In this work, we apply a common mesh for FESOM2, namely the CORE-II mesh (https://fesom.de/models/meshessetups/, last access: 18 December 2020). The CORE-II mesh features low resolution (∼ 1∘) in mid-latitude areas and high resolution in coastal regions, the Equator and north of 50∘ N. It has about 127 k horizontal vertices and has 47 progressively thickening vertical layers from top to bottom. Since our work includes the simulation of tidal motions, the instant sea surface displacement can exceed 10 m at some spots, which requires either thickening the uppermost vertical layer (from 5 to 20 m) or selecting an appropriate vertical coordinate. Here we keep the vertical layer configuration while changing the vertical coordinate to the z-star coordinate. To keep a positive thickness for the uppermost layer, the z-star coordinate distributes ocean surface displacement into changes in layer thicknesses for all vertical layers except the bottom layer. A standard time step for FESOM2 configuration is 2700 s, which is too long to resolve fast-travelling barotropic tides. Through sensitivity tests, an optimal time step of 720 s has been determined (see Appendix ). In addition, since the model considers tidal motions and some related internal gravity waves, the Courant–Friedrichs–Lewy (CFL) stability condition could be constrained by the vertical advection term . Thus, a vertical velocity splitting method is applied in this work to keep vertical advection and oceanic mixing stable . Instead of explicitly treating the whole vertical advection term, when the vertical Courant number exceeds unity, the excess part of the vertical velocity would be treated implicitly.

Except for the customised model configuration above, we adopt other generic settings for FESOM2 in this work. The model starts from the Polar Science Centre Hydrographic Climatology (PHC3; ) and is driven by the Coordinated Ocean–ice Reference Experiments phase II (CORE-II) reanalysis atmospheric forcing ranging from 1948 to 2009. In addition, the sea surface salinity is restored to climatology values during the simulation. The horizontal viscosity in the model applies an ocean kinetic energy backscatter parameterisation scheme . Constant background mixing is set as 10-4 and 10-5 m2s-1 for vertical viscosity and diffusivity. In addition to the constant background mixing, we apply the K-profile parameterisation (KPP; ) in this work. The Gent–McWilliams scheme and the Redi isoneutral diffusion scheme are applied to the parameterisation of subgrid eddy-induced mixing. Note here that the Gent–McWilliams parameterisation applied is formulated following .

We implement a global tidal potential module in FESOM2 to consider the real tidal motions. The tidal potential in FESOM2 can be expressed as 1Ω=Ωg+Ωe+ΩSAL=αΩg+βgη. The tidal forcing is expressed in the model as the gradient of the tidal potential Ω, which consists of three parts according to Eq. (). The lunisolar gravitational potential Ωg is calculated by considering the real-time position of the Sun and Moon with an ephemeris approach . Except for the lunisolar gravitational potential term, two correction terms should also be considered. The solid Earth tide Ωe driven by the Sun and Moon has a counteracting effect to the ocean tides, which is expressed as a portion of the lunisolar gravitational potential. Thus, Ωg+Ωe can be written as αΩg, where α represents the effective Earth elasticity factor. Though α is distinct for diurnal tidal components , an identical factor of 0.69 is applied in this work following . The self-attraction and loading (SAL) effect ΩSAL considers the seafloor deformation and the changing of the earth gravity field caused by the weight distribution of seawater. To determine the SAL effect, one needs an explicit calculation based on a convolution integral (e.g. ). However, this method is costly, and thus we use a simplified form βgη. η and g represent sea surface elevation and the gravitational acceleration. The scale factor β has been estimated in previous work (e.g. ) and is set to 0.1 here.

