A parameterization scheme of vertical mixing due to inertial internal wave breaking in the ocean general circulation model

Based on the theoretical spectral model of inertial internal wave breaking （fine structure） proposed previ- ously, in which the effects of the horizontal Coriolis frequency component f-tilde on a potential isopycnal are taken into account, a parameterization scheme of vertical mixing in the stably stratified interior be- low the surface mixed layer in the ocean general circulation model （OGCM） is put forward preliminarily in this paper. Besides turbulence, the impact of sub-mesoscale oceanic processes （including inertial internal wave breaking product） on oceanic interior mixing is emphasized. We suggest that adding the inertial inter- hal wave breaking mixing scheme （F-scheme for short） put forward in this paper to the turbulence mixing scheme of Canuto et al. （T-scheme for short） in the OGCM, except the region from 15°S to 15°N. The numeri- cal results ofF-scheme by usingWOA09 data and an OGCM （LICOM, LASG/IAP climate system ocean model） over the global ocean are given. A notable improvement in the simulation of salinity and temperature over the global ocean is attained by using T-scheme adding F-scheme, especially in the mid- and high-latitude regions in the simulation of the intermediate water and deep water. We conjecture that the inertial internal wave breaking mixing and inertial forcing of wind might be one of important mechanisms maintaining the ventilation process. The modeling strength of the Atlantic meridional overturning circulation （AMOC） by using T-scheme adding F-scheme may be more reasonable than that by using T-scheme alone, though the physical processes need to be further studied, and the overflow parameterization needs to be incorporated. A shortcoming in F-scheme is that in this paper the error of simulated salinity and temperature by using T-scheme adding F-scheme is larger than that by using T-scheme alone in the subsurface layer.

Contribution of surface wave-induced vertical mixing to heat content in global upper ocean

Compared with observations,the simulated upper ocean heat content(OHC)determined from climate models shows an underestimation bias.The simulation bias of the average annual water temperature in the upper 300 m is 0.2℃lower than the observational results.The results from our two numerical experiments,using a CMIP5 model,show that the non-breaking surface wave-induced vertical mixing can reduce this bias.The enhanced vertical mixing increases the OHC in the global upper ocean(65°S–65°N).Using non-breaking surface wave-induced vertical mixing reduced the disparity by 30%to 0.14℃.The heat content increase is not directly induced by air-sea heat fluxes during the simulation period,but is the legacy of temperature increases in the first 150 years.During this period,additional vertical mixing was initially included in the climate model.The non-breaking surface wave-induced vertical mixing improves the OHC by increasing the air-sea heat fluxes in the first 150 years.This increase in air-sea heat fluxes warms the upper ocean by 0.05–0.06℃.The results show that the incorporation of vertical mixing induced by nonbreaking surface waves in our experiments can improve the simulation of OHC in the global upper ocean.

The sensitivity of numerical simulation to vertical mixing parameterization schemes: a case study for the Yellow Sea Cold Water Mass

The vertical mixing parameterization scheme,by providing the eff ects of some explicitly missed physical processes and more importantly closing the energy budgets,is a critical model component and therefore imposes signifi cant impacts on model performance.The Yellow Sea Cold Water Mass(YSCWM),as the most striking and unique phenomenon in the Yellow Sea during summer,is dramatically aff ected by vertical mixing process during its each stage and therefore seriously sensitive to the proper choice of parameterization scheme.In this paper,a hindcast of YSCWM in winter of 2006 was implemented by using the Regional Ocean Modeling System(ROMS).Three popular parameterization schemes,including the level 2.5 Mellor-Yamada closure(M-Y 2.5),Generic Length Scale closure(GLS)and K-Profi le Parameterization(KPP),were tested and compared with each other by conducting a series of sensitivity model experiments.The infl uence of diff erent parameterization schemes on modeling the YSCWM was then carefully examined and assessed based on these model experiments.Although reasonable thermal structure and its seasonal variation were well reproduced by all schemes,considerable diff erences could still be found among all experiments.A warmer and spatially smaller simulation of YSCWM,with very strong thermocline,appeared in M-Y 2.5 experiment,while a spatially larger YSCWM with shallow mixed layer was found in GLS and KPP schemes.Among all the experiments,the discrepancy,indicated by core temperature,appeared since spring,and grew gradually by the end of November.Additional experiments also confi rmed that the increase of background diff usivity could eff ectively weaken the YSCWM,in either strength or coverage.Surface wave,another contributor in upper layer,was found responsible for the shrinkage of YSCWM coverage.The treatment of wave eff ect as an additional turbulence production term in prognostic equation was shown to be more superior to the strategy of directly increasing diff usivity for a coastal region.

