1989), while the details of the stable daytime stratification regime are still relatively unknown due to the lack of observations in these shallow stable layers (Soloviev and Lukas 2014). Presented in this section is a short summary of the diurnal cycle outlining some of the larger gaps in the current understanding.
A schematic of the diurnal cycle is depicted in Fig. 1. For depths less than LMO, shear turbulence dominates buoyancy forces, and this region is denoted by the turbulent near-surface region in Fig. 1. Cooling at night causes the surface layer to be gravitationally unstable, generating convection cells that extend to the seasonal pycnocline, creating a well-mixed OSBL (Shay and Gregg 1986). Ocean convection has been well studied, and it has been shown that ε ∝ B0 below the near-surface turbulent region (Shay and Gregg 1986).
Schematic of the diurnal cycle of turbulence. The shaded region represents the OSBL. The turbulent near-surface region is the depth at which turbulent production is greater than the buoyancy flux.
Citation: Journal of Physical Oceanography 46, 10; 10.1175/JPO-D-15-0172.1
In the morning, the rising sun provides a stabilizing buoyancy flux into the OSBL. This buoyancy flux varies with depth (Paulson and Simpson 1977) and, under favorable wind conditions, the near surface of the ocean will begin to restratify. The depth to which significant heating occurs is expected to be related to LMO (Kudryavtsev and Soloviev 1990; Large et al. 1994). Below this restratification depth, a remnant layer exists that is isolated from surface wind forcing (Brainerd and Gregg 1993). A decrease in ε is observed in this remnant layer with an exponential decay in time (Brainerd and Gregg 1993; Caldwell et al. 1997; Callaghan et al. 2014).
Equation (4) only accounts for surface forcing due to the wind stress and surface buoyancy flux and does not account for other processes that could affect ε such as breaking waves (Craig and Banner 1994), Langmuir circulations (McWilliams et al. 1997; Belcher et al. 2012), shear instabilities (Woods 1968), horizontal processes associated with ocean fronts (D’Asaro et al. 2011), or breaking internal waves (Wain et al. 2015), to name a few. These processes all generate TKE, which would lead to an underestimation of ε relative to (4).
3. Data and methods
Observations of the OSBL were obtained during the Subtropical Atlantic Surface Salinity Experiment (STRASSE) aboard the Navire Océanographique (N/O) Thalassa (Reverdin et al. 2015). This experiment took place during August and September 2012 as part of the larger Salinity Processes in the Upper Ocean Regional Study (SPURS) project. The location of the experiment is shown in Fig. 2. The latitude of the experiment site was about 25.6°N, corresponding to an inertial period of 27.7 h.
Location for the five ASIP deployments (shown in black) and three Trèfle deployments (shown in red) during late August–early September 2012.
Citation: Journal of Physical Oceanography 46, 10; 10.1175/JPO-D-15-0172.1
a. Meteorological observations
Radiative fluxes and wind speed measurements were recorded aboard the N/O Thalassa. The wind stress and buoyancy flux were calculated using the TOGA COARE 3.0 algorithm (Fairall et al. 2003). Figure 3a shows the 10-m wind speed 
Time series of observations for (a) surface buoyancy flux B0 (blue), wind speed U10 (orange), and direction UDIR (green); (b) significant wave height Hs (red), peak frequency σp (blue), and mean frequency σm (green); and (c) the turbulent Langmuir number La (red), the friction velocity 
Citation: Journal of Physical Oceanography 46, 10; 10.1175/JPO-D-15-0172.1
b. Wave and current observations
Observations of surface gravity waves and velocity profiles were made with a cloverleaf buoy, the Trèfle, equipped with a downward-facing Teledyne RD Instruments 300-kHz acoustic Doppler current profiler (ADCP), an MTi-G global positioning system (GPS)–motion sensor package manufactured by Xsens, and a Nortek Vector velocimeter mounted at 0.5-m depth to obtain the near-surface velocity. The buoy was tethered to a surface velocity program (SVP) drifter with a 50-m drogue in order to reduce its windage-induced drift. A custom datalogger performed collection and consistent time stamping of the three data streams. The ADCP profiled from 3.5 to 78.5 m with a 1-m depth resolution and an effective range of roughly 75 m.
