Surface waves and internal tides have a great
contribution to vertical mixing processes in the upper ocean. In this
study, three mixing schemes, including non-breaking
surface-wave-generated turbulent mixing, mixing induced by the wave
transport flux residue and internal-tide-generated turbulent mixing,
are introduced to study the effects surface waves and internal tides
on vertical mixing. The three schemes are jointly incorporated into the
Marine Science and Numerical Modeling (MASNUM) ocean circulation model as a
part of the vertical diffusive terms, which are calculated by the surface
wave parameters simulated from the MASNUM wave model and the surface
amplitudes of the mode-1 M
Turbulence in the ocean is hard to describe superficially and characterize dynamically. Fortunately, in recent years great progress in understanding the turbulence has been achieved by a combination of experiments, simulations and theories (Baumert et al., 2005; Umlauf and Burchard, 2020). Turbulence has a great contribution to the vertical mixing processes in the upper ocean, which is important for regulating the sea surface temperature (SST) and thermal structure. Accurate parameterization of the vertical mixing process is the key for ocean general circulation models (OGCMs) to simulate realistic ocean dynamics and thermal environments. However, the factors influencing vertical mixing in the upper ocean still remain unclear, so there are substantial biases in the simulated SST, mixed layer depth (MLD) and dynamic quantities within the ocean interior such as potential vorticity, temperature and salinity for most ocean models (Ezer, 2000; Qiao et al., 2010; Wang et al., 2019; Song et al., 2020; Zhuang et al., 2020).
In the sea surface layer, turbulence can be generated by wind and surface waves (Agrawal et al., 1992; Qiao et al., 2004; Babanin, 2017), Langmuir circulation (Li and Garrett, 1997; Li and Fox-Kemper, 2017; Yu et al., 2018) and surface cooling at night (Shay and Gregg, 1986). Among them wind energy input to the surface waves is estimated as 60–70 TW (Wang and Huang, 2004), which is much greater than all other mechanical energy sources (Wunsch and Ferrari, 2004). Most of the wave energy is dissipated locally through wave breaking (Donelan, 1998) and enhances the turbulent mixing near the sea surface. Meanwhile, previous studies indicated that non-breaking surface waves (NBSWs) are able to affect depths much greater than wave breaking (Huang et al., 2011) and even penetrate into the sub-thermocline ocean (Babanin and Haus, 2009; Wang et al., 2019). Despite the fact that parameterization schemes of wave-induced mixing have been developed and adopted in OGCMs, there is still remaining controversy about the effects of wave-induced turbulence mixing in the upper ocean (Huang and Qiao, 2010; Kantha et al., 2014).
Generally, the effects of surface waves on upper-ocean dynamic processes include momentum transport by the Stokes drift through the “Coriolis–Stokes” forcing (Li et al., 2008; Zhang et al., 2014; Wu et al., 2019), enhanced near-surface mixing by wave breaking (Donelan, 1998) and modulation of the surface wind stress by wave roughness (Craig and Banner, 1994; Sullivan et al., 2007; Yang et al., 2009). The Coriolis–Stokes forcing induced by surface waves has a positive impact on the simulated current profile in the whole wind-driven layer, since the ocean Ekman transport and Ekman spiral profile are modified (Polton et al., 2005; Wu et al., 2019). A non-breaking wave-induced mixing scheme for shear-driven turbulence was proposed, in which the viscosity and diffusivity can be calculated as functions of the Stokes drift (Huang and Qiao, 2010; Qiao et al., 2010). Turbulent mixing induced by wave–current interaction occurs in the subsurface layers due to the Langmuir turbulence, which can improve ocean circulation modeling (Huang and Qiao, 2010; Qiao et al., 2016; Yu et al., 2018). For the small-scale and mesoscale motions, the effects of surface waves are also significant by modifying the surface current gradient variability and the eddy transport when the turbulent Langmuir number is small (Jayne and Marotzke, 2002; Romero et al., 2021), and the effects will become larger when the model resolution increases (Hypolite et al., 2021). On the whole, the effects of NBSWs on the dynamical structure are not negligible.