Oceanic vertical mixing of the lower halocline water in the Chukchi Borderland and Mendeleyev Ridge

Oceanic vertical mixing of the lower halocline water(LHW)in the Chukchi Borderland and Mendeleyev Ridge was studied based on in situ hydrographic and turbulent observations.The depth-averaged turbulent dissipation rate of LHW demonstrates a clear topographic dependence,with a mean value of 1.2×10^(-9) W/kg in the southwest of Canada Basin,1.5×10^(-9) W/kg in the Mendeleyev Abyssal Plain,2.4×10^(-9) W/kg on the Mendeleyev Ridge,and2.7×10^(-9) W/kg on the Chukchi Cap.Correspondingly,the mean depth-averaged vertical heat flux of the LHW is0.21 W/m^(2) in the southwest Canada Basin,0.30 W/m^(2) in the Mendeleyev Abyssal Plain,0.39 W/m^(2) on the Mendeleyev Ridge,and 0.46 W/m^(2) on the Chukchi Cap.However,in the presence of Pacific Winter Water,the upward heat released from Atlantic Water through the lower halocline can hardly contribute to the surface ocean.Further,the underlying mechanisms of diapycnal mixing in LHW—double diffusion and shear instability—was investigated.The mixing in LHW where double diffusion were observed is always relatively weaker,with corresponding dissipation rate ranging from 1.01×10^(-9) W/kg to 1.57×10^(-9) W/kg.The results also show a strong correlation between the depth-average dissipation rate and strain variance in the LHW,which indicates a close physical linkage between the turbulent mixing and internal wave activities.In addition,both surface wind forcing and semidiurnal tides significantly contribute to the turbulent mixing in the LHW.

SENSITIVITY STUDY OF THE EFFECTS OF WAVE-INDUCED VERTICAL MIXING ON VERTICAL EXCHANGE PROCESSES

The hydrodynamic model COHERENS-SED, developed by the present authors through introducing wave-enhanced bottom stress, wave dependent surface drag coefficient, wave-induced surface mixing, SWAN to COHERENS, is modified to account for wave-induced vertical mixing. The COHERENS-SED model can also be used for one-dimensional, two-dimensional, three-dimensional current and salinity calculations. One-dimensional model and three-dimensional model are used to study the effects of the wave-induced vertical mixing. The horizontal current velocity profiles obtained by the model are in good agreement with the analytical velocity profiles under the same input conditions. Numerical results show that higher wave height would generally generate larger vertical eddy viscosity and lower horizontal velocity. The results for fresh water in Yellow River Delta show that the wave-induced vertical mixing increases the momentum of fresh water transferring ability downwards to seabed and salt water＇s mixing with upper fresh water. Fresh water flume length is compressed considerably.

SALT-FINGERING OF POLLUTANT VERTICAL MIXING IN STATIC THERMAL-STRATIFIED WATER

Pollutant vertical mixing in stratified waters is a key factor that affects the vertical pollutant distribution in deep thermal-stratified reservoirs. This article presents an experimental study of the vertical mixing in thermal-stratified waters and an analysis of the retarded tracer jet diffusion in the thermocline layer. In the experiment, Reynolds number rapidly decreases from 104 to 10I. The stronger the stratification, the more seriously retarded the mixing will be. Some small tracer blobs may penetrate the thermocline layer into the hypolimnion layer even the main tracer cloud is retarded. According to its appearance, it can remain with salt-fingering, where the blobs are isolated away from the main cloud and mixed with the surround cold water in the hypolimnion layer. Therefore, the vertical distribution of the tracer under the thermocline layer would take larger values than expected. According to measurements, the isolated blob contents are accounted for about 5%-20% of the main tracer cloud, and are decreased with the increase of the stratification intensity. Results also show that the stronger the stratification, the smaller finger width would be. The averaged width of the incipient fingers is proportional to -0.3272 of the thermal Rayleigh number, Rat, in the turbulent jet fluid. power of the temperature gradient, AT/Az, or - 0.2823 power