The CVMIX_TIDAL parameterisation is implemented in FESOM2 along with the CVMIX library . It is expressed as additional vertical diffusivity and vertical viscosity terms in the model. Take vertical diffusivity (kv) as an example. 2kv′=kv+ΓϵN2=kv+qΓE(x,y)F(z)ρN2 In Eq. (), the term kv represents the original vertical diffusivity, which is the sum of constant background vertical diffusivity and KPP vertical diffusivity in this work. ρ and N denote seawater density and buoyancy frequency, respectively. The mixing efficiency Γ, which is set to 0.2 following , represents the fraction of dissipated mechanical energy that leads to oceanic mixing. ϵ represents the tidal energy dissipation rate, which can be further expanded as qE(x,y)F(z)/ρ. The tidal dissipation efficiency q is estimated to be 0.33, indicating that one-third of the tidal energy is dissipated locally, while the rest is radiated away and dissipated remotely as propagating low-mode internal waves. Note that the remotely dissipated energy is already contained in the background vertical diffusivity in an OGCM . The horizontal and vertical distribution functions of tidal energy dissipation are expressed as E(x,y) and F(z), which can be further expanded as below. 3E(x,y)=12ρ0Nbκh2〈u2〉4F(z)=e-(H+z)/ζζ(1-e-H/ζ) In Eq. (), E(x,y) means the parameterised energy conversion rate from barotropic to baroclinic tides. ρ0 and Nb represent the reference seawater density and bottom buoyancy frequency, respectively. 〈u2〉 is the temporal mean square tidal velocity, representing the barotropic tide energy. κ and h are the wavenumbers and amplitude scales of ocean topography, representing the bottom roughness. It should be noted here that κ is a tuning variable so that the global integral of E(x,y) fits the general value (, 1 TW). In Eq. (), the vertical distribution function F(z) is a bottom intensified exponential profile whose depth integral is unity. ζ, which is suggested as 500 m, denotes the e-folding scale of F(z) from the bottom -H. The additional vertical viscosity is equal to the additional vertical diffusivity. That means the parameterisation considers the viscosity–diffusivity ratio (also known as the Prandtl number) as unity, which agrees with the Prandtl number in the KPP scheme beneath the surface boundary layer.

We set three experiments with the above configuration to investigate the influence of tide-induced mixing on the ocean state. The control run is named NOTIDE, which does not consider any kind of tidal effect. The first comparison run, LSTIDE, considers the lunisolar tidal potential in the momentum equations. The second comparison run, CVTIDE, does not simulate real ocean tides but applies the parameterisation of tide-induced mixing (CVMIX_TIDAL). It should be noted that all other model configurations are identical among the three sensitivity runs. Following the spin-up strategy of , the three sensitivity experiments start from the PHC3 climatology and are periodically forced by the CORE-II forcing. Each experiment is conducted for five consecutive cycles, namely R1 to R5. Each cycle corresponds with the year 1948 to 2009. Unless otherwise specified, all the model results shown in this paper are the average of the last 50 model years (1960 to 2009 in R5).

We compare model results with the World Ocean Atlas 2018 (WOA18; ). The decadal-averaged annual dataset with a resolution of 0.25∘ is obtained. For comparability, the in situ temperatures from the WOA18 dataset are converted to potential temperatures. Unless otherwise specified, temperatures refer to potential temperatures in the below context.

Figure  shows the temperature differences between the sensitivity runs and WOA18. In the upper layer, LSTIDE generally reduces the temperature biases in the low-latitude areas of the three major oceans, indicating lower temperature biases than CVTIDE. However, in the subpolar North Pacific Ocean, CVTIDE shows a better reduction of the warm biases than LSTIDE. In the intermediate layer, LSTIDE generally reduces the temperature biases in most mid- and low-latitude areas. But CVTIDE has lower temperature biases in the whole Arctic region. In addition, neither CVTIDE nor LSTIDE presents significant improvements to the Southern Ocean. In the deep layer, CVTIDE shows a cooling effect in the Southern Ocean, but LSTIDE shows a warming effect in the basins of the three major oceans, showing lower temperature biases in the global view. Figure  is the same as Fig.  but for salinity. In the upper layer, CVTIDE mainly reduces the salinity biases in the tropical Pacific Ocean. In contrast, LSTIDE reduces the salinity biases in the tropical Pacific Ocean and the tropical Indian Ocean. In the intermediate layer, CVTIDE reduces salinity biases in the tropical Pacific Ocean and the tropical Indian Ocean. In contrast, LSTIDE reduces salinity biases in the North Pacific Ocean and North Atlantic subtropical gyre area. In the deep layer, only LSTIDE shows improvements in the low-latitude area in the Atlantic Ocean.