Wave motions were quantified using the xSens MTI-G GPS motion sensor package, which consists of a GPS and a 6 degrees of freedom inertial motion unit (IMU) sampled at 10 Hz. The GPS and IMU compose an attitude heading reference system (AHRS) that utilizes a Kalman filter to combine the inertial motions and GPS position. The vertical motion was subsequently bandpass filtered using a fourth-order Chebyshev type-II filter with a 40-dB stop band ripple and cutoff frequencies 0.025 and 3 Hz, applied forwards and then backward to eliminate phase delay, resulting in an eighth-order, 80-dB ripple filter. One-dimensional wave spectra were calculated every 30 min from the AHRS heave. The calculated significant wave height 
The surface Stokes velocity was used in conjunction with 
Observations of near-surface currents from each of the three Trèfle deployments. (a) The mean velocity at 40 m, (b) the along-wind, (c) crosswind velocities relative to 40 m, and (d) the velocity magnitude relative to 40 m. The MLD and XLD are shown by the black–white dashed and dotted lines, respectively. The Trèfle deployment numbers corresponding with the wave observations are shown in red along the top. The magnitude changes little with the exception of the near-surface currents during the day.
Citation: Journal of Physical Oceanography 46, 10; 10.1175/JPO-D-15-0172.1
c. Microstructure measurements
Measurements of the turbulent dissipation rate, temperature, and salinity were obtained with the Air–Sea Interaction Profiler (ASIP; Ward et al. 2014). ASIP is an autonomous, upwardly rising microstructure profiler designed to sample the OSBL. A total of 347 profiles from 40-m depth to the surface were obtained over five ASIP deployments. Each deployment ranged from 24 to 48 h in duration with the exception of the fifth deployment, which was only 10 h. The average time between successive profiles during each deployment was about 20 min.
The time–depth evolution of temperature T and buoyancy frequency N2 are shown in Fig. 5. The density ratio in the OSBL, defined by 
Observations over the five ASIP deployments (numbered 1 to 5 along the top) of (a) temperature T and the log10 of the (b) Brunt–Väisälä frequency squared N2, (c) shear squared S2, (d) gradient Richardson number Ri = N2/S2, (e) turbulent dissipation rate ε, and (f) normalized turbulent dissipation rate ε/ε0. The MLD and XLD are shown by the black–white dashed and dotted lines, respectively.
Citation: Journal of Physical Oceanography 46, 10; 10.1175/JPO-D-15-0172.1
Dissipation rates of ε were measured using two airfoil shear probes mounted on the front of ASIP (Sutherland et al. 2013). Assuming isotropic turbulence, ε can be calculated from profiles of the microstructure shear (Osborn 1974). The microstructure shear was sampled at 1000 Hz, and vertical profiles were divided into 1-s segments where the power spectral density was calculated using Welch’s method. The mean rise velocity of ASIP was 0.5 m s−1, thus giving a vertical resolution for ε of 0.5 m. Details of the processing algorithm for ε can be found in Ward et al. (2014). Figure 5e shows the measured turbulent dissipation rate for the five deployments. In addition, Fig. 5f shows ε normalized by ε0, calculated by (4), which takes into account turbulence generated from the mean shear and convective buoyancy forcing. The constants a and b in (4) are found to a = 0.5 and b = 0.3, which is consistent with previous results (Shay and Gregg 1986; Lombardo and Gregg 1989; Brainerd and Gregg 1993; Caldwell et al. 1997; Callaghan et al. 2014).
The mixed layer depth (MLD) was calculated using the temperature threshold of 0.2°C relative to the temperature at z = −0.5 m (Kara et al. 2000; de Boyer Montégut et al. 2004). The MLD over the five ASIP deployments is shown by the black–white dashed line in Fig. 5. The active mixing layer depth (XLD) is defined as the depth where ε decreases to an assumed background level and is no longer being influenced by surface forcing (Sutherland et al. 2014a). The XLD is calculated assuming a background dissipation of 10−9 m−2 s−3 (Sutherland et al. 2014b). Differences between the MLD and XLD have been shown to be important in scaling observations of ε with surface forcing (Brainerd and Gregg 1995; Stevens et al. 2011; Sutherland et al. 2014a). The XLD is indicated by the black–white dotted line in Fig. 5.
Mean values for the day and night profiles of temperature, current speed, ε, 
Mean day (red) and night (blue) profiles of (a) temperature, (b) velocity magnitude, (c) ε, (d) ε /ε0, and Ri = N2/S2. Night is defined between 0100 and 0400 LMT and day is 1300 to 1600 LMT. Shaded regions enclosed by the dotted lines represent 95% confidence intervals as calculated with a bootstrap method. Current and temperature vary between day and night in the upper 10 m, while ε is affected down to the seasonal pycnocline at approximately z = −30 m.
