Dynamic Response of Sea-Crossing Rail-cum-Road Cable-Stayed Bridge Influenced by Random Wind–Wave–Undercurrent Coupling

Sea-crossing bridges are affected by random wind–wave–undercurrent coupling loads, due to the complex marine environment. The dynamic response of long-span Rail-cum-Road cable-stayed bridges is particularly severe under their influence, potentially leading to safety problems. In this paper, a fluid–structure separation solution method is implemented using Ansys–Midas co-simulation, in order to solve the above issues effectively while using less computational resources. The feasibility of the method is verified by comparing the tower top displacement response with relevant experimental data. From time and frequency domain perspectives, the displacement and acceleration responses of the sea-crossing Rail-cum-Road cable-stayed bridge influenced by wave-only, wind–wave, and wind–wave–undercurrent coupling are comparatively studied. The results indicate that the displacement and acceleration of the front bearing platform top are more significant than those of the rear bearing platform. The dominant frequency under wind–wave–undercurrent coupling is close to the natural vibration frequencies of several bridge modes,such that wind–wave–undercurrent coupling is more likely to cause a resonance effect in the bridge. Compared with the wave-only and wind–wave coupling, wind–wave–undercurrent coupling can excite bridges to produce larger displacement and acceleration responses: at the middle of the main girder span, compared with the wave-only case, the maximum displacement in the transverse bridge direction increases by 23.58% and 46.95% in the wind–wave and wind–wave–undercurrent coupling cases, respectively;at the tower top, the variation in the amplitude of the displacement and acceleration responses of wind–wave and wind–wave–undercurrent coupling are larger than those in the wave-only case, where the acceleration change amplitude of the tower top is from-0.93 to 0.86 m/s^(2) in the waveonly case, from-2.2 to 2.1 m/s^(2) under wind–wave coupling effect, and from-2.6 to 2.65 m/s^(2) under wind–wave–undercurrent coupling effect, indicating that the tower top is mainly affected by wind loads, but wave and undercurrent loads cannot be neglected.

Study on the Floating Plant Climatic Adaptation of Undercurrent Constructed Wetland in North China

[Objective] The aim was to choose appropriate floating plant in the wetland in the north China.[Method] Pistia stratiotes L.,Eichhornia crassipes,and Hydrocharis dubia（Bl.） Backer were planted in the aquatic biological pool of constructed subsurface flow wetland system in the reservoir.Through filed investigation,the growth of the three kinds of plants was studied and their adaptability to the northern climate was concluded.[Result] Judging from the growth speed and state of the three kinds of floating plants,the biological characteristic of Pistia stratiotes L.can perfectly adapt the environment in the pool in the reservoir,followed by the Eichhornia crassipes.The growth state of the Hydrocharis dubia（Bl.） Backer was the worst one and it can not adapt to the north environment.[Conclusion] It provided references for the choice of artificial floating plant in the north area.

Examination of seasonal variation of the equatorial undercurrent termination in the Eastern Pacifi c diagnosed by ECCO2

Seasonal variations of the equatorial undercurrent(EUC) termination in the Eastern Pacific,and their mechanism were examined using the Estimating the Circulation and Climate of the Ocean,PhaseⅡ(ECCO2).The ECCO2 reproduced a weak and shallow eastward EUC east of the Galapagos Islands,with annual mean transport of half of EUC to the west of the Islands.The diagnosis of zonal momentum equation suggests that the zonal advection(nonlinear terms) drives the EUC beyond the Islands rather than the pressure gradient force.The EUC in the Far Eastern Pacific has the large st core velocity in boreal spring and the smallest one in boreal summer,and its volume transport exhibits two maxima in boreal spring and autumn.The seasonal variability of the EUC in the Eastern Pacific is dominated by the Kelvin and Rossby waves excited by the zonal winds anomalies in the central and Eastern Pacific that are associated with the seasonal relaxation or intensification of the trade wind.In the Far Eastern Pacific to the east of 120°W,the eastward propagation Kelvin waves play a dominate role in the seasonal cycle of the EUC,results in a semiannual fluctuation with double peaks in boreal spring and autumn.A construction of water mass budget suggests that approximately 24.1% of the EUC water east of 100°W has upwelled to the mixed layer by0.35 m/d.The estimated upwelling is stronge st during boreal autumn and weake st during boreal winter.It is also found that approximately 42.6% of the EUC turns westward to feed the south equatorial current(SEC),13.2% flows north of the equator,and 20.1% flows south of the equator,mainly contributing to Peru-Chile undercurrent.