In the bulk of the stratified ocean interior, it is believed that
internal waves are one of the dominant sources to induce turbulent mixing
(Munk and Wunsch, 1998; Wunsch and Ferrari, 2004). The total
internal wave energy input was estimated as
The internal wave energy in the ocean interior, which generates turbulence processes and diapycnal diffusivity (Jayne, 2009; st. Laurent et al., 2012), is redistributed from large- to small-scale motions by wave–current interactions. The dynamic processes were modulated through shearing and straining actions of the fine-scale internal waves (Gregg and Kunze, 1991; Kunze et al., 2006; Jayne, 2009). As a key mechanism, subharmonic instability may transfer the energy from the internal tides to the shear-induced turbulent diapycnal mixing (MacKinnon and Gregg, 2005; Pinkel and Sun, 2013). The parameterization of the turbulent mixing induced by internal waves was introduced into ocean models and makes the simulated mixing coefficients and dynamic processes, including horizontal currents and meridional overturning circulation, agree better with large eddy simulation (LES) results or observations than the original schemes (Kunze et al., 2006; Jayne, 2009; Huussen et al., 2012; Shriver et al., 2012). However, the effects of IT-generated turbulent mixing on the dynamical processes has not been understood clearly.
The Indian Ocean (IO) is the third-largest ocean in the world and has an
important low-latitude connection to the Pacific Ocean through the
Indonesian Archipelago (Fig. 1). On one hand, the mean wind pattern of the
southern Indian Ocean (SIO) is similar to the Atlantic and Pacific Ocean, with
westerly winds at high latitude (Southern Ocean) and trade winds at low
latitudes; on the other hand, a complex annual cycle associated with the
seasonally reversing monsoons is dominant in the northern Indian Ocean (NIO).
As a result, wind waves, which are a prominent feature of the ocean
surface, undergo large seasonal variations in the NIO (Kumar et al.,
2013, 2018). Previous investigations showed that the annual
and seasonal (during summer monsoon period, i.e., June–September) average
significant wave height (SWH) in the NIO ranges from 1.5–2.5 and 3.0–3.5 m, respectively, based on the European Centre for Medium-Range Weather
Forecasts (ECMWF) ReAnalysis V5 (ERA5) product (Anoop
et al., 2015). In the SIO, the average SWH between 35 and
22
Bathymetric map (color codes in meters) in the Indian Ocean. Red lines
(7
Previous studies, such as Simmons et al. (2004) and Nagai and Hibiya (2015), constructed baroclinic ocean models to compute the energy flux from barotropic tides into internal waves. The Navier–Stokes equations with accurate tidal potential forcing, tidal open boundary conditions and non-hydrostatic approximation were calculated to simulate the generation, development, propagation and dissipation processes of ITs in high-resolution numerical experiments. The induced turbulent mixing coefficients can then be estimated in terms of the local dissipation efficiency, the barotropic to baroclinic energy conversion and the buoyancy frequency. In fact, the estimation of the IT-generated turbulent mixing in these previous studies was implicit. The simulated internal-tide processes will become inaccurate if the temperature and current structure cannot be modeled accurately. On the contrary, we attempt to derive an analytic and explicit expression of the vertical diffusive terms induced by NBSWs and ITs based on the theory of turbulence dynamics as well as surface and internal wave statistics. The mixing schemes introduced in this study will be calculated directly in terms of the parameters of the NBSWs and ITs. The present study provides another way and preliminary attempt to study the mixing processes induced by internal tides. It should be more convenient to improve the simulation further because the mixing schemes are independent of the ocean model.
In this study, the vertical mixing schemes induced by non-breaking surface waves and internal tides are incorporated into the MASNUM ocean circulation model (Han, 2014; Han and Yuan, 2014; Zhuang et al., 2018). The vertical mixing schemes are introduced in Sect. 2. Section 3 describes the model and experiment design. Model results are given in Sect. 4. The relevant discussion is given in Sect. 5, and the conclusions are summarized in Sect. 6.
Previous studies indicated that NBSWs are able to enhance the turbulent
mixing in the upper ocean (Babanin and Haus, 2009; Dai et al., 2010;
Huang and Qiao, 2010; Qiao et al., 2016). The ability to simulate the SST
and MLD can obviously be improved via the incorporation of the related
NBSW-induced turbulent mixing schemes into OGCMs (Lin et al., 2006;
Xia et al., 2006; Song et al., 2007; Aijaz et al., 2017; Wang et al., 2019).