The tidal effects also demonstrate improvements to different extents at different depths of each basin. Figure  shows basin-averaged temperature and salinity biases at each vertical layer in the model. In the left panels, LSTIDE shows significant improvements to the temperature biases in the Pacific, Atlantic, and Indian oceans deeper than 1000 m. CVTIDE only reduces temperature biases in the Arctic Ocean at 500–2000 m in depth. Also, both CVTIDE and LSTIDE reduce temperature biases in the Southern Ocean deeper than 4000 m. In the right panels, we can only find improvements in LSTIDE. Salinity biases are slightly reduced in the Atlantic and Pacific oceans, around 1500 m in depth. We should also note that in Fig. j, significant salinity biases emerge on the surface Arctic Ocean. These result from the differences between the PHC3 and WOA datasets. Our model starts with the PHC3 climatology, which integrates the WOA dataset and the Arctic Ocean Atlas.

CVTIDE and LSTIDE also greatly influence the hydrography in the continental shelf and slope areas, which cannot be clearly shown in Figs. –. By assembling grids with the same bathymetry and averaging the temperature and salinity biases, the bathymetry-averaged biases with respect to depths are shown in Fig. . In Fig. a, the model results in the control run demonstrate significant temperature biases near continental shelf and slope topographies, and both CVTIDE and LSTIDE decrease the biases in these areas. By comparing Fig. c with Fig. e, CVTIDE has a better improvement near the bottom of the continental shelf and slope, while LSTIDE significantly reduces temperature biases at 1000–4000 m in depth, which is not shown in CVTIDE. In Fig. b, significant salinity biases in the control run concentrate in the shallow continental shelf areas. It is shown in Fig. d and f that CVTIDE decreases salinity biases at the near-bottom continental shelf area, while LSTIDE decreases salinity biases in the whole layer of the continental shelf area. Neither of the two comparison runs demonstrates a significant improvement to other areas, except for the slight modification of LSTIDE around 1500 m in depth.

Figure  shows the results of sea ice thickness (SIT) in the polar regions. Both tidal effects alter the sea ice results, but the patterns are different.

In the Arctic region, CVTIDE generally decreases SIT in the Labrador Shelf, East Greenland Shelf and the Sea of Okhotsk but increases SIT in the Canadian Arctic Archipelago (CAA). LSTIDE shows a slighter SIT decrease than CVTIDE in the Sea of Okhotsk and Labrador Shelf but increases SIT in the Greenland Sea. One of the most significant differences between LSTIDE and CVTIDE is that LSTIDE shows a remarkable SIT decrease in the CAA. The mean SIT in the CAA in the control run is 6.01 m; LSTIDE decreases by 0.60 m, while CVTIDE increases by 0.03 m. In the Antarctic region, both CVTIDE and LSTIDE show similar patterns, including a general SIT decrease around Antarctica and an SIT increase on the Weddell Sea continental shelf and Ross Sea continental shelf. On the West Antarctic Peninsula Continental Shelf, SIT decreases in CVTIDE but increases in LSTIDE. Generally speaking, CVTIDE shows a more significant impact on SIT than LSTIDE.

We should also point out that CVTIDE consistently reduces SIT in both regions at shelf-break areas, which are indicated by the dashed grey lines. However, LSTIDE does not show this consistency. The difference is further discussed in Sect. .

The left column of Fig.  shows that CVTIDE and LSTIDE affect AMOC differently. CVTIDE weakens the AMOC upper cell by 0.50 Sv and strengthens the lower cell by 0.75 Sv, while LSTIDE strengthens the AMOC upper cell by 1.50 Sv and weakens the lower cell by 0.25 Sv. That indicates CVTIDE weakens the North Atlantic Deep Water (NADW) formation and strengthens the Antarctic Bottom Water (AABW) formation, while LSTIDE behaves the opposite.

The results of PMOC are shown in the right column of Fig. . The main effect of CVTIDE on the PMOC occurs in the south Indo-Pacific Ocean. The deep water upwelling at 20∘ S is enhanced by 4 Sv. LSTIDE has a more significant effect than CVTIDE. Figure f features two cells: the south cell upwells deep water in the tropical Indo-Pacific Ocean, while the north cell upwells deep water in the subarctic North Pacific Ocean. Both cells enhance deep water upwelling by 5 Sv, and the upwelled deep waters are released to the Indo-Pacific Ocean's intermediate layer (about 1000–2000 m). The north cell in Fig. f shows consistency with the North Pacific bathymetry, which is further discussed in Sect. .

