The diurnal nature of the surface fluxes cause the upper ocean to cyclically stir and restratify. During the nighttime, the negative net heat flux cools the surface of the ocean ( Figure 1A ), and results in unstable stratification ( Figures 1C, G ) and convective deepening of the OML. Convective plumes penetrate into the subsurface depths reaching the diurnal pycnocline, as can be seen from the horizontally averaged root mean squared fluctuating vertical velocity, which varies over an order of magnitude, and the Brunt- Väisäla frequency squared (N2)

where g is the acceleration due to gravity, ρ 0 is the reference density and 〈 ρ 〉 is the total horizontally averaged density, ( Figures 1B, C ) which peaks at around 4 × 10 − 4 s   − 2 within the pycnocline ( Figure 1G ). As the daytime begins and the shortwave is absorbed by up the ocean bulk, most of the turbulence is suppressed and thermal stratification begins to build and the OML shallows ( Figures 1F, G ). The increased stratification traps horizontal momentum within a very thin layer, called the diurnal warm layer, enhancing the near-surface shear. The squared shear S 2 ( Figure 1D ) is calculated as:

where 〈 u 〉 and 〈 v 〉 are the plane averaged zonal and meridional velocities respectively. This shear layer descends towards the pycnocline, as the net heat flux begins to decrease after reaching its peak value. Note that, at all times the oscillating surface wind stress also continues to produce shear turbulence, but it is enhanced near the surface during daytime and near the pycnocline during the nighttime. This phenomena has also been documented in previous studies (Moulin et al., 2018; Hughes et al., 2020a). Figure 1E shows the reduced squared shear S 2 - 4 N 2 , where positive values indicate that the water column is unstable to KH-like shear instability. The competition between this diurnal jet and stratification makes the near-surface unstable to shear instabilities. In addition, we also see the subsurface depths getting unstable as this shear layer descends (Moulin et al., 2018; Wijesekera et al., 2020). Evaporation leads to a persistent unstable gradient of near surface salinity ( Figure 1F ), which is present even during daytime. This enhances the convective instability during nighttime and also compensates for the increase in the overall stratification during daytime due to thermal heating alone. This also causes enhanced mixing, especially during daytime, as will be discussed further.

Surface evaporation tends to increase the SSS (Asher et al., 2014; Drushka et al., 2014; Boutin et al., 2016). The accumulation of heat and excess salinity in the top layer over colder and fresher deeper waters are the conditions favorable for double diffusive salt-fingering instability (Soloviev and Lukas, 1997). This is quantified using the density ratio R and Turner angle T u defined as:

where α and β are the thermal expansion and haline contraction coefficients, and T z and S z denote the plane averaged vertical temperature and salinity gradients (Ruddick, 1983). For warm/salty waters over cold/fresh,   − 45 ° < T u < 45 ° , indicating salt-fingering (SF) instability is likely, whereas − 45 ∘ < T u < 90 ∘ indicates absolute stability. However T u < − 90 ∘ or T u > 90 ∘ denotes static instability ( N 2 < 0 ). The former is caused due to the overwhelming effect of destabilizing thermal gradient and the latter vice versa. Figure 2B shows the temporal evolution of T u for two consecutive diurnal cycles. During the daytime, the entire water column down to the pycnocline is susceptible to salt-fingering instability. L424 This can also be verified from the T/S profiles in Figure 2D during daytime. Figure 2E shows the contribution of both scalar gradients to the overall stratification. They are defined as:

The salinity gradient compensates the temperature gradient in the daytime, however keeping the overall stratification stable. When the surface heat flux changes sign from positive to negative, indicating a shift from daytime to nighttime, both the scalars contribute negatively to the stratification, causing convective static instability. This implies that both N T 2 , N S 2 < 0 . However, since the boundary condition of temperature changed from heating to cooling, it takes some time to adjust. Hence initially, even if both N T 2 , N S 2 < 0 , but | N T 2 | < | N S 2 | , making the contribution of salinity gradient the dominant effect in destabilizing the density gradient. This can also be seen through Turner angle, where the near surface values are more than 90° just as the heat flux changes sign from positive to negative. After some time however, the values of Turner angle become less than -90° indicating that surface cooling dominates the convective mixing. The convection almost homogenizes both the T/S profiles, leaving almost negligible gradient, except near the top, where the localized effects of both surface cooling and evaporation persist ( Figures 2D, E ). As soon as the shortwave begins however, even when the heat fluxis still negative, the turbulence begins to decrease due to the build up of thermal stratification and increased potential energy. At that instant, the convection switches back to being salinity dominated and the whole cycle repeats the next day.