According to Yuan et al. (2011, 2013),
Zhuang et al. (2020) expressed the vertical viscosity,
Apart from NBSWs, the residue of the wave transport flux is also able to
contribute to inducing mixing in the ocean circulation through the
Reynolds average upon characteristic wavelength scale (Yang et al.,
2009, 2019). Yang et al. (2009) proposed a mixing scheme
for the wave transport flux residue (WTFR), which has been adopted in
OGCMs (Shi et al., 2016; Yu et al., 2020). The results show that the
simulated SST and MLD are remarkably improved, especially in summer and in
the strong current regions. In tropical cyclone conditions, the
performance of the model to simulate ocean response could also be greatly
improved if the wave transport flux residue mixing scheme is introduced.
The coefficients of the wave transport flux residue mixing are expressed as
follows:
In the stratified ocean interior, ITs are able to provide
about half of the mechanical power required for the ocean interior turbulent
mixing (Wunsch and Ferrari, 2004; Zhao, 2018; Vic et al., 2019; Whalen et
al., 2020). However, current field observations are insufficient for
constructing the whole internal-tide map in the IO. Satellite altimetry is
able to provide sea surface height (SSH) measurements to observe the global
ITs (Ray and Mitchum, 1996). Zhao et al. (2016)
presented a method to extract the M
Yuan et al. (2013) presented a second-order turbulence closure model
to estimate the turbulence kinetic energy and dissipation in terms of the
velocity shear module of non-breaking waves. The subsurface
displacements of ITs, pressure anomalies and currents can be
derived from the SSH amplitudes following vertical models (Zhao and
Alford, 2009; Wunsch, 2013; Zhao, 2014). The detailed derivation process
about the velocity shear module of the internal tide can be found in
Appendix A. For the mode-1 M
The effects of the new vertical mixing schemes are introduced into
OGCMs. The modified equations can be written as
The three-dimensional MASNUM ocean circulation model (Han and Yuan,
2014; Zhuang et al., 2018) is used to evaluate the effects of NBSW- and
IT-generated turbulent mixing and WTFR-induced mixing. The two-level
single-step Eulerian forward–backward time-differencing scheme and the
The model domain is in an area of 50
The initial temperature and salinity are interpolated based on annual
mean Levitus94 data (Levitus and Boyer, 1994; Levitus et al.,
1994) with the horizontal resolution of 1
It is worth noting that the time interval of 10 years should be appropriate for ocean simulation from the quiescent state to a relatively stable circulation background. The average kinetic energy, which can be regarded as a model stability index, fluctuated obviously in the first 2 years, then became stable gradually in the third year and was completely steady from the fourth to the 10th year. The conclusion is similar to many previous studies (e.g., Xia et al., 2006; Qiao et al., 2010; Han, 2014; Yu et al., 2020).
The MASNUM wave spectrum model (Yuan et al., 1991, 1992; Yang et al., 2019) is used to simulate the parameters of surface waves in the IO. The energy-balanced equations are solved in the model based on the wavenumber spectrum space. The characteristic inlaid scheme is adopted for the wave energy propagation to improve the original wave model (Yuan et al., 1992). The wave model has been validated by observations (Yu et al., 1997) and widely accepted in ocean engineering and numerical simulation (e.g., Qiao et al., 1999; Xia et al., 2006; Qiao et al., 2010; Shi et al., 2016; Yang et al., 2019; Yu et al., 2020; Sun et al., 2021). The results showed that the simulated SWH and mean wave period are consistent with satellite observations.
The model domain, resolution, topography and surface wind stress flux data are consistent with those in the MASNUM ocean circulation model. The boundary conditions are from the JONSWAP spectrum (Hasselmann et al., 1973). The wave model is integrated from the quiescent state for 10 climatological years with the same period as the ocean circulation model. Actually, the configuration of the wave model is simpler than the OGCM, and the model design in this study is almost the same as that in Xia et al. (2006) and Qiao et al. (2010). Therefore, we believe that the experiment using the MASNUM wave model is able to characterize the spatial pattern and variation of surface waves in the IO.
The wave spectrum
To assess the effects of the NBSW, WTFR and IT on the vertical mixing and simulated thermal structure in the upper ocean, five experiments (Table 1) are denoted as Exp 1–5 and designed as follows.