Distribution of Vertical Turbulent Mixing Parameter Caused by Internal Tidal Waves and Solitary Waves in the South Yellow Sea

Many observations show that in the Yellow Sea internal tidal waves (ITWs) possess the remarkable characteristics of internal Kelvin wave, and in the South Yellow Sea (SYS) the nonlinear evolution of internal tidal waves is one of the mechanisms producing internal solitary waves (ISWs), which is different from the generation mechanism in the case where the semidiurnal tidal current flows over topographic drops. In this paper, the model of internal Kelvin wave with continuous stratification is given, and an elementary numerical study of nonlinear evolution of ITWs is made for the SYS, using the generalized KdV model (GKdV model for short) for a continuous stratified ocean, in which the different effects of background barotropic ebb and flood currents are considered. Moreover, the parameterization of vertical turbulent mixing caused by ITWs and ISWs in the SYS is studied, using a parameterization scheme which was applied to numerical experiments on the breaking of ISWs by Vlasenko and Hutter in 2002. It is found that the vertical turbulent mixing caused by internal waves is very strong within the upper layer with depth less than about 30m, and the vertical turbulent mixing caused by ISWs is stronger than that by ITWs.

The effect of the wave-induced mixing on the upper ocean temperature in a climate model

The significant underestimation of sea surface temperature （SST） and the temperature in the upper ocean is one of common problems in present climate models. The influence of the wave-induced mixing on SST and the temperature in the upper ocean was examined based on a global climate model. The results from the model coupled with wave-induced mixing showed a significant improvement in the simulation of SST and the temperature in the upper ocean compared with those of the original model without wave effects. Although there has still a cold bias, the new simulation is much closer to the climatology, especially in the northern ocean and tropical ocean. This study indicates that some important physical processes in the accurate simulation of the ocean may be ignored in present climate models, and the wave-induced mixing is one of those factors. Thus, the wave-induced mixing （ or the effect of surface waves） should be incorporated properly into climate models in order to simulate or forecast the ocean, then climate system, more accurately.

Observations and Simulations of the Circulation and Mixing around the Andaman-Nicobar Submarine Ridge

Using data collected by an Acoustic Doppler Current Profiler （ADCP） on a research cruise in April 2010 in the eastern Indian Ocean, the vertical cun＇ent structures surrounding the Andaman-Nicobar Submarine Ridge （ANSR） are analyzed to investigate the hydrographic responses to the topography in this region. The results show that the topography of ANSR can induce internal waves around the submarine ridge that have a maximum current velocity of 1 m s 1 The spatial struc- ture of the turbulent kinetic energy （TKE） and shear in this region during 2010 is investigated using the high-resolution Princeton Ocean Model （POM） forced by the satellite-based Advanced Scatterometer （ASCAT） winds including the tide, The results show that the model successfully simulates the internal waves around the ANSR. Numerical experiments further indicate that both the topography and tide play an important role in the gen- eration of the internal waves in this region.

Can Langmuir Circulations Solve the Problem of Insufficient Upper-Ocean Mixing?

Insufficient vertical mixing in the upper ocean during summer is a common problem of oceanic circulation and climate models.The turbulence associated with non-breaking waves is widely believed to effectively solve this problem.In many studies,non-breaking surface wave processes are attributed to the effects of Langmuir circulations(LCs).In the present work,the influences of LCs on the upper-ocean thermal structure are examined by using one-and three-dimensional ocean circulation,as well as climate,models.The results indicated that the effect of vertical mixing enhanced by LCs is limited to the upper ocean.The models evaluated,including those considering LC effects alone and the combined effects of LCs and wave breaking,failed to produce a reasonable summertime thermocline,resulting in a large cold bias in the subsurface layer.Therefore,while they can slightly reduce the biases of mixed layer depths and sea surface temperatures in models,LCs are insufficient to solve the problem of insufficient vertical mixing.Moreover,restriction of non-breaking surface wave-induced processes in LCs may be questionable.