Variational iteration method for solving perturbed mechanism of western boundary undercurrents in the Pacific

A class of perturbed mechanisms for the western boundary undercurrents in the Pacific is considered. The model of generalized governing equations is studied. Employing the method of variational iteration, an approximate solution of corresponding model is obtained. It is proved from the results that the solution for the variational iteration method can be used for analysing operation of the perturbed mechanism of western boundary undercurrents in the Pacific.

PRELIMINARY STUDY ON THE FORMATION MECHANISM OF COUNTER WESTERN BOUNDARY UNDERCURRENTS BELOW THE THERMOCLINE——A CONCEPTUAL MODEL

Based on a simple conceptual model of stratified ocean, the criterion of the geostrophic velocity inversion in and below the thermocline was derived as h ′·η′<0 and ρ 1|η′|≤Δρ| h ′|, meaning that the slopes of the thermocline( h ′) and the sea surface(η′) must be opposite to each other, and that h ′ must be strong enough to satisfy the latter inequality. The criterion was applied to discuss the features of the western boundary undercurrents, the counter undercurrents of the western boundary currents below the thermocline, and to discuss the dynamics of their formation finally resulting from the combination of the basin scale circulation and local geostrophic balance. The formation mechanism, multi core structure, and transport variations of the Mindanao Undercurrent and those of other undercurrents, such as the North Equatorial Undercurrent and the Kuroshio undercurrent, can be satisfactorily explained by the above results.

The seasonal variation of undercurrent and temperature in the equatorial Pacific jointly derived from buoy measurement and assimilation analysis

Based on the TOGA-TAO buoy chain observed data in the equatorial Pacific and the assimilation analysis results from SODA(simple ocean data assimilation analysis), the role of the meridional cells in the subsurface of the tropical Pacific was discussed. It was found that, the seasonal varying direction of EUC(the quatorial Undercurrent)in the Peacific is westwards beginning from the eastern equatorial Pacific in the boreal spring. The meridional cell south of the equator plays important role on this seasonal change of EUC.On the other hand, although the varying direction is westwards, the seasonal variation of temperature in the same region gets its minimum values in the boreal autumn beginning from the eastern equatorial Pacific.The meridional cell north of the equator is most responsible for the seasonal temperature variation in the eastern equatorial Pacific while the meridional cell south of the equator mainly controls the seasonal temperature change in the central Pacific. It is probably true that the asymmetry by the equator is an important factor influencing the seasonal cycle of EUC and temperature in the tropical Pacific.

Climatology and seasonal variability of the Mindanao Undercurrent based on OFES data

The simulation of an ocean general circulation model for the earth simulator （OFES） is transformed to an isopycnal coordinate to investigate the spatial structure and seasonal variability of the Mindanao Under- current （MUC）. The results show that （1） potential density surfaces, δ0=26.5 and δ0=27.5, can be chosen to encompass the M UC layer. Southern Pacilic tropical water （SPTW）, Antarctic Intermediate Water （AAIW） and high potential density water （HPDW） constitute the MUC. （2） Climatologically, the MOC exists in the form of dual-core. In some months, the dual-core structure changes to a single-core structure. （3） Choosing section at 8°N for calculating the transport of the MUC transport is reliable. Potential density constraint provides a good method for calculating the transport of the MOC. （4） The annual mean transport of the MUC is 8.34 × 106 m3/s and varies considerably with seasons： stronger in late spring and weaker in winter.