Citation: Journal of Physical Oceanography 46, 10; 10.1175/JPO-D-15-0172.1
The day and night probability density function (PDF) and cumulative distribution function (CDF) of ε and 
PDF of (a),(b),(c) ε and (d),(e),(f) ε0 for the day (red) and night (blue) times of Fig. 6 for (left) −4 m < z < 0 m, (middle) −8 m < z < −4 m, and (right) −12 m < z < −8 m The lines show the CDF with the corresponding scale on the right side of the figure.
Citation: Journal of Physical Oceanography 46, 10; 10.1175/JPO-D-15-0172.1
4. Diurnal variability of temperature and velocity
Figure 8 shows the evolution of 
(a) Temperature at zs = −0.5 m (Ts, red) and zr = −25 m (Tr, blue) and (b) T′ = T − Tr observed over the ASIP deployments. The black and gray lines in (b) are the XLD and the MLD, respectively. The diurnal variability in Ts was observed to be 0.2°–0.3°C and T′ began descending in the early afternoon, approximately 1500 LMT, before the surface buoyancy flux changed sign.
Citation: Journal of Physical Oceanography 46, 10; 10.1175/JPO-D-15-0172.1
Figure 9 shows the diurnal velocity variability over the three Trèfle deployments. The velocity anomalies begin in the along-wind direction in the morning and turn with the local inertial frequency during the day. The velocity anomaly has a similar pattern as the temperature anomaly in Fig. 8 where the anomaly begins in a shallow layer during the morning, descending in the afternoon, and is erased when the surface buoyancy flux becomes destabilizing.
Diurnal velocity anomalies relative to zr = −25 m, identical to the calculation of T′, for the (a) along-wind component u′, (b) crosswind component υ′, and (c) the magnitude of the velocity vector (u′2 + υ′2)1/2. The gray lines show the MLD and the black lines show the XLD. The time–depth variability of (u′2 + υ′2)1/2 is similar to T′ (Fig. 8), which is consistent with having similar diffusivities for temperature and momentum.
Citation: Journal of Physical Oceanography 46, 10; 10.1175/JPO-D-15-0172.1
The diurnal velocity response is more clearly seen in the surface velocity, which is averaged over the upper 5 m, as seen in Fig. 10. The magnitude of the diurnal jet is consistently observed to be approximately 0.15 m s−1. This near-uniform diurnal jet magnitude is consistent with the observations of Price et al. (1986), who found that the magnitude should only be dependent on the shortwave radiation and independent of the wind stress. However, there is day to day variability with regards to the timing of the peak of the diurnal jet in addition to the evolution of the along- and crosswind components (Fig. 10).
Diurnal jet calculated from the observed velocity (black) averaged over the upper 5 m relative to the velocity at 25 m, where 
Citation: Journal of Physical Oceanography 46, 10; 10.1175/JPO-D-15-0172.1
5. Composite day
Wind variability predominantly occurred over time scales greater than the diurnal period (Fig. 3), allowing for the creation of a single composite day by phase averaging the forcing and response components as functions of the local time of day. The composite day allows for a detailed analysis of the mean diurnal response of the ocean while filtering out processes that were not phase coherent within the diurnal cycle. This method has proven useful in interpreting the mean diurnal response in regions with strong buoyancy forcing (Caldwell et al. 1997; Smyth et al. 2013; Drushka et al. 2014; Sutherland et al. 2014b).
Figure 11 shows the composite day for the surface forcing and ocean response. The phase averaging was performed with a temporal resolution of 1 h and a depth resolution of 1 m. The phase-averaged surface buoyancy flux B0 and wind stress τ are shown in Fig. 11a. The surface buoyancy flux had a clear diurnal structure with little observed variation. Although the wind speed varied from 2 to 10 m s−1 over all the deployments (Fig. 3a), there was no clear diurnal structure in τ around the mean value of 0.06 N m−1 (Fig. 11a).
Composite day for (a) B0 (blue) and τ (orange) and the log10 of (b) N2, (c) S2, (d) Ri, (e) ε, and (f) ε/ε0 vs LMT. The MLD (black–white dashed) and XLD (black–white dotted) are calculated from the composite values of T and ε.
Citation: Journal of Physical Oceanography 46, 10; 10.1175/JPO-D-15-0172.1
The near-surface stratification N2 (Fig. 11b) and shear squared S2 (Fig. 11c) were both observed to increase after B0 became stabilizing, with N2 lagging S2 by a few hours. Both N2 and S2 reached near-surface maxima at close to 1400 LMT after which these maxima descended to greater depths. In the afternoon as the depth of the OSBL increased, the magnitude of N2 and S2 both decreased.
