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.

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.

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.

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.

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）.

Structure and Temporal Variability of Mediterranean Water in Hydrological and Marine Seismic Data South of Portimao Canyon (Gulf of Cadiz), from 1999 to 2002

Hydrological and marine seismic data, collected in the Gulf of Cadiz (respectively in July 1999, 2000, 2001 and 2002, and in April 2000 and 2001) are analysed to reveal the various structures of Mediterranean Water (MW). Both the hydrological and seismic data clearly identify the MW undercurrents on the Iberian slope, detached MW eddies (meddies and a cyclone) and smaller fragments of MW (filaments and small eddies). Seismic reflectivity and synthetic reflectivity computed from hydrology, indicate that strong acoustic reflectors, associated with 8 - 64 m thick homogeneous water layers, are found above and below meddies and filaments, around the MW undercurrents, but mostly in the lower part of cyclones and below submesoscale eddies. Reflectors are also observed in the near surface layers where thermohaline contrasts are quite pronounced. The successful use of seismic data to locate submesoscale MW structures, superior to that of hydrology, is related to the improved horizontal resolution.