Numerical experiment design.
It is worth noting that the climatological experiments, which should be regarded as the multiyear mean simulation, are designed in this study, so it is inappropriate for the simulated results to be compared with the Argo data because there should be a considerable difference between the climatologic data and real-time in situ observations. The WOA13 data, which represent the multiyear (1955–2012) mean results, and the multiyear (1993–2021) mean OSCAR data will be a good choice to evaluate the ocean climatological modeling.
In this section, the comparable results for the climatological temperature construction in the upper ocean are used to assess the effects of NBSWs, ITs, and WTFR on vertical mixing.
As a typical example, the vertical distribution of the monthly mean vertical
temperature diffusive terms in logarithmic scale along the zonal transect of
10.5
One can see that all of the terms decay with the depth below the sea
surface. In January, BTST is
Vertical profiles of the monthly mean vertical temperature
diffusive terms in logarithmic scale along 10.5
The same as Fig. 2, but in July.
The climatologic experiments are designed in this study because of the NCEP monthly climatological sea surface flux forcing fields and the daily global climatological lateral boundary conditions in the simulation, so the WOA13 monthly climatology data can be used in comparisons as a reference.
Figures 4–7 show the comparisons of the upper-ocean temperature vertical
structure between the WOA13 data and the model results of the five
experiments along transects of 30.5
The vertical temperature profiles along 30.5
The same as Fig. 4, but in July.
The same as Fig. 4, but along 7.5
The same as Fig. 4, but along 7.5
The difference for Exp 3 is much smaller than that of Exp 1 and Exp 2 because of the incorporation of the IT-generated turbulent mixing, especially in layers with depths between 20 and 50 m. This implies that the IT strengthens the vertical mixing of the ocean interior and improves the simulation further. It is worth noting that the experiment with the classic M-Y 2.5 scheme and the IT-generated turbulent mixing scheme is omitted; the reason is that the results have not been improved if only the IT-generated turbulent mixing is incorporated because the simulated surface mixing is insufficient and even deteriorated in some regions because colder water will be drawn from the lower layers with depths deeper than 100 m into the upper ocean.
However, the simulation is slightly improved in Exp 4 compared with Exp 1 because the BSMT, which is induced by the WTFR, is remarkably smaller than the BTW, so the WTFR-induced mixing is too insufficient to significantly improve simulating the upper-ocean temperature structure. Similarly, there is less difference between Exp 3 and Exp 5, implying that the effects of the WTFR on enhancing vertical mixing are much weaker than the NBSW in the surface layers and the IT in the ocean interior.
In Exp 1, the simulated temperature along 30.5
Figure 8 shows the monthly variability of the root mean square errors
(RMSEs) of the temperature in the upper 100 m layers between the WOA13 data
and the model results. Actually, the RMSEs are calculated based on the
simulated temperature only in the whole IO (the regions outside the IO
have been removed) as the following expression:
The study area is divided into three zones (Zones 1–3 marked in Fig. 1).
The zone partition of the IO in this study is designed based on previous
studies and the dynamic patterns of the IO. On one hand, previous studies
(Talley et al., 2011; Kumar et al., 2013, 2018) showed
different zone partitioning criteria, which often included the NIO, SIO
and tropical regions. On the other hand, the principal upper-ocean flow
regimes of the IO are the subtropical gyre of the SIO and the monsoonally
forced circulation of the tropics and NIO. All effects of the
Indonesian throughflow (ITF) should also be considered. Taking the above
factors into account, the whole IO was divided into three parts. Zone 1
represents the NIO including the Arabian Sea and the Bay of Bengal. Zone 2
represents the tropics and subtropical regions in the SIO with all
effects of the subtropical gyre and the ITF. Zone 3 represents the
region in the south of Zone 2 in the SIO. In Zone 2, there is a complete
cyclonic circulation system between the Equator and 20
In Zone 1, the RMSEs for Exp 2 are smaller than for Exp 1 in all of the