The Contribution of Waves in Mixing Processes of the Patos Lagoon Plume

The analysis of wave effects above salinity is important in order to define mixing processes and their potential to change density gradients, since action in the region of the Patos Lagoon plume is highly dynamic. This paper aims to evaluate the influence of waves on the mixing pattern of the adjacent continental shelf. Constantly marked by tides and circulation variations, changing from flood to ebb tide, salinity stands as a major parameter for analysis. The study is based on hydrodynamic numerical modeling experiments using the TELEMAC3D model and waves generated by the wind using the TOMAWAC coupled model. The comparison between the situations considering the waves generated by the wind and without waves was made through time series analysis, stratification series, transversal cross sections, longitudinal cross sections, salinity mean fields and diagrams by Richardson and Brünt-V?is?l?s frequency parameters. With the cross sections analysis, the mixing effect generated by the waves was observed, demonstrating clearly that the waves were capable of raising the superficial salinity in regions far from the Patos Lagoon entrance, while at the entrance, the wave effects enhanced the mixing on the deepest layers, decreasing the saline intrusion and expanding the plume more radially on the surface. The space-temporal diagrams were effective to demonstrate the modulation effect of the waves over the salt mixing of saline waters, revealing that wave effects decrease the stratification as well as the Brünt-V?is?l?s frequency and increase the period of buoyancy, due to the mixing increase.

Typhoon-Induced Ocean Waves and Stokes Drift:A Case Study of Typhoon Mangkhut(2018)

Ocean waves and Stokes drift are generated by typhoons.This study investigated the characteristics of ocean waves and wave-induced Stokes drift and their effects during Typhoon Mangkhut using European Centre for MediumRange Weather Forecasts(ECMWF)ERA5 datasets and observational data.The results revealed that the typhoon generated intense cyclones and huge typhoon waves with a maximum wind speed of 45 m/s,a minimum pressure of955 h Pa,and a maximum significant wave height of 12 m.The Stokes drift caused by typhoon waves exceeded 0.6m/s,the Stokes depth scale exceeded 18 m,and the maximum Stokes transport reached 6 m^(2)/s.The spatial distribution of 10-m wind speed,typhoon wave height,Stokes drift,Stokes depth,and Stokes transport during the typhoon was highly correlated with the typhoon track.The distribution along the typhoon track showed significant zonal asymmetry,with greater intensity on the right side of the typhoon track than on the left side.These findings provide important insights into the impact of typhoons on ocean waves and Stokes drift,thus improving our understanding of the interactions between typhoons and the ocean environment.This study also investigated the contribution of Stokes transport to the total net transport during typhoons using Ekman-Stokes Numbers as a comparative measure.The results indicated that the ratio of Stokes transport to the total net transport reached up to 50%within the typhoon radius,while it was approximately 30%outside the radius.Strong Stokes transport induced by typhoon waves led to divergence in the transport direction,which resulted in upwelling of the lower ocean as a compensation current.Thus,Stokes transport played a crucial role in the vertical mixing of the ocean during typhoons.The findings suggested that Stokes transport should be paid more attention to,particularly in high latitude ocean regions,where strong winds can amplify its effects.

The Suspended Sediment Concentration Distribution in the Bohai Sea,Yellow Sea and East China Sea