6. Restratification length scale
Price et al. (1986) introduced two diagnostic depth scales associated with restratification, which they called the trapping depth DT and penetration depth DP. The trapping depth is defined as the mean depth of the temperature anomaly in the OSBL, where the temperature anomaly is defined in (8).
The trapping and penetration depths were also calculated from the composite day values of T and Q, as shown in Fig. 12. Before 1200 LMT, the minimum DP was very similar to the minimum DT, suggesting that heat and momentum are mixed in the same manner, consistent with Price et al. (1986). At 1200 LMT, DT = DP = 10 m, which is larger than LMO but similar in magnitude to the minimum MLD and XLD (Fig. 12).
Depth scales associated with restratification calculated from the composite day. Depths include the Monin–Obukhov length LMO (green), penetration depth DP (purple), trapping depth DT (yellow), the MLD (gray), XLD (black), as well as 
Citation: Journal of Physical Oceanography 46, 10; 10.1175/JPO-D-15-0172.1
Figure 12 shows that 
7. Richardson number statistics
The gradient Richardson number, where Ri is defined by (11), is calculated for each profile and the statistical distribution as a function of local time of day is investigated. The vertical resolution of Ri is limited by the vertical resolution of the ADCP currents, which is 1 m. Figure 13a shows the temporal evolution of the peak of the PDF of Ri at various depth intervals. For depths z < −4 m, the PDF of Ri has a peak at 0.25, which is indicative that this region may be predominantly unstable. For greater depths, −4 m < z < −14 m, there is a diurnal structure to the peak of the Richardson number distribution, where Ri is lower during the day than in the evening. The timing of the decrease in Ri varies for each depth interval, with deeper observations decreasing later than shallower ones. Observations of Ri increase again at ≈1800 LMT, coinciding with 
Diurnal evolution of (a) the log10 of the peak Richardson number associated with the PDF calculated for each hour of the composite day, (b) the fraction of observed values of Ri < 0.25, and (c) the fraction of observed values of Ri < 0.65. The colors denote the different depth intervals as shown by the legend at the top. The dashed and dotted lines in (a) show Ri = 0.25 and 0.65, respectively. The local minima in the mode during the day correspond with a greater occurrence of low Richardson numbers.
Citation: Journal of Physical Oceanography 46, 10; 10.1175/JPO-D-15-0172.1
Another important aspect of Ri is the fraction of occurrences where Ri < 0.25, which we will denote 
The evolution of stability can be seen from the diurnal evolution of 
(a) Diurnally averaged shear S and (b) stratification N normalized by the law of the wall shear and diurnally averaged ε normalized by (c) ε0 as calculated by (4) and (d) εS as calculated by (18). The black–white dashed line shows the mean time of N0.65[〈t0.65(z)〉], which corresponds to a descent rate of 2 m h−1.
Citation: Journal of Physical Oceanography 46, 10; 10.1175/JPO-D-15-0172.1
8. Enhanced shear = enhanced ε?
The region with the greater number of occurrences of Ri < 0.25 coincided with enhanced 
Assuming that the primary source for ε is from shear production, then 
9. Summary and discussion
Presented here are observations of the diurnal structure of the ocean surface boundary layer (OSBL) obtained in the subtropical North Atlantic during August/September 2012. High-resolution observations in the OSBL were made with the Air–Sea Interaction Profiler (ASIP), an autonomous vertical microstructure profiler that profiles upward to the free surface. The fact that ASIP is autonomous and vertically rising allowed for accurate microstructure observations far from the effects of any ship-induced contamination to the near-surface turbulent processes. ASIP was used in conjunction with a cloverleaf buoy (the Trèfle) that resolved velocities in the near-surface region. This pairing of instruments allowed for coincident velocity and microstructure measurements of the diurnal jet in the OSBL.
During the campaign, several diurnal warming events were observed due to the low wind speeds and high solar insolation. These diurnal warming events followed a typical pattern with a daytime increase in SST of 0.2° to 0.5°C occurring at close to 1400 local mean time (LMT). The increase in SST was accompanied by an increase in near-surface velocity, that is, a diurnal jet, which began in the along-wind direction each morning and slowly turned cum sole due to the Coriolis force. The magnitude of the diurnal jet was observed to be on the order of 0.1 m s−1, consistent with previous observations near this latitude (Price et al. 1986).