months, indicating the improvement of the NBSW in the upper-ocean simulation
in the NIO. Compared with Exp 2, the RMSEs for Exp 3 are smaller in most of
the months except November, December and January. This implies that the IT
enhances vertical mixing and improves the simulation further. The
possible reason for few effects of the IT from November to January is
that, on one hand, the mixed layer depths in the NIO are relatively
shallower in boreal winter so that the averaged velocity shear module of
the internal tides is smaller and the IT-induced mixing is weaker; on the
other hand, the strength of the surface waves is more intensive, so the
NBSW-induced mixing is relatively sufficient. The largest declines occurred
in May, when the RMSE decreased 14.0 % from 1.72
In Zone 2, the NBSW is ineffective because the RMSEs for Exp 2 are almost
equal to, or even larger than, those for Exp 1. This is a long-standing issue
about the trivial effects of the NBSW in the tropical area (Qiao et
al., 2010; Zhuang et al., 2020), implying that only the NBSW should not be
enough to improve the tropical simulation. To solve this issue, coupled
atmosphere–wave–ocean–ice modeling is one solution (Song et
al., 2012; Wang et al., 2019). Another way is incorporation of the
additional mechanism into OGCMs, such as the IT-generated turbulent
mixing added in Exp 3 and Exp 5. The RMSEs for Exp 3 are obviously smaller
than for Exp 1 and Exp 2 in the whole climatologic year except March,
implying that the combination of the NBSW and the IT is able to improve the
simulation of the temperature structure in the tropical area. Additionally,
the RMSEs in Zone 2 are smaller than in Zones 1 and 3 on the whole, and the
RMSEs in Zone 2 for Exp 3 and Exp 5 are even less than 0.9
In Zone 3, the results are similar to those in Zone 1. The RMSEs for Exp 2
are smaller than for Exp 1 in most months, and the RMSEs for Exp 3 are
the smallest ones among the first three experiments. The largest declines
occurred in January, when the RMSE decreases 20.8 % from 1.50
Furthermore, in Zones 1–3, the effects of WTFR are much weaker and similar to those in Figs. 4–7 because the RMSEs for Exp 4 and 5 are almost equal to, and even larger than, those for Exp 1 and 3. The possible reason is that the values of the WTFR-induced diffusion terms are about 4 to 6 orders smaller than NBSW, which is too low to enhance vertical mixing, especially in the surface layers.
Variation of the RMSE of temperature between the simulated monthly mean results in the five experiments and the monthly WOA13 data in Zones 1–3 (shown in Fig. 1).
The thermal structure in the regions with depths from 100 to 300 m are
also compared with the WOA13 data. The simulated temperature is generally
cooler than the WOA13 data along 30.5
Furthermore, the intermediate and deep-water masses in the IO are often
effected by the Southern Ocean, including Antarctic Intermediate Water,
Circumpolar Deep Water and North Atlantic Deep Water. These cooler water
masses are carried by the meridional overturning circulation into the IO
throughout the south of the South Equatorial Current in the subtropical Indian
Ocean (Talley et al., 2011), but the situation did not appear in the
simulated current fields. Therefore, another important reason should be that
it is hard to accurately simulate the meridional overturning circulation in
the present experiments, especially the meridional transport of heat.
This makes the simulated temperature cooler or warmer than the WOA13 data along
30.5
In addition, it is worth noting that the initialization design is also
important for ocean modeling. The comparison between the annual mean
temperature between the Levitus94 and WOA13 data shows that the temperature
from the Levitus94 data is obviously cooler than that from the WOA13 data in
the ACC regions (45–75
Lozovatsky et al. (2022) demonstrated that internal wave instabilities appear to be a dominant mechanism for generating energetic mixing based on an analysis of in situ observations of the turbulent kinetic energy dissipation rate and buoyancy frequency profiles. Actually, designing a universal and flexible IT-induced mixing scheme for ocean modeling based on in situ observations still needs a lot of work. The three schemes introduced in this study are just preliminary research on the contribution of upper-ocean vertical mixing.
The thermocline structure, which is normally defined as the depth of the 20
The comparison of Z20 and Z26 depths along the Equator from
the WOA13 data and the model results.
