The method of linear stability analysis LSA; see Methods and refs 18 , 40 , 41 , 42 is applied to the hourly profiles of density and velocity at a location in the middle equatorial Pacific. This method enables to detect potential instabilities occurring in the thermocline. From both databases, we obtained large amount of possible mixing events featured as density overturns and potential instabilities. We show that the mixing events occurred not only in the upper part of the thermocline but also deep down to the centre and lower part of it. The equatorial Pacific is a region with accumulated Argo float observations.
Among them, a large portion of the overturns occurred after , a period when most of the fine-resolution profiles exist. The horizontal distributions of the detected overturns are shown in Fig. Away from these regions, fewer overturns are detected. The thick black curve and thin black curves denote the centre depth of maximum N 2 ; and bounds depths of half of the mean pycnocline. Overlapped by the overturns in Fig. The occurrence probability refers to the ratio of the number of Argo profiles that contain overturn s to the number of total qualified Argo profiles see Methods in a given area.
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Here, the time span is January —June Despite the scale selection, the results are still indicative for inferring the relationship between mixing events and TIWs. We further graph the overturns with their corresponding instantaneous pycnocline layers PLs against both longitudes Fig. The synoptic overturns are confined to the temporally averaged PL Fig. It is noticeable that a large fraction occurred below the centre of the average pycnocline Fig. We emphasize that the deep-reaching overturns in the pycnocline in the meantime also reached to the lower flank of the EUC. This can be inferred from Fig.
This result is confirmed in the following by LSA examinations. Figure 1c shows the meridional distribution of the detected overturns. The overturns and PLs shown on the physical depths Fig.
To provide an overview of the vertical distribution of the overturns relative to their corresponding pycnocline, we redistribute the overturns with respect to a transformed and normalized vertical coordinate Fig. This coordinate is referred to the depth of N 2 max , and normalized in the upper lower half of the pycnocline by the thicknesses of the upper lower half of each PL. It shows that overturns occur not only in the upper part of the PL but also below the centre of the PL. Although in Fig.
According to direct turbulence measurements 13 , 32 , this depth mostly belongs to the upper core layer, which refers to a layer that is located above the EUC core and accompanied with strong TIW-induced turbulence. In the depths above 0. It is noteworthy that the TIW-related upper core layer is seemingly separated from the surface-driven deep cycle layer In general, TIWs are active from boreal summer to winter, while inactive in boreal spring It is shown that the occurrence probability is indeed subject to similar seasonal variation: they peak in August and December, and have minimum values in boreal spring April to June and October.
This seasonality is statistically significant. In b , c and d , the occurrence probability is calculated over the years — The results strongly indicate the modulating effect of TIWs on the occurrence of deep-reaching overturning in the pycnocline. Given that overturning and mixing usually accompany with each other, the result not only confirms the notion that TIWs lead to enhanced turbulence and mixing in the upper part of the thermocline 13 but also implies that the modulation effects of TIWs on mixing can reach deeper depths of the pycnocline.
As density here is dominated by temperature 32 , in the remainder of the study we focus on the thermocline instead of the pycnocline. In the following, we will further verify the impact of TIWs in enhancing the occurrence of overturns by comparing overturn properties of TIW periods with those of non-TIW periods. To this end, we followed ref.
The reason why we adopted this strategy is because a large portion of the fine resolution Argo profiles and overturns are found between the years and , whereas the TAO velocity measurement and hence the TIW KE index are not available since This leads to the occurrence probability of 6. The results demonstrate again that TIWs are associated with a higher occurrence of overturns. The observed higher occurrence of deep-reaching overturns during TIWs, so far established in the seasonal and period-to-period cycles, calls for a physical interpretation.
Two ways may be employed to demonstrate this physical interpretation.
Thermocline fluctuations in the western tropical Indian Ocean during the past 35 ka
One is the LSA, which can determine the potential instabilities of an observed flow by providing locations and other detailed properties of the exponentially growing unstable modes see Methods and refs 18 , 40 , 41 , The monthly counts of the potential instabilities in terms of the critical levels of the detected unstable modes; see Methods is shown on physical depth in Fig. In Fig. In addition, the long-term averaged monthly depths of the EUC core, the thermocline centre and the upper and lower thermocline bounds defined as the depths of half the maximum vertical temperature gradient , are overlaid on the three panels of Fig.
Shown are counts in m bins. In each panel, the red curve denotes the average depth of EUC core, the black thick curve denotes the average depth of the thermocline centre and the two black thin curves denote the average upper and lower bounds of the thermocline. A prominent feature is the seasonal variation of the potential instabilities Fig. Within the thermocline, more potential instabilities were found in boreal summer to winter, while relatively few potential instabilities were found in boreal spring.
There were also fewer potential instabilities occurring during October and November. Another distinguished characteristic is the deep-reaching nature of the potential instabilities. Potential instabilities occurring below the upper thermocline bound are as many as those above it. As the numbers of hourly profiles in each month and at each depth are nearly the same, the occurrence probability of the instabilities Fig.