Homotopic Mapping Solving Method for Perturbed Mechanism of Western Boundary Undercurrents in Equator Pacific

The perturbed boundary undercurrent is an exceptional event in the tropical atmosphere and ocean. It is a complicated nonlinear system. Its appearance badly affects not only natural conditions such as climate and environment, but also global economic development and human living, and brings about many calamities. Thus there is very attractive study on its rules in the international academic circles. Many scholars made more studies on its local and whole behaviors using different methods, such as self-anamnestic principle, Fokker-Plank Equation method, higher order singular pedigree and predictable study, rapid change on boundary, indeterminate adaptive control, multi-eogradient method and so on. Nonlinear perturbed theory and approximate method are very attractive studies in the international academic circles. Many scholars considered a class of nonlinear problems for the ordinary differential equation, the reaction diffusion equations, the boundary value of elliptic equation, the initial boundary value of hyperbolic equation, the shock layer solution of nonlinear equation and so on. In this paper, a class of perturbed mechanism for the western boundary undercurrents in the equator Pacific is considered. Under suitable conditions, using a homotopic mapping theory and method, we obtain a simple and rapid arbitrary order approximate solution for the corresponding nonlinear system. For example, a special case shows that using the homotopic mapping method, there is a high accuracy for the computed value. It is also provided from the results that the solution for homotopic mapping solving method can be used for analyzing operator for perturbed mechanism of western boundary undercurrents in the equator Pacific.

Asymptotic solution for a perturbed mechanism of western boundary undercurrents in the Pacific

This paper consider a class of perturbed mechanism for the western boundary undercurrents in the Pacific. The model of generalized governing equations is studied. Using the perturbation method, it constructs the asymptotic solution of the model. And the accuracy of asymptotic solution is proved by the theory of differential inequalities. Thus the uniformly valid asymptotic expansions of the solution are obtained.

Subthermocline anticyclonic gyre east of Mindanao and its relationship with the Mindanao Undercurrent

The quasi-permanent anticyclonic gyre （ACG） east of Mindanao is a dominant feature of the subthermocline circulation in the southem Philippine Sea, and it is believed closely associated with the continuous northward alongshore flow of the Mindanao Undercurrent （MUC）. In this study, the structure and variability of this ACG were investigated using the 1950-2012 output of the Oceanic General Circulation Model for the Earth Simulator （OFES）, which can reproduce well the structure of the climatological intermediate-layer circulation and satellite-observed sea level variations in the southern Philippine Sea. Between 26.8-27.3 ao, the ACG covers a large area from the Mindanao coast to 131 ~E and from 3~N to 10~N. Its anticyclonic flow structure is unrelated to the surface Halmahera Eddy. The eddy-resolving simulation of the OFES revealed that the ACG consists of two components. The southern ACG （SACG） is centered at -6~N, while the northern ACG （NACG） is centered at -10~N. Seasonal and interannual variations of the ACG are linked to the variations of the northward MUC transport along the Mindanao coast, and the role of the SACG is more important than the NACG. Stronger （weaker） ACGs lead to greater （smaller） MUC transport. On the interannual timescale, the SACG shows a spectrum peak at 4-8 years, while the NACG has enhanced power within the 3-5-year band. A lead-lag correlation analysis indicates that interannual variations of the ACGs and the MUC transport are partly associated with the E1 Nifio-Southern Oscillation. Possible causes for the ACG variability are discussed.