Since tidal mixing is stimulated by topographies, tidal mixing and vertical diffusivity are bottom-enhanced. Figure a–c show the near-bottom vertical diffusivity in the three sensitivity runs. Compared with the control run, Fig. b shows observably that the CVMIX_TIDAL parameterisation enhances vertical diffusivity by a large value in the deep ocean. In CVTIDE, the vertical diffusivity is enhanced where bottom topography roughness is large, such as seamounts, deep ocean ridges and shelf-break areas. The pattern of LSTIDE is very different compared with CVTIDE, and we cannot see a coherent enhancement of vertical diffusivity in the near-bottom ocean. The global mean vertical diffusivity profiles (Fig. d) also demonstrate that compared with CVTIDE, LSTIDE does not enhance vertical diffusivity significantly in the deep ocean.

Figure  demonstrates that CVTIDE and LSTIDE show similar patterns in changing the global barotropic streamfunction. The patterns of streamfunction differences in Figs. b and c mainly consist of two loops. The “blue loop” is mainly located in the Indo-Pacific Ocean: the southward transport enhances the ITF and finally contributes to the ACC, and its recirculation is located in the western Pacific Ocean. The “red loop” enhances the ACC separately. The blue and red loops are stronger in LSTIDE than those in CVTIDE. CVTIDE enhances the ITF and the ACC through the Drake Passage by 1.72 and 4.79 Sv, while the values of LSTIDE are 3.92 and 10.34 Sv, respectively. In addition, we can find an essential difference regarding the blue loop: the blue loop extends to the subpolar Pacific Ocean and the South Atlantic Ocean in LSTIDE but not in CVTIDE. The difference determines the PMOC–AMOC connection, which is discussed in Sect. .

Based on the energy budget equation (see Appendix ), we diagnose the energy terms from the model results and list the global integration values in Table . Due to the additional energy input in LSTIDE (Tide and KE in Table ), three energy dissipation terms (bottom drag, vertical viscous dissipation and horizontal viscous dissipation) are enhanced compared with NOTIDE and CVTIDE, especially for bottom drag. The additional energy sink in these three terms accounts for about 1 TW. The remaining 3.5 TW of the total 4.6 TW tidal potential power is converted from kinetic energy to barotropic potential energy.

Figure  shows the horizontal distribution of vertically integrated bottom drag and viscous dissipation. Because of the strong tidal currents in marginal seas and continental shelf areas, LSTIDE enhances bottom drag and viscous dissipation significantly in these areas. Like the vertical diffusivity, the vertical viscosity is also enhanced in the CVMIX_TIDAL parameterisation, but the effect is negligible (Fig. e).

Even though the global integration of buoyancy flux shows no difference in the three runs, the horizontal distribution shows differences (Fig. ). Regional integration values over the Kuril–Aleutian Ridge area (120∘ E–120∘ W, 30∘ N–60∘ N) in NOTIDE, CVTIDE and LSTIDE are -1.22, -1.52 and -2.78 TW, respectively. In the Indonesian Archipelago area (90–150∘ E, 15∘ S–15∘ N), regional integration values in NOTIDE, CVTIDE and LSTIDE are -0.82, -1.13 and -1.19 TW, respectively. Compared with CVTIDE, LSTIDE shows a stronger enhancement of buoyancy flux in the Kuril–Aleutian Ridge and Indonesian Archipelago but a weaker enhancement in other mid-latitude areas. The lower panels of Fig.  indicate that with tidal currents in LSTIDE, turbulent buoyancy flux plays an essential role in the oceanic mixing and buoyancy flux (see Appendix ).

As shown in (their Fig. 4), internal tides are important links between surface tides and oceanic mixing. Indeed, demonstrate that the conversion rate of internal tide energy in a global tide model depends on the model resolution. Thus, if the model mesh cannot resolve internal tides, the internal-tide-induced mixing is missing in the model result. Figure  presents the ratio of mode-1 internal tide wavelengths to the mesh resolution. We can find that most of the model areas cannot resolve propagating internal tides in the mid-latitude area, especially for semidiurnal ones in Fig. b. In addition, even though the unstructured model mesh has a higher resolution in shelf-slope areas, it still cannot resolve internal tides therein because the wavelengths of internal tides are smaller in these areas. So we infer that LSTIDE has a strong dependence on the model resolution.