From Fig. 9 one can see that the Z20 and Z26 depths are both shallow in the west and deep in the east. The simulations of the thermal structure in the five experiments depict this pattern successfully, but there is still an obvious difference between the WOA13 data and the results, especially in the east regions in January for Z26 depths and in July for Z20 depths. One of the main reasons should be that the ITF may be simulated inaccurately because of inaccurate topography in the Indonesian regions and the open boundary conditions. The accurate simulation of the ITF should be a difficult issue because of the complicated topography and ocean–atmosphere interaction in the Indonesian Archipelago. Many OGCMs are incapable of reproducing the patterns of the ITF (Nagai et al., 2017; Santoso et al., 2022). Another reason is that this area is full of eddies produced by horizontal velocity shear, but our ocean model still lacks an accurate and reasonable parameterization of eddy-induced mixing, which needs more future work. For Z26 depths, the RMSEs for Exp 1 and Exp 4 are the largest in almost all of the months; this implies that the WTFR-induced mixing has little effect on the modeling, which is consistent with the comparison results above (Figs. 4–8). The NBSW- and IT-generated turbulence mixing can improve the simulated thermal structure as two of the key factors because of the smallest RMSEs (from February to July for Exp 2 and from August to January for Exp 3 and Exp 5). For Z20 depths, the NBSW and the IT have negative effects on the modeling because the RMSEs for Exp 2–Exp 5 are obviously larger than those for Exp 1. The reason is that the Z20 isothermal simulated in Exp 1 is generally deeper than the WOA13 data because the simulated temperature in the regions with depths from 130 to 200 m is warmer than the WOA13 data, and the enhanced vertical mixing induced by the NBSW and the IT will make the Z20 isothermal deepen further and deviate more from the WOA13 data (solid curves in Fig. 9a and b). Therefore, more optimization and improvement of the experimental design will be implemented in future work to make the simulated results more accurate.
In order to evaluate the modeling results further, the existing Argo-derived
gridded products, which are named Barnes objective analysis-Argo (BOA-Argo)
datasets (Li et al., 2017), are also chosen. The climatologic monthly
mean BOA-Argo data (multiyear mean from 2004 to 2014) are used and can be
downloaded directly from
Figures 10 and 11 show the comparison of the temperature structure between
the monthly BOA-Argo data and the model results in January. The vertical
distributions are similar to those from the WOA13 data (see panel a in
Figs. 4, 6, 10 and 11). The difference between the BOA-Argo data and the
model results along 30.5
The vertical temperature profiles along 30.5
The same as Fig. 10, but along 7.5
The mixed layer (ML), which is characterized by quasi-uniform temperature
and salinity, is crucial in understanding the physical processes in the
upper ocean. The MLD variability is influenced by many processes including
wind-induced turbulence, surface warming or cooling, air–sea heat exchange
and turbulence–wave interaction (Chen et al., 1994; Kara et al., 2003; de
Boyer Montégut et al., 2004; Abdulla et al., 2019). There are different
methods to define the MLD (Kara et al., 2003). The threshold criterion,
which is a widely favored and simple method for finding the MLD
(Kara et al., 2003; de Boyer Montégut et al., 2004), is used in
this study. In the threshold criterion, the MLD is defined as the depth at which
the temperature or density profiles change by a predefined amount relative
to a surface reference value. Various temperature threshold criteria were
used to determine the MLD globally, such as 0.2
Figure 12 shows the comparisons of the MLDs between the WOA13 data and the
model results in January. The MLDs for Exp 1 are generally shallower than
WOA13 in the whole IO and the Southern Ocean because of insufficient
simulated mixing processes, which leads to underestimation of the vertical
mixing in the upper ocean, especially during summer. The conclusion is
similar to the global and regional simulations in previous studies
(Kantha and Clayson, 1994; Qiao et al., 2010; Wang et al., 2019; Zhuang
et al., 2020). The accumulation of weak vertical mixing during the
10-year climatologic modeling will make more heat staying in the surface
layer, which will lead to warmer SST and shallower MLDs. In fact, from Fig. 12 one can see that the obviously shallower MLDs are generally in the ACC
regions where the simulated vertical mixing from the original experiment is
dramatically weak. In addition to the ACC regions, the obviously shallower
MLDs also appear in the east regions of the Arabian Sea because of the weak
vertical mixing. Furthermore, the simulated MLDs in most of the tropical and
southern regions of the IO are partially shallower than the WOA13 data.
Adopting the threshold criterion of 1.0
The distribution of the MLD calculated from WOA13 data and the differences of the MLD between the WOA13 data and the results simulated in Exp 1–Exp 5. RMSEs of the MLD are shown in the upper left corner of the panels. Deep yellow and white areas correspond to land, and the calculated MLDs are deeper than 150 m.