Relationship between a function of the northward pressure gradient and the Pacific Equatorial Undercurrent

The Equatorial Undercurrent（EUC） plays an important role in ocean circulation and global climate change. Near the equator, as the Coriolis parameter goes to 0, equatorial currents cannot be described by geostrophy in which the pressure gradient force term is balanced by the Coriolis force term. Many previous studies focus on the relationships between the EUC and El Ni？o-Southern Oscillation（ENSO）, the thermocline, sea surface topography, the distribution of equatorial wind stress and other atmosphere-ocean factors. However, little attention has been paid to the northward pressure gradient（NGT）, which may also be important to the EUC. The pressure can be regarded as a complex nonlinear function of terms including temperature, salinity and density.This study attempts to reveal the connection between a function of the northward pressure gradient（FNP） and the EUC. The connection is derived from primitive equations, by simplifying the equations with using scaling analysis, and shows that the beta effect may be the main reason why the FNP is important to the EUC. The vertical structure of the EUC can be partially described by the FNP. The NGT has an obvious influence on the EUC while the eastward pressure gradient has a relatively smaller effect.

The North Equatorial Current/Undercurrent volume transport and its 40-day variability from a mooring array along 130°E

Traditionally,the estimated volume transport of the North Equatorial Current/Undercurrent(NEC/NEUC)is based on geostrophic equations and/or model results;however,direct observational evidence has not been acquired.We focused on one-year mooring observation data collected along 130°E and calculated the NEC/NEUC volume transport and explore its variability.Results show that the mean NEC and NEUC volume transports calculated from the mean velocity structures in the upper 950 m are 39 Sv and 6 Sv,respectively.Analysis of daily mooring data indicated that the volume transport of the NEC is approximately 52(±14)Sv and the volume transport of the NEUC is approximately 18(±13)Sv.A significant 40-day variation existed for the volume transport of both the NEC and NEUC.Overall,the intraseasonal variability of the NEC is vertically coherent with that of the NEUC.Observations indicated that the NEUC has three cores centered at approximately 8.5°N(~500 m),12.5°N(~700 m),and 17.5°N(~900 m),of which the middle core(12.5°N)is the strongest.The 40-day variability of the NEC and NEUC is related to the variability of local wind stress curl anomalies among various Madden-Julian Oscillation phases.When local wind field generates a negative(positive)wind stress curl anomaly,a weaker NEC(NEUC)and stronger NEUC(NEC)would occur.

The inversion of the Equatorial Undercurrent in the western tropical Pacific during 1986/1987 El Nino event

On the basis of time series measurements of winds, currents, temperature and salinity from equatorial current meter mooring and acoustic Doppler current profiler during the PRC/USA joint air-sea interaction studies in the western tropical Pacifc Ocean and sea level data provided by Prof. Wyrtki, analyses are made of the physical process and mechanism for the exceptionally inverse phenomenon (westward) of the Equatorial Undercurrent (EUC) in the western tropical Pacific after entering the mature stage of 1986/1987 ENSO event, and the numerical simulation is also conducted by 'cross section' model. The results indicate that the inversion of the EUC is related to that of pressure gradient force near the equator under the influence of non-local permanent westerlies.

DYNAMIC AND THERMOHALINE PROPERTIES OF THE MINDANAO UNDERCURRENT Ⅰ. DYNAMIC STRUCTURE

Hydrographic data from eleven 1986-1991 cruises at zonal sections near 8°N from the Philippine coast to 130°E were used to examine the dynamic structure of the western boundary currents there in the present study focusing on the Mindanao Undercurrent (MUC).The MUC with maximum velocity >10 cm/ was found to be a feature of both the individual cruises and multiyear mean velocity field as a countercurrent below the Mindanao Current (MC). Usually, the MUC occupies depths below 200 dbar and consists of more than one core.Its vertical and horizontal scales are 500 - 1000 m and 100-250 km, respectively , and vary greatly and irregularly . The spatial distribution of the MUC agreed with that of the westward deepening isopycnals in and below the thermocline . In the individual cruises , the volume transports of the MUC relative to 1500 dbar varied from 6.2 to 28.4×106m3 (average of 14.4× 10 6m3/s) while those relative to 3000 dbar varied from 15.4 to 43.9 ×106 m3/s (average of 25.4 ×106 m3/s ). The multiyear mean MUC transport was 5.9×106 m3/s relative to 1500 dbar and 8.7 × 106m3/s relative t0 3000 dbar . The difference between the multiyear mean MUC transport and that of individual cruises resulted from the MUC spatial variation .