The distribution of the suspended sediment concentration （SSC） in the Bohai Sea, Yellow Sea and East China Sea （BYECS） is studied based on the observed turbidity data and model simulation results. The observed turbidity results show that （i） the highest SSC is found in the coastal areas while in the outer shelf sea areas turbid water is much more difficult to observe, （ii） the surface layer SSC is much lower than the bottom layer SSC and （iii） the winter SSC is higher than the summer SSC. The Regional Ocean Modeling System （ROMS） is used to simulate the SSC distribution in the BYECS. A comparison between the modeled SSC and the observed SSC in the BYECS shows that the modeled SSC can reproduce the principal features of tlte SSC distribution in the BYECS. The dynamic mechanisms of the sediment erosion and transport processes are studied based on the modeled results. The horizontal distribution of the SSC in the BYECS is mainly determined by the current-wave induced bottom stress and the fine-grain sediment distribution. The current-induced bottom stress is much higher than the wave-induced bottom stress, which means the tidal currents play a more significant role in the sediment resuspension than the wind waves. The vertical mixing strength is studied based on the mixed layer depth and the turbulent kinetic energy distribution in the BYECS. The strong winter time vertical mixing, which is mainly caused by the strong wind stress and surface cooling, leads to high surface layer SSC in winter. High surface layer SSC in summer is restricted in the coastal areas.

A study of the mixed layer of the South China Sea based on the multiple linear regression

Multiple linear regression （MLR） method was applied to quantify the effects of the net heat flux （NHF）, the net freshwater flux （NFF） and the wind stress on the mixed layer depth （MLD） of the South China Sea （SCS） based on the simple ocean data assimilation （SODA） dataset. The spatio-temporal distributions of the MLD, the buoyancy flux （combining the NHF and the NFF） and the wind stress of the SCS were presented. Then using an oceanic vertical mixing model, the MLD after a certain time under the same initial conditions but various pairs of boundary conditions （the three factors） was simulated. Applying the MLR method to the results, regression equations which modeling the relationship between the simulated MLD and the three factors were calculated. The equations indicate that when the NHF was negative, it was the primary driver of the mixed layer deepening; and when the NHF was positive, the wind stress played a more important role than that of the NHF while the NFF had the least effect. When the NHF was positive, the relative quantitative effects of the wind stress, the NHF, and the NFF were about i0, 6 and 2. The above conclusions were applied to explaining the spatio-temporal distributions of the MLD in the SCS and thus proved to be valid.

Unveiling controls of the latitudinal gradient of surface pCO_(2) in the Kuroshio Extension and its recirculation regions(northwestern North Pacific)in late spring

In the northwestern North Pacific,annual net air-sea CO_(2) flux is greatest in the Kuroshio Extension(KE)zone,owing to its low annual mean partial pressure of CO_(2)(pCO_(2)),and it decreases southward across the basin.To quantify the influences of factors controlling the latitudinal gradient in CO_(2) uptake,sea surface pCO_(2) and related parameters were investigated in late spring of 2018 in a study spanning the KE,Kuroshio Recirculation(KR),and subtropical zones.We found that the sea-to-air pCO_(2) difference(ΔpCO_(2))was negative and at its lowest in the KE zone.ΔpCO_(2) gradually increased southward across the KR zone,and the sea surface was nearly in air-equilibrium with atmospheric CO_(2) in the subtropical zone.We found that northward cooling and vertical mixing were the two major processes governing the latitudinal gradient in surface pCO_(2) and ΔpCO_(2),while biological influences were relatively minor.In the KE zone affected by upwelling,the vertical-mixing-induced increase in surface pCO_(2) likely canceled out approximately 61%of the decrease in surface pCO_(2) caused by cooling and biological activities.Moreover,the prolonged air-sea equilibration for CO_(2) and relatively short hydraulic retention time jointly led to the low surface pCO_(2) in the KE zone in spring.Ultimately,the cooling KE current flows out of the region before it can be re-equilibrated with atmospheric CO_(2).

A comparison of two global ocean-ice coupled models with different horizontal resolutions

A global eddy-permitting ocean-ice coupled model with a horizontal resolution of 0.25° by 0.25° is estab- lished on the basis of Modular Ocean Model version 4 （MOM4） and Sea Ice Simulator （SIS）. Simulation results are compared with those of an intermediate resolution ocean-ice coupled model with a horizontal resolution of about 1° by 1°. The results show that the simulated ocean temperature, ocean current and sea ice concentration from the eddy-permitting model are better than those from the intermediate resolu- tion model. However, both the two models have the common problem of ocean general circulation models （OGCMs） that the majority of the simulated summer sea surface temperature （SST） is too warm while the majority of the simulated subsurface summer temperature is too cold. Further numerical experiments show that this problem can be alleviated by incorporating the non-breaking surface wave-induced vertical mixing into the vertical mixing scheme for both eddy-permitting and intermediate resolution models.

