Comparative Analysis of the Generalized Omega Equation and Generalized Vertical Motion Equation

Research on vertical motion in mesoscale systems is an extraordinarily challenging effort.Allowing for fewer assumptions,a new form of generalized vertical motion equation and a generalized Omega equation are derived in the Cartesian coordinate system(nonhydrostatic equilibrium)and the isobaric coordinate system(hydrostatic equilibrium),respectively.The terms on the right-hand side of the equations,which comprise the Q vector,are composed of three factors:dynamic,thermodynamic,and mass.A heavy rain event that occurred from 18 to 19 July 2021 in southern Xinjiang was selected to analyze the characteristics of the diagnostic variable in the generalized vertical motion equation(Qz)and the diagnostic variable in the generalized Omega equation(Qp)using high-resolution model data.The results show that the horizontal distribution of the Qz-vector divergence at 5.5 km is roughly similar to the distribution of the Qp-vector divergence at 500 hPa,and that both relate well to the composite radar reflectivity,vertical motion,and hourly accumulated precipitation.The Qz-vector divergence is more effective in indicating weak precipitation.In vertical cross sections,regions with alternating positive and negative large values that match the precipitation are mainly concentrated in the middle levels for both forms of Q vectors.The temporal evolutions of vertically integrated Qz-vector divergence and Qp-vector divergence are generally similar.Both perform better than the classical quasigeostrophic Q vector and nongeostrophic Q vector in indicating the development of the precipitation system.

Effect of Working Position on Vertical Motion Straightness of Open Hydrostatic Guideways in Grinding Machine

Hydrostatic guideways have various applications in precision machine tools due to their high motion accuracy. The analysis of motion straightness in hydrostatic guideways is generally ignoring the external load on the slider. A variation force also exists, caused by the different working positions, together with the dead load of the slider and that of other auxiliary devices. The effect of working position on vertical motion straightness is investigated based on the equivalent static model, considering the error averaging effort of pressured oil film in open hydrostatic guideways. Open hydrostatic guideways in LGF1000 are analyzed with this approach. The theoretical results show that the slider has maximum vertical motion straightness when the working position is closer the guiderail of Y axis. The vertical motion straightness reaches a minimum value as the working position is located at the center of the two guiderails on the Y axis. The difference between the maximum and minimum vertical motion straightness is 34.7%. The smaller vertical motion straightness is attributed to the smaller spacing of the two pads centers, along the Y direction. The experimental results show that the vertical motion straightness is 4.15 μm/1200 mm, when the working position is located in the middle of the Xbeam, and 5.08 pro/1200 mm, when the working position is approaching the Y guiderails, denoting an increase of 18.3%. The changing trends of the measured results validate the correctness of the theoretical model. The research work can be used to reveal the variation law of accuracy of the open hydrostatic guideways, under different working positions, to predict the machining precision, and provides the basis for an error compensation strategy for gantry type grinding machines.

Sinusoidal Vertical Motion Suppression and Flow Noise Calculation for a Sonobuoy

The flow noise associated with sinusoidal vertical motion of a sonobuoy restrains its working performance.In practice,a suspension system consisting of elastic suspension cable and isolation mass is adopted to isolate the hydrophone from large vertical motions of the buoy on the ocean surface.In the present study,a theoretical model of vertical motion based on the sonobuoy suspension system was proposed.The vertical motion velocity response of the hydrophone of a sonobuoy can be obtained by solving the theoretical model with Runge-Kutta algorithm.The flow noise of the hydrophone at this response motion velocity was predicted using a hybrid computational fluid dynamics(CFD)-Ffowcs Williams-Hawkings(FW-H)technique.The simulation results revealed that adding the elastic suspension cable with an appropriate elastic constant and counterweight with an appropriate mass have a good effect on reducing the flow noise caused by the sonobuoy vertical motion.The validation of this hybrid computational method used for reliable prediction of flow noise was also carried out on the basis of experimental data and empirical formula.The finds of this study can supply the deep understandings of the relationships between flow noise reduction and sonobuoy optimization.

A Linear Diagnostic Equation for the Nonhydrostatic Vertical Motion W in Severe Storms

A linear diagnostic equation for the nonhydrostatic vertical motion W in severe storms is derived in the Cartesian-earth-spherical coordinates. This W diagnostic equation reveals explicitly how forcing factors work together to exert influence on the nonhydrostatic vertical motion in severe storms. If high-resolution global data are available in Cartesian coordinates with guaranteed quality, the Lax-Crank-Nicolson scheme and the Thomas algorithm might provide a promising numerical solution of this diagnostic equation. As a result, quantitative analyses are expected for the evolution mechanisms of severe storms.

Monitoring absolute vertical land motions and absolute sea-level changes from GPS and tide gauges data over French Polynesia

In this study,we estimate the absolute vertical land motions at three tidal stations with collocated Global Navigation Satellite System(GNSS)receivers over French Polynesia during the period 2007-2020,and obtain,as ancillary results,estimates of the absolute changes in sea level at the same locations.To verify our processing approach to determining vertical motion,we first modeled vertical motion at the International GNSS Service(IGS)THTI station located in the capital island of Tahiti and compared our estimate with previous independent determinations,with a good agreement.We obtained the following estimates for the vertical land motions at the tide gauges:Tubuai island,Austral Archipelago-0.92±0.17 mm/yr,Vairao village,Tahiti Iti:-0.49±0.39 mm/yr,Rikitea,Gambier Archipelago-0.43±0.17 mm/yr.The absolute variations of the sea level are:Tubuai island,Austral Archipelago 5.25±0.60 mm/yr,Vairao village,Tahiti Iti:3.62±0.52 mm/yr,Rikitea,Gambier Archipelago 1.52±0.23 mm/yr.We discuss these absolute values in light of the