DYNAMIC AND THERMOHALINE PROPERTIES OF THE MINDANAO UNDERCURRENT,PART Ⅱ: THERMOHALINE STRUCTURE

Hydrographic data from eleven 1986 - 1991 cruises at zonal sections near 8°N from the Philippine coast to 130°E were used to examine thermohaline smictim and waer mass properties of the western boundary cnrrents there, especially those of the Mindanao Underconnt (MUC). The finding that the MLC consisted of two water masses with salinity of M.6 at 26.9 σt and 34.52 at 27. 2 σt which were remnants of the lower part of the southern Pacific Subtropical Waer (SPSW) and of the Antarctic Intermediate Water (AAIW) of South Pacific origin, respectively, showed that the MUC was not a local transient but originaed elsewhere. As the MUC flowed from 7 .5°N to 8°N, part of it carrying the SPSW turns anticyclonically and eastward. The Northem Pacilic Intermediate Watr (NPIW) often joins the MUC, which suggests that the NPIW carried by the MC partly to northward as a result of the shear between the MC and the MUC or other proceesses. The shear instability provides the energy for the irregular fluctuation of the MUC.

The relation between the Mindanao Current and Mindanao Undercurrent on seasonal scale

The ocean general circulation model for the earth simulator（OFES） products is applied to estimate the transports of the Mindanao Current（MC） and the Mindanao undercurrent（MUC） and explore the relation between them on seasonal scale. In general, the MUC is composed of the lower part of the Southern Pacific Tropical Water（SPTW）and Antarctic Intermediate Water（AAIW）. While the deep northward core below 1 500 m is regarded as a portion of MUC. Both salinity and potential density restrictions become more reasonable to estimate the transports of MC/MUC as the properties of water mass having been taken into consideration. The climatological annual mean transport of MC is（37.4±5.81）×10~6 m^3/s while that of MUC is（23.92±6.47）×10~6 m^3/s integrated between 26.5 σ_θ and 27.7 σ_θ, and（17.53±5.45）×10~6 m^3/s integrated between 26.5 σ_θ and 27.5 σ_θ in the OFES. The variations of MC and MUC have good positive correlation with each other on the seasonal scale： The MC is stronger in spring and weaker in fall, which corresponds well with the MUC, and the correlation coefficient of them is 0.67 in the OFES.The same variations are also appeared in hybrid coordinate ocean model（HYCOM） results. Two sensitive experiments based on HYCOM are conducted to explore the relation between MC and MUC. The MUC（26.5〈σ_θ〈27.7） is strengthening as the MC increases with the enhancement of zonal wind field. It is shown,however, that the main part of the increasement is the deeper northward high potential density water（HPDW）,while the AAIW almost remains stable, SPTW decreases, and vice versa.

Persistent mixing bursts in the equatorial Pacific thermocline induced by persistent equatorial waves

A recent study by Liu et al.(2020)suggested that due to the saturation of equatorially trapped planetary waves with different dynamical types,temporal periods,meridional and baroclinic modes,complex layer structures of vertical velocity shear and hence turbulent mixing could frequently occur in the thermocline of the eastern equatorial Pacific.We investigated the occurrence of the interior turbulent mixing as indicated by shear instabilities,above the Equatorial Undercurrent(EUC)core at three equatorial sites along 140°W,170°W,and 165°E,respectively,based mainly on data from the Tropical Atmosphere and Ocean(TAO)mooring array.We found that turbulent mixing bursts persisted in the thermocline of all three sites.Specifically,the interior turbulent mixing layers(ITMLs)could occur in probability of approximately 68%,53%,and 48%at the three sites,respectively.The overall occurrence probability shows obvious and similar biannual variations at 140°W and 170°W,which is higher in boreal from late summer to winter and lower in spring.Vertically,the ITMLs are primarily located above the EUC core and prevail in deeper(shallower)layers from late summer to winter(spring).Most ITMLs(70%)lasted for hours to 3 days,and a few of them(15%)for more than 7 days.The thicknesses of ITMLs were concentrated between 15 and 55 m.At 165°E,the vertical distribution of ITML occurrence probability was different from that at 140°W and 170°W,as it did not show a preference for depths;the durations of ITMLs are short(also from hours to several days)and their thicknesses were between 5 and 25 m.These properties,particularly the high occurrence probability,and short durations demonstrated the persistence of thermocline mixing in the western to eastern equatorial Pacific thermocline and confirmed the generation mechanism by persistent equatorial waves as well.