Evidence can be found in the model results. In Fig. , compared with CVTIDE (Figs. c and d), LSTIDE (Figs. e and f) shows a weaker reduction of hydrographic biases near the bottom of shelf breaks. The internal tides at shelf-slope areas cannot be resolved in LSTIDE, which weakens the mixing effect. Tidal mixing on shelf breaks also affects SIT. Unlike other places where the temperature decreases monotonically with depth, the polar regions have colder water near the surface than in the deeper layers. Thus in polar regions, the tidal mixing on shelf-slope areas would lead to a warmer surface ocean, which should decrease the SIT. In our result, LSTIDE shows a smaller SIT decrease than CVTIDE on the shelf-slope area, such as the Labrador Shelf and the Antarctic continental shelf (Fig. ). The effect of the resolution is also reflected in the model vertical diffusivity. Both observational results and CVMIX_TIDAL parameterisation suggest larger vertical diffusivities near the bottom, which is caused by the tide–topography interaction. However, vertical diffusivities in the near-bottom layers are not generally higher in LSTIDE than in NOTIDE (Fig. c). The lack of resolving internal tides causes the underestimation of vertical shear, thus leading to a different result compared with CVTIDE. The buoyancy flux results (Fig. b and c), which are most directly connected to oceanic upwelling, also show weaker mixing effects in mid-latitude areas in LSTIDE compared with CVTIDE. Figure  shows the model mesh can roughly resolve propagating internal tides in tropical areas, where strong mixing can be found in LSTIDE. LSTIDE (Fig. f) shows strong mixing and upwelling in the equatorial Indo-Pacific Ocean, which is not clearly shown in CVTIDE (Fig. d). We think this comes from the underestimation of tidal dissipation efficiency (q). The tidal dissipation efficiency is set to 0.33 in this work, but previous work indicates higher efficiencies in the Indonesian Archipelago area .

Figure  also implies trapped internal tides beyond critical latitudes. According to the dispersion relationship of internal tides, where the inertial frequency is higher than a tidal frequency (f>ω), internal tides at the tidal frequency would not have a wave solution, resulting in trapped internal tides instead of propagating internal tides (latitudes higher than the dashed lines in Fig. ). Unlike propagating internal tides, trapped internal tides can only be dissipated in a small domain, leading to a higher local dissipation rate and thus stronger local mixing. The Kuril Ridge and Aleutian Ridge, which connect the Sea of Okhotsk and the Bering Sea with the North Pacific Ocean, are the main generation sites for trapped diurnal internal tides. Large dissipation rates by trapped internal tides are validated in previous modelling research , and intense mixing is also observed therein .

LSTIDE demonstrates intense mixing in the Kuril Ridge and Aleutian Ridge, resulting in higher buoyancy flux than NOTIDE in these areas (Fig. c). LSTIDE does not change the vertical diffusivity significantly. Still, it enhances the upwelling in the North Pacific. We explain this by tide-induced turbulent buoyancy flux (Fig. f and Appendix ). The strong mixing upwells an additional 5 Sv of deep water in the North Pacific (around 50∘ N) to the intermediate layer and then spreads to the south (Fig. f). The strong mixing in the Indonesian Archipelago also results in strong upwelling. The upwelled water from both the Indonesian Archipelago and Kuril–Aleutian Ridge contributes to the ITF (Fig. c) and flows into the Indian Ocean. Stronger PMOC helps to reduce temperature biases in the intermediate Indo-Pacific Ocean (Fig. f): the upwelling of the deep water reduces the warm biases in the North Pacific Ocean and cold biases in the tropical Indo-Pacific Ocean in NOTIDE.

Trapped internal tides and related mixing can be simulated with LSTIDE because in the high-latitude areas, the CORE-II mesh is fine enough to resolve trapped internal tides (Fig. ). As a comparison, even though CVTIDE does not show much influence on the PMOC in the North Pacific Ocean, it shows similar but weaker patterns in reducing the temperature biases in the intermediate layer. This is probably for two reasons: (1) most of the trapped internal tides' energy is dissipated locally, so the tidal dissipation efficiency is close to unity (q≈1) in this area instead of 0.33 from CVTIDE, and (2) the simulation is not long enough to become stable. It should also be emphasised here that even though the PMOC lower cell in the North Pacific is reported in most previous work (e.g. ), our results in LSTIDE demonstrate a different shape for the PMOC lower cell in the North Pacific. The significant upwelling occurs in the Aleutian Ridge, and the upwelling has great consistency with the topography (take the brown transect in Fig. f as an example). The diurnal tidal mixing beyond critical latitudes causes an upwelling along the bottom boundary, which is not reported in previous work. Nevertheless, our result supports some previous arguments that the upwelling caused by near-boundary mixing is more important than interior mixing in closing the THC.