In this subsection, the simulated horizontal velocities in the surface layer are analyzed to evaluate the effects of NBSWs and ITs on ocean currents. Previous studies indicated that NBSWs and ITs have complicated impacts on simulated currents for OGCMs (e.g., Huang and Qiao, 2010; Wu et al., 2019). Only the results simulated in Exp 1–Exp 3 are discussed in detail, and the results in Exp 4 and Exp 5 are omitted here because the effects of the WTFR-induced mixing are relatively small. This situation is similar to the simulated temperature structure and MLDs in Sect. 4.2 and 4.3.
Figure 13 shows the comparisons of the surface velocities between the
monthly mean OSCAR data (Bonjean and Lagerloef, 2002) and the
model results of Exp 1–Exp 3 in January and July. The simulated surface
velocities are chosen as those at the depth of 2 m interpolated by the model
results. The OSCAR surface current products with a horizontal resolution of
1
The distribution of surface currents from the OSCAR
climatologic data and the differences by subtracting the OSCAR data from the
mean results from Exp 1
Furthermore, we calculated the three-dimensional vertical vorticity and eddy kinetic energy (EKE) in Exp 1–Exp 5 to evaluate the effects of mixing induced by NBSWs and ITs on the mesoscale eddy activity. However, the difference of the vertical vorticity and the EKE among the five experiments was too complicated to summarize some dynamic processes and physical mechanisms. The reason should be that the climatological modeling in this study, on one hand, may be inappropriate to analyze mesoscale or small-scale processes because of the relatively coarse resolution, smoothed surface forcing, open boundary conditions and topography data; on the other hand, the induced vertical mixing may not be a key mechanism for eddy activity, as previous studies indicated that surface waves affect eddies through the interaction among the turbulence, circulation and Langmuir circulation when the turbulent Langmuir number is small (Jayne and Marotzke, 2002; Romero et al., 2021); subharmonic instability may transfer the energy from the internal tides to the shear-induced turbulent diapycnal mixing (MacKinnon and Gregg, 2005; Pinkel and Sun, 2013). Especially in the east region of the tropical Indian Ocean, the effects of the ITF on mesoscale or small-scale processes have not yet been simulated exactly in existing OGCMs (e.g., Nagai et al., 2017; Santoso et al., 022). Additional improvements of the mixing schemes and the ocean modeling will be studied further in the future.
We evaluate the impacts of three different mixing schemes, including NBSW-generated turbulent mixing, WTFR-induced mixing and IT-generated turbulent mixing, on the upper-ocean thermal structure simulation in the IO. The comparisons of the temperature structure and the MLDs between the WOA13 data, which are regarded as the observations, and the model results imply that the simulation is significantly improved by incorporating the NBSW- and IT-generated turbulent mixing into the MASNUM ocean circulation model, but the effects of the WTFR are trivial, and the simulated MLDs are even deteriorated in some regions. However, based on numerical experiments, Yang et al. (2019) demonstrated that the WTFR may play an important role in SST cooling if the wind and surface waves are strong. During the period of tropical cyclone Nepartak passage, the simulated SST cooling distribution and the cooling amplitude are more consistent with the observations if the WTFR-induced mixing scheme is incorporated, which presents warming and cooling effects on the left and right sides of the typhoon track (Yu et al., 2020). The effects of the WTFR under the typhoon conditions will be further examined in future work.
In addition, the three mixing schemes are incorporated into the MASNUM model as part of the vertical diffusive terms, thus avoiding issues that may result from adding the mixing coefficients to those from the M-Y 2.5 scheme directly. The analysis of the numerical results indicates that the NBSW (and WTFR sometimes) leads to improved simulations of upper-ocean temperature structure and MLDs due to the enhanced mixing that draws warmer water from the surface to the subsurface layers with depths from about 10 to 40 m. Then the IT, which can improve the simulations further, may enhance the mixing that draws warmer water from the subsurface layers to the ocean interior (Fig. 14). In summary, the combination of NBSW- and IT-generated turbulent mixing results in a better match with observations of upper-ocean temperature structure and MLDs. The mixing schemes introduced in this study contain the effects of surface waves and internal tides, which are thought to supplement the physical mechanism for the vertical mixing processes in OGCMs because the original turbulent mixing schemes, such as the M-Y 2.5 scheme, neglected the interaction between surface waves and currents (Huang and Qiao, 2010; Huang et al., 2011). The M-Y 2.5 mixing scheme combined with the NBSW- and IT-induced mixing schemes should become more complete for modeling vertical mixing processes. In our opinion, it is important to study NBSW- and IT-induced mixing for promoting the development of the ocean and coupling models.