Several length scales were investigated associated with the diurnal cycle of SST. The classic Monin–Obukhov length 
The diurnal jet enhances the near-surface shear relative to that expected for a logarithmic velocity profile. One of the main results of this paper is that the increased shear acts to increase ε, presumably through the production of TKE from the interaction of the Reynolds stress and the mean shear. This process is juxtaposed with the increased stratification acting to reduce the vertical diffusion of the Reynolds stress. Taking into account the observed shear, which is approximately 5 times greater than expected for the observed surface stress, leads to a turbulence scaling (which we denote 
This interpretation, that is, that the reduction in ε is due to a decrease in the Reynolds stress, is slightly different to the conclusions of Smyth et al. (1997), who attributed the decay of ε below a stratified layer as a result of a decrease in the vertical advection of TKE, while shear production persisted in the remnant layer albeit cut off from surface forcing. The interpretation of Smyth et al. (1997) was based on a lack of correlation between ε, N2, S2, and Ri within the remnant layer, and therefore a decrease in shear production was deemed unlikely. However, as we have shown, the stratification above the remnant layer limits the diffusion of the Reynolds stress, and it is this that is separated from the surface. The observed exponential decay of ε cut off from surface forcing (Brainerd and Gregg 1993; Smyth et al. 1997; Callaghan et al. 2014) is also consistent with a decrease in the Reynolds stress, as ε is proportional to the Reynolds stress, rather than a reduction in vertical advection of TKE.
The diurnal jet is also accompanied by a greater occurrence of Ri < 0.25, which is indicative of shear instability. While this increased occurrence is limited to 10% to 20% of the observed values of Ri in the upper 10 m, the 1-m vertical resolution of the ADCP could lead to an underestimate of the shear and hence an overestimate of Ri. It does appear that the conditions are favorable for shear instability, but higher-resolution velocity measurements would be required to confirm this. While the enhanced values of ε appear to be associated with the enhanced shear of the diurnal jet, it may be that shear instability may prove to be an integral part of the enhanced turbulence as it will generate turbulence in addition to the wind stress as the stratification does appear to limit the vertical diffusion of momentum. This statement is at least qualitatively consistent with Fig. 14d, where 
One aspect of the diurnal jet that we were unable to clearly address is whether any memory of previous diurnal events exists, as suspected by Woods and Strass (1986), or whether the jet is formed onto a “clean slate” as hypothesized by Stommel et al. (1969). Figure 10 shows a very different evolution for the diurnal jet during each day. Deployment three in particular shows the diurnal jet on 09/07 to have characteristics of an inertial oscillation, while the next day has a very strange response with little along-wind increase. This interaction between the inertial and diurnal response can also be seen in the currents throughout the OSBL (Fig. 4), but a much longer time series than this one would be required to investigate this interaction.
These observations present new insight into the complicated processes associated with shallow, stable boundary layers in the ocean. During conditions of low wind and high solar insolation an interesting feedback mechanism occurs, which acts to increase the turbulence intensity relative to the wind forcing. The increased stratification creates a delicate balance between the increased near-surface shear and the limited vertical extent of the constant stress layer to create slightly enhanced values of ε relative to turbulence in neutral buoyancy conditions. This process could be an important component to the air–sea transfer of momentum, heat, and trace gases in tropical regions as the diurnal jet is expected to occur wherever a diurnal temperature variability is observed. The enhanced ε relative to wind forcing is expected to have an impact on estimates of the air–sea transfer of water soluble gases, such as CO2 and O2 (Lamont and Scott 1970; Ward et al. 2004; McGillis et al. 2004; Zappa et al. 2007), as a wind stress parameterization would underestimate the gas transfer velocity in regions with large diurnal variability. This enhanced turbulence would lead to an increase in the flux of CO2 from the sea to the atmosphere as diurnal cycling predominantly occurs in tropical and subtropical regions where the partial pressure of CO2 is greater in the sea than in the atmosphere.
Acknowledgments
The authors are grateful for funding support from the National Science and Engineering Research Council of Canada from the scholarship PGSD3-410251-2011, the Office of Naval Research under Award N62909-14-1-N296, and the Norwegian Research Council under PETROMAKS2 233901 Project. LM thanks Olivier Peden and Olivier Ménage for their help with the Trèfle and A. Marsouin and P. Le Borgne from Météo-France for help in processing the radiative fluxes data. The STRASSE cruise and data analysis was supported by LEFE/IMAGO and CNES/TOSCA grants. The authors thank Bill Smyth and one anonymous reviewer for their helpful comments, which greatly improved the manuscript.
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