The model also shows interesting results in the spin-up. The time series of several main constituents of the global THC is demonstrated in Fig. . In Fig. a and b, we find that both CVTIDE and LSTIDE show a stronger PMOC and ITF than the control run from the beginning. In the fourth and fifth cycles, the discrepancies of PMOC and ITF between CVTIDE/LSTIDE and NOTIDE become stable. In Fig. c, it is shown that in the first cycle, the strength of AMOC upper cell in both CVTIDE and LSTIDE is weaker than that in the control run. However, from the second cycle, the strength of the AMOC upper cell in LSTIDE starts to surpass that in NOTIDE. The strength of the AMOC upper cell in CVTIDE is weaker than that in NOTIDE in all cycles. As mentioned in Sect. , the CVMIX_TIDAL scheme applies the same formula to the model viscosities, potentially increasing model dissipation and leading to a weaker circulation on shelf-slope areas. Thus, the wind-driven circulation, the poleward heat flux and the AMOC upper cell are weakened, which corresponds with previous work (e.g. ). But a major difference between CVTIDE and LSTIDE embodies the subsequent enhancement of the AMOC upper cell in LSTIDE. Results from LSTIDE reveal that the upwelling in the North Pacific and Indonesian Archipelago is linked to the North Atlantic. Figures f and c indicate that the enhancement of mixing in the North Pacific and Indonesian Archipelago results in a stronger PMOC and ITF. The ITF mass transport finally forms the blue loop in the barotropic streamfunction difference (Fig. c). The westernmost part of this loop extends to the South Atlantic, which seems to have no connection with the North Atlantic. But note here that the vertical structure of oceanic circulation cannot be revealed by the barotropic streamfunction. Nevertheless, Fig. e further shows that the upper cell of AMOC is enhanced, and the effect originates from the South Atlantic. Conversely, even though CVTIDE also has a stronger ITF and a blue loop streamfunction difference, it does not strengthen the upper cell of AMOC because the blue loop is restricted in the Indo-Pacific Ocean and does not extend to the South Atlantic (Fig. b). The connection between the Indo-Pacific Ocean and the Atlantic Ocean is the Agulhas leakage. The Agulhas leakage is strengthened in LSTIDE (Fig. c), but the pattern is cut off in CVTIDE (Fig. b). And that explains why the strengthening of PMOC and ITF only leads to AMOC increase in LSTIDE. The importance of Agulhas leakage in connecting cross-basin circulation is also reported in . In addition, we rule out the possibility that the tidal mixing in the Atlantic itself causes the strengthening of the AMOC upper cell for two reasons: (1) in Fig. e, the AMOC cell does not show a closed overturning circulation, which means 1.5 Sv of AMOC is not upwelled in the Atlantic Ocean north to 30∘ S, and (2) the transect plot does not show either stronger vertical diffusivity or turbulent buoyancy flux in the Atlantic Ocean (figure not shown). The cycle revealed in our result corresponds well with a previous paper (, their Fig. S14.1c). The enhancement of ITF due to tidal mixing is also reported in previous research , and the link between the stronger PMOC lower cell and the stronger AMOC upper cell can also be found in .

As for the AMOC lower cell, LSTIDE shows a weakening effect, while CVTIDE shows a strengthening effect (Fig. d). It is widely believed that the global tidal mixing and wind-driven upwelling in the Southern Ocean affect the MOC . Since the model configuration applies the same atmospheric forcing in the three sensitivity runs, the reason concerning wind stress would be excluded. Moreover, considering the vertical advection–diffusion balance , the tidal mixing should strengthen the MOC, as CVTIDE shows. As discussed above, LSTIDE has the disadvantage of demonstrating tide-induced mixing in the vast mid-latitude areas due to the resolution; thus, the AMOC lower cell is weakened instead of strengthened in LSTIDE. We also suspect that the enhanced vertical diffusivities may be added to deep convection areas, directly leading to stronger convection. However, the CVMIX_TIDAL parameterisation implies that the enhanced vertical diffusivities are not added to areas where gravitational instability occurs (N2<0). So we finally conclude that the AMOC lower cell is enhanced due to tidal mixing, and more AABW formation in the Weddell Sea is a result instead of a reason for the strengthening of the AMOC lower cell. A similar conclusion can be found in .