Sketch of the enhancing processes of the vertical mixing induced by three different mechanisms, including NBSW-generated turbulent mixing, WTFR-induced mixing and IT-generated turbulent mixing. SIT and TFR mixing represent the shear-induced turbulent and transport flux residue mixing, respectively. WE means the water exchange.
It is worth noting that the circulation and temperature structure of the
IO have not yet been characterized by the ocean model in the present study
because of the non-ignorable difference between the WOA13 data and the
simulation results. The RMSEs in the NIO, including the Arabian Sea and the
Bay of Bengal, are even generally larger than 1.2
We have to admit that the issues about the simulation in the IO cannot be solved entirely when the NBSW- and IT-induced mixing schemes are adopted, but it should be more convenient to improve the ocean modeling further because the mixing schemes are independent of the ocean models. A multi-scale process coupling model, including the atmosphere, ocean currents, tides, surface waves, and internal wave and tide component models, will be established in the future for accurate and high-resolution ocean and atmosphere modeling. The NBSW- and IT-induced mixing schemes and the related results in this study are helpful and valuable for establishing the coupling model.
This study uses the MASNUM ocean circulation model for testing and
validating the effects of three different mixing schemes, including
NBSW-generated turbulent mixing, WTFR-induced mixing and
IT-generated turbulent mixing, on the upper-ocean thermal structure
simulation in the IO. The major findings are summarized as follows.
The diffusive terms calculated by NBSW-generated turbulent mixing are
dominant if the depth is less than 30 m, while WTFR-induced mixing is
extremely weak because the values are about 4 to 6 orders smaller than the
NBSW. In the ocean interior with depths from 40 to 130 m, the diffusive
terms calculated by the IT-generated turbulent mixing are the largest ones
in regions with large topographic relief. The effects of these schemes on the upper-ocean simulation are tested.
The results show that the simulated thermal structure, MLDs and surface
currents are improved by the NBSW because of the enhanced mixing in
the sea surface, while the effects of the WTFR are trivial. The IT may strengthen the vertical mixing of the ocean interior and
improve the simulation further. In summary, the combination of the NBSW and
IT may strengthen vertical mixing and improve the upper-ocean
simulation.
Internal-tide-induced mixing plays an important role in the vertical and
horizontal distribution of water mass properties. Based on the Navier–Stokes
equations, the solvability simplification is realized based on the
spatiotemporal scale, controlling mechanism and actual characteristics of
the ITs. The IT is considered to be weakly nonlinear, the shear terms of the
larger-scale motions in the equations are approximately linear, and the
molecular and turbulent mixing terms in the equations are too small to be
ignored. The
The MASNUM ocean circulation and wave spectrum models can be downloaded at
ZZ wrote the paper with the help of all the co-authors. QZ, YY and ZS provided constructive feedback on the paper. YY designed and developed the theoretical basis of the improved vertical mixing scheme. CZ, XZ, TZ and JX gave help and advice on data processing and numerical experiments.
The contact author has declared that none of the authors has any competing interests.
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The authors thank the reviewers for their careful reviews and constructive comments in improving the article, as well as the editors who kindly edited and polished this paper with great effort.
This work is supported by the Basic Scientific Fund for National Public Research Institutes of China (grant no. 2020Q04), the National Natural Science Foundation of China (grant nos. 42106031, 42006008), Shandong Provincial Natural Science Foundation, China (grant no. ZR202102240074), and the National Program on Global Change and Air–Sea Interactions: “Distribution and Evolution of Ocean Dynamic Processes” (phase II, grant no. GASI-04-WLHY-01), “Parameterization assessment for interactions of the ocean dynamic system” (phase II, grant no. GASI-04-WLHY-02).
This paper was edited by Riccardo Farneti and reviewed by Ruibin Ding and one anonymous referee.