A quasi-synoptic interpretation of water mass distribution and circulation in the western North Pacific II:Circulation

Using the data of conductivity-temperature-depth （CTD） intensive observations conducted during Oct-Nov. 2005, this study provides the first three-dimension quasi-synoptic description of the circulation in the western North Pacific. Several novel phenomena are revealed, especially in the deep ocean where earlier observations were very sparse. During the observations, the North Equatorial Current （NEC） splits at about 12°N near the sea surface. This bifurcation shifts northward with depth, reaching about 20°N at 1 000 m, and then remains nearly unchanged to as deep as 2 000 m. The Luzon Undercurrent （LUC）, emerging below the Kuroshio from about 21°N, intensifies southward, with its upper boundary surfacing around 12°N. From there, part of the LUC separates from the coast, while the rest continues southward to join the Mindanao Current （MC）. The MC extends to 2 000 m near the coast, and appears to be closely related to the subsurface cyclonic eddies which overlap low-salinity water from the North Pacific. The Mindanao Undercurrent （MUC）, carrying waters from the South Pacific, shifts eastward upon approaching the Mindanao coast and eventually becomes part of the eastward undercurrent between 10°N and 12°N at 130°E. In the upper 2 000 dbar, the total westward transport across 130°E between 7.5°N and 18°N reaches 65.4 Sv （1 Sv = 10-6 m3s^-1）, the northward transport across 18°N from Luzon coast to 130°E is up to 35.0 Sv, and the southward transport across 7.5°N from Mindanao coast to 130°E is 27.9 Sv.

Performance of Subsurface Constructed Wetland in River Rehabilitation

[ Objective] This study was to research the treatment effect of different media in undercurrent wetland on contamination, so as to pro- vide reference for rehabitating water body of river along small towns. [ Method ] Three different media of gravel, cobblestone and shale were used to rehabilitate water quality of contaminated river. [ Result ] Gravel, cobblestone and shale all performed well in removing TN, TP and CODw,, in contaminated water, of which gravel stuffed undercurrent wetland run best, averagely removing 49.4% TN, 34.7% and 48. 5% COD~, respectively. [ Conclusion] Undercurrent constructed wetland can effectively improve the water quality of contaminated river, and it is cheaper in cost and simpler in operation, thus suitable for generalizing in small towns of China.

Analysis of Equatorial Currents Observed by Eastern Indian Ocean Cruises in 2010 and 2011

Hydrographic and direct current measurements were made in the Eastern Equatorial Indian Ocean in May 2010 and April 2011 as part of the Eastern Indian Ocean Cruises(EIOC) organized by the South China Sea Institute of Oceanology(SCSIO).Analyses of the shipdrift Acoustic Doppler Current Profiler(ADCP) data indicate that the equatorial currents observed in May 2010 are characterized by a strongly eastward surface current(Wyrtki Jets,WJs) with a maximum velocity of 0.9 m s 1,while that observed in April 2011 is weak and without a consistent direction.The strongly eastward WJ transports the surface water eastward,resulting in a deeper upper mixed layer,as shown in the temperature and salinity profiles.However,it was found that the Equatorial Undercurrent(EUC) in the Eastern Indian Ocean is strong in April 2011 and weak in May 2010.The EUC was located approximately at the position of the thermocline,and it had higher salinity(up to approximately 35.5 psu) than the upper and lower waters.