To supplement the findings above, we also plot the buoyancy Reynolds number, calculated as:

where ϵ is the turbulent kinetic dissipation (defined in the next section) and N 2 is the squared Brunt Vaisala frequency. This quantity can be interpreted as the ratio of Ozmidov to Kolmogorov length scales. For R e b < 20 , there is weak buoyancy controlled turbulence, while for R e b > 100 the turbulence is energetic (Bouffard and Boegman, 2013). Previous studies have indicated that salt-fingering can enhance mixing for R e b < 200 (Nagai et al., 2015). Figure 2C shows that during daytime, R e b < 200 almost throughout the diurnal thermocline, which further supports that salt-fingering is the major contributor to turbulent mixing. The TS diagram ( Figure 2F ) provides another description of these dynamics. It has been plotted every 6 hours, for the whole of day 2 (after initialization). By day 2.25, when the neat heat flux is positive, in the top 7m or so the presence of warm and salty waters over cold and fresh waters and indication of salt-fingering can be seen here as well. Soon after nighttime begins (day 2.5), a small inversion can be seen in both the scalars due to the net surface destabilizing buoyancy flux. During peak night times, the profiles have been almost homogenized down to the pycnocline, which can be seen by both day 2.5 and 3. Note that the changes in these T/S properties only occur for depths less than about 15m, as the OML itself is about 13m. These changes in time have profound consequences on irreversible turbulent mixing, discussed in the next section.

Figure 3 shows the evolution of horizontally averaged turbulence statistics from the ocean’s response. The small scale turbulent kinetic energy ( Figure 3B ) is defined as:

where, u i   ′ , the fluctuating velocity, is calculated from the horizontally averaged mean field as u i   ′ = u i − 〈 u i 〉 ( 〈 . 〉 denotes horizonatlly averaged quantity). During nighttime, TKE is enhanced within the whole mixed layer due to convection, while it is restricted to the near-surface during daytime. The mixed layer depth (MLD) for both the test cases, calculated using a density threshold criteria of 0.01 kg/m³ is also plotted. It varies diurnally for both the cases, however the combined case has greater MLD than the case without evaporation. Using higher thresholds may cause MLD to not shallow much during daytime. A continued increase over time of MLD for the combined case, can be observed as the net surface buoyancy flux integrated over a day is non-zero (and positive) and the surface wind stress also continues to provide a source of mechanical turbulence all the time. There is some leakage of TKE below the mixed layer as well, which is likely due to the downward propagation of internal waves from the pycnocline. The shear production P ( Figure 3C ) shows the variability of mechanically generated turbulence, given by

The enhanced values near the surface are the direct result of the stress applied, while the descent of the shear layer causes shear instability and turbulence, as discussed before ( Figure 1E ). The subsurface enhancement of shear production within the pycnocline can be seen during nighttime, producing internal waves. The turbulent buoyancy flux.

represents the conversion of energy from TKE to available potential energy (APE) and vice versa ( Figure 3E ). This includes contributions from both the scalars respectively. Positive values indicate APE being converted to TKE, through convection, while negative values show the energy spent in destroying stable stratification (conversion from TKE to APE). During nighttime, the turbulence is mostly convective in nature, while during the daytime, the shear-induced turbulence has to work against the stable stratification. The turbulent kinetic dissipation ϵ is the sink of TKE, denoting how much energy is spent in overcoming the viscous stresses.

As discussed before, depending on the time of the day, the turbulence could be either mechanical or convective in nature. The dissipation also follows this variability ( Figure 3D ). During the daytime, the values of ϵ and P are comparable near the surface and during descent of the shear layer. However, in the convective regime, the buoyancy flux tries to balance ϵ , throughout the mixed layer. This has also been reported in previous studies (Shay and Gregg, 1986; Lombardo and Gregg, 1989; Ivey and Imberger, 1991; 214 Imberger, 1985).