The occurrence probability is defined as the ratio of the number of unstable modes over the number of profiles in m bins. The red curve denotes the average depth of EUC core, the black thick curve denotes the average depth of the thermocline centre and the black thin curves denote the average depths of the thermocline bounds.
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When all the potential instabilities are redistributed on the depth that is referenced to the thermocline centre of each profile Fig. The centre coincides well with the peak at 0. In addition, potential instabilities occur also in and below the centres of the thermocline. Alternatively, when the potential instabilities are redistributed on the vertical coordinate that is referenced to the EUC core of each profile Fig.
The relation of the deep-reaching potential instabilities to TIWs is further illustrated from a period-to-period point of view in Fig. In these two panels, we show the occurrence probability of potential instabilities in the TIWs and non-TIWs periods, respectively, on the depth referenced to the EUC core. Consequently, the results clearly demonstrate the enhancement effect of TIWs on the occurrence of potential instabilities in both the upper and lower flanks of the EUC.
The red curve denotes the average depth of EUC core and the black curve denotes the average depth of the thermocline centre.
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The lower bound of the higher-occurrence frequency is generally confined to the centres of the thermocline and the EUC. This feature is consistent with the occurrence of the potential instabilities. This may be because the shear in the depths is weak Fig.
Hence, although a large portion of Ri is small resulted from weak stratification , there was not enough KE available in the mean flow to drive unstable modes that have high-enough growth rate 18 that could pass the growth rate criterion used in the LSA see Methods. In a , b and c , the red curve denotes the average depth of the EUC core and the black curve denotes the average depth of the thermocline centre.
In c , contour of 0. The different colour scales in a and b are noteworthy. As mentioned, the annual cycle of the occurrence frequency of low Ri should have resulted from not only the shear of EUC and the TIWs, but also the thermal structure of the upper ocean. All the processes and properties are ultimately also related to wind stresses and exhibit seasonal variations. For example, in boreal spring the wind reduces, the shear weakens and the water warms with increased stratification in the subsurface layers; since late summer, the wind stress increases, the shear strengthens and the surface water cools down with decreased stratification.
Nevertheless, the contribution of TIWs to the low Ri and therefore the generation of potential instabilities could be roughly isolated from the EUC. This was done by separating the individual shear they induce. The shear squared induced by the background EUC is calculated as , where are the day low-pass-filtered velocities, representing the background flows, whereas the shear squared associated with the TIWs is estimated as the difference between the original and the background shear squared: Fig.go site
In addition, as a prominent feature, the TIW-induced shear is centred just above the EUC core and covers both the upper core layer and the layers immediately below the EUC core, in particular during TIW seasons boreal summer to winter. This explains the occurrence of potential instabilities occurring below the centres of both the EUC and thermocline Fig. The portion of the TIW-induced shear is calculated as Fig. These results indicate that the TIWs provide a modulating effect on the generation of unstable disturbances.
In years of stronger TIWs, larger occurrence probability of unstable modes are observed. The dashed line denotes zero. The correlation coefficient between the ONI and the occurrence probability Fig. Moreover, the extension range of potential instabilities differs between two conditions Fig. In the present study, we show the existence of overturns in the deep depths of the thermocline. We also show that the potential instabilities are organized in a physically quite reasonable structure. Given the good coincidence of the determined potential instabilities and the measured mixing during November Supplementary Figs 3 and 4 , it is anticipated that the potential instabilities during other time are also associated with mixing, although the mixing intensity and accompanying heat fluxes can not be correctly estimated yet.
In the cold tongue of the equatorial Pacific, maintaining cool SSTs in the presence of intense solar heating requires a combination of subsurface mixing and vertical advection to transport surface heat downward 43 , 53 , 54 , 55 , To best simulate the oceans, numerical models need to reproduce or properly represent the TIWs and the associated turbulence. Although the main structure of TIWs can be reproduced in some coarse resolution ocean general circulation models OGCMs 30 , the small-scale structures of the frontal areas of TIWs, which are key regions of turbulence generation 28 , 29 , 61 , 62 , remain unresolved by coarse resolution OGCMs and ocean-atmospheric coupled models.
This shortage may lead to underestimates of thermocline mixing by the oversimplified vertical mixing parameterizations incorporated in coarse resolution OGCMs 60 and hence to model-data deviations not only in the equatorial ocean but also in mid-latitudes 63 , The Thorpe method 38 is commonly used for estimating dissipation rate and vertical turbulence diffusivities, which is based on the size of detected density overturn patch and the stratification intensity over the patch, of a measured potential density profile.
In this work the Thorpe method is applied only for overturn detection, rather than diffusivity estimation because the resolution of the Argo profiles is still too low for such estimation. The Thorpe method is suitable to be applied in the thermocline where the stratification is strong; in contrast, care should be taken in layers of low stratification due to its sensitivity to noise 65 ; therefore, both the upper and lower layers of low stratifications defined by are omitted from our analysis.