CVTIDE and LSTIDE also demonstrate that the ACC transport through the Drake Passage is larger than that in NOTIDE (Figs.  and e). We can see from Fig. e that the strength of ACC in all three sensitivity runs decreases during the five cycles, but the decreasing rate is lower in the comparison runs, which can be explained by Fig. . Figure d and f show that both comparison runs have similar effects on changing potential density in the Southern Hemisphere. In the mid- and low-latitude areas, both tidal effects demonstrate denser seawater in the upper ocean and lighter seawater in the lower ocean, indicating the promotion of ocean potential energy caused by the tidal mixing. In the high-latitude areas, both comparison runs show denser seawater from the surface to the bottom, indicating the reduction of ocean potential energy due to the deep convection. In depths below 1000 m, both CVTIDE and LSTIDE show potential density decrease at subtropical latitudes. The decrease in potential density is caused by the mixing and advection effect indicated by the global MOC (GMOC). For example, Fig. e shows that strong mixing and upwelling take place in the tropical region, and the upwelled water further advects to the south (similar to Fig. f). The advection effect causes the “blue tongue” pattern in Fig. f (1000–2000 m in depth). In addition, the potential density increase at subpolar latitudes can be explained by the AABW formation. In the above context, our results show that the tidal mixing in CVTIDE causes the strengthening of the AABW formation. This is also why the potential density increase at subpolar latitudes is more substantial in CVTIDE than in LSTIDE. Even though CVTIDE and LSTIDE alter potential density differently, both experiments increase the meridional density gradients in the Southern Ocean, which prevents the strength of ACC from decreasing due to the thermal wind relation. Thus we conclude that both CVTIDE and LSTIDE affect the ACC strength by enhancing the meridional density gradient. Similar results are also shown in that with tidal mixing parameterisation, the ACC transport is stronger by 25 % compared with their control run.

The “barotropic tide–baroclinic tide–oceanic mixing” chain is considered the most crucial tidal effect on the ocean and climate. But we are still questioning if there are any effects from tides other than internal tide mixing. Since CVTIDE only considers internal tide mixing effects, and LSTIDE considers real-tide effects, we can answer this question by comparing LSTIDE with CVTIDE.

The most significant difference is the energy in the model. If the tidal potential term is added to the ocean primitive equation, tide energy is thus input to the system (Table ). The global tidal potential power is 4.6 TW in our model. However, most of the energy goes to the barotropic potential energy, indicating a lack of internal tides in the system. If the model resolved more internal tides, the surface tide amplitudes and the conversion to barotropic potential energy would be smaller due to the internal wave drag (e.g. ). This part of energy would be redistributed to the buoyancy flux and energy dissipation terms, depending on the conversion rate between surface tides and internal tides. External energy input not only leads to higher kinetic energy but also higher energy dissipation. Comparing Fig. b with Fig. c, we find that the bottom drag is significantly enhanced in LSTIDE compared to CVTIDE. Regarding the viscous dissipation, LSTIDE shows remarkable enhancement on continental shelves (Fig. f), while CVTIDE does not show significant changes compared with NOTIDE. The reason is that LSTIDE has strong tidal shear caused by the bottom drag of barotropic tides on continental shelves, while CVTIDE only increases viscosity and diffusivity on shelf breaks and seamounts, indicating an effect of internal tides.

Additionally, we find that considering the strong tidal shear on continental shelves can reduce model biases. Both Figs. e and f indicate that in LSTIDE, the temperature and salinity biases on continental shelves (e.g. bottom depth less than 100 m) are better reduced compared with CVTIDE. Via a coupled climate model, also found that local hydrographic biases can be reduced when considering tidal shear effects on continental shelves.

From a mathematical point of view, adding periodic tidal motions can also affect stress terms, leading to a tidal residual effect. Even though tidal velocities can roughly be eliminated via time-averaging, the stress terms can always leave non-zero cross terms. These effects are more remarkable in regional simulations than global ones. Our results show that only the sea ice distribution in the CAA is significantly affected by the tidal residual effect. Figure  shows that in LSTIDE, the SIT in the CAA is reduced by about 10 %. Adding strong tidal currents in the narrow channels can lead to an additional ocean-to-ice stress, and the theoretical basis can be referred to in (1979, their Eq. 3). Our results also show that the additional stress causes sea ice transports from CAA to the adjacent areas.