The westward intrusion of south Pacific water at the western tip of the New Guinea Island

From the eastern Indonesian cruise from November 14 to 23, 2007, CTD （conductivity, temperature, depth profiler）/ADCP （acoustic Doppler current profiler）casting and seawater sampling were done at 25 stations around Waigeo Island near New Guinea Island. It was found overall westward intrusion of the south Pacific waters into the Seram Sea and southward spreading of the north and south Pacific waters into the Seram Sea. There is westward residual flow along the channel between Waigeo and New Guinea within upper 200 m with the maximum speed up to 50 cm/s, and much weaker eastward flow in the lower layer （〈 10 cm/s） due to blocking by the shallow sill at the west of the Dampier Strait. The abrupt change of bottom topography induces active horizontal and vertical mixing which results in a three-layered current system with a major through-flow of-0.99 Sv （Sv = 106 ma/s） into the Seram Sea; the transports in the upper and the lower layers are -1.14 Sv and -0.24 Sv （westward）, respectively, and in the middle there is a return flow with the transoort of ＋0.39 Sv （eastward）.

A climatic dataset of ocean vertical turbulent mixing coefficient based on real energy sources

Using data on wind stress, significant height of combined wind waves and swell, potential temperature, salinity and seawater velocity, as well as objectively-analyzed in situ temperature and salinity, we established a global ocean dataset of calculated wind- and tide-induced vertical turbulent mixing coefficients. We then examined energy conservation of ocean vertical mixing from the point of view of ocean wind energy inputs, gravitational potential energy change due to mixing(with and without artificially limiting themixing coefficient), and K-theory vertical turbulent parameterization schemes regardless of energy inputs. Our research showed that calculating the mixing coefficient with average data and artificial limiting the mixing coefficient can cause a remarkable lack of energy conservation, with energy losses of up to 90% and changes in the energy oscillation period. The data also show that wind can introduce a huge amount of energy into the upper layers of the Southern Ocean, and that tidesdo so in regions around underwater mountains. We argue that it is necessary to take wind and tidal energy inputs into account forlong-term ocean climate numerical simulations. We believe that using this ocean vertical turbulent mixing coefficient climatic dataset is a fast and efficient method to maintain the ocean energy balance in ocean modeling research.

Three-dimensional mixed convection squeezing flow

The unsteady mixed convection squeezing flow of an incompressible Newtonian fluid between two vertical parallel planes is discussed. The fluid is electrically conducting. The governing equations are transformed into ordinary differential equations （ODEs） by appropriate transformations. The transformed equations are solved successfully by a modern and powerful technique. The effects of the emerging parameters on the flow and heat transfer characteristics are studied and examined. The values of the skin friction coefficient and the local Nusselt number are tabulated and analyzed.

Characteristics and Mechanisms of the Sudden Warming Events in the Nocturnal Atmospheric Boundary Layer:A Case Study Using WRF

Although sudden nocturnal warming events near the earth＇s surface in Australia and the United States have been examined in previous studies, similar events observed occasionally over the Loess Plateau of Northwest China have not yet been investigated. The factors that lead to these warming events in such areas with their unique topography and climate remain not clear. To understand the formation mechanisms and associated thermal and dynamical features, a nocturnal warming event recorded in Gansu Province （northwest of the Loess Plateau） in June 2007 was investigated by using observations and model simulations with the Weather Research and Forecasting （WRF） model. Observations showed that this near-surface warming event lasted for 4 h and the temperature increased by 2.5℃. During this event, a decrease in humidity occurred simultaneously with the increase of temperature. The model simulation showed that the nocturnal warming was caused mainly by the transport of warmer and drier air aloft downward to the surface through enhanced vertical mixing. Wind shear played an important role in inducing the elevated vertical mixing, and it was enhanced by the continuous development of the atmospheric baroclinicity, which converted more potential energy to kinetic energy.