The irreversible mixing, defined as the sink of APE, is calculated following Gregg (2021) ( Figure 3F ).

where χ ρ is the rate of destruction of density variance or scalar dissipation.

Here κ T , S are the sum of the molecular and eddy diffusivity of the scalars evaluated from the subgrid scale model and N * 2 is the buoyancy frequency squared calculated from the sorted density profile (Arthur et al., 2017). The irreversible mixing also follows a diurnal cycle, where we observe high values during nighttime, as convective turbulence is an efficient mixing mechanism. During the daytime, most of the energy produced by the shear goes into dissipation, rather than mixing, however, the opposite happens during nighttime. With the change of sign of net heat flux, different peaks in mixing can also be seen. The first peak occurs during the transition from daytime to nighttime due to the fact that now both the scalars are destabilizing the density gradient. It is here that the T u also shifts from showing salt-fingering to salinity dominated convective static instability ( Figure 2B ). The second peak is again just when the shortwave heating begins and the convection shifts from being cooling dominated to salinity dominated. Similar behavior can also be seen in mixing efficiency η ( Figure 3G ), which is defined as the ratio of sink of APE to the sum total of sink of APE and sink of TKE. In other words, it provides the relative amount of energy going into irreversible mixing, as compared to viscous dissipation. Here as well, high values of more than 0.5 can be seen during nighttime, when convective turbulence dominates. Such high values are also found in previous studies (Gayen et al., 2013; Wykes et al., 2015; Sohail et al., 2018; Ivey et al., 2021). We also calculate the turbulent eddy diffusivity following Osborn and Cox (1972).

Within the OML, during nighttime, the eddy diffusivity ( Figures 3H , S2 ) reaches values around 10 − 1 m²/s, while in the daytime, it remains about 10 − 3 m²/s, due to less mixing by shear-driven turbulence. Note that the presence of evaporation increases both mixing and diapycnal diffusivity and has a deeper MLD, as compared to the case without it ( Figures 3B , S3 ). The peaks in both κ ρ , e d d y and η during the transition times are a result of the shifting nature of convection, as discussed above. These varying regimes of high and low mixing has consequences on SSS and SST as discussed in the next section.

Figure 4 shows the comparison between the two cases: with and without evaporation. Vertically integrated mixing ( Figure 4B ) shows that the case with evaporation has about two orders of magnitude greater mixing than the case without evaporation especially during daytime. During nighttime, the difference is not so much although, as nighttime convection is predominantly controlled by the surface cooling, especially in the later hours. This can also be seen in the magnitude of mixing, plotted at 5m depth ( Figure 4C ). The difference is very evident during daytime, and we also see the two peaks during transition times, which are missing for the case without evaporation. But during late nighttime, the difference decreases as the surface cooling begins to dominate evaporative flux, for nighttime convection. During transition from daytime to nighttime and vice versa, peaks in mixing can also be observed in the case with evaporation ( Figures 4C , 3F ). These peaks correspond to the changing nature of convection (from being salinity dominated to temperature dominated, and vice versa) during these transition periods, as discussed before. Throughout the day, evaporation continues to enhance mixing throughout the water column, which also leads to better prediction of the other variables. SST and SSS are compared for both the cases with the available mooring data ( Figures 4D, E ). Note that the salinity at 0.6m depth is used as a proxy for mooring SSS. It can be clearly seen that the case with evaporation better predicts SSS than the case without it. This is due to the enhanced mixing caused by double diffusive salt-fingering, especially during daytime, which leads to increase in SSS. The other mechanism of entrainment of saltier subsurface waters is not efficient so as to increase the SSS. This mechanism is responsible for SSS evolution for the case without evaporation, and has been discussed in previous studies (Sarkar and Pham, 2019). Similarly, the case with evaporation gives a much better match with the mooring SST. The reduced amplitude of the diurnal SST in the case with evaporation, especially during daytime is due to the enhanced mixing caused by the salt-fingering. However, in the case without evaporation, we are not providing any salt flux, and hence the mixing is also reduced, causing higher amplitude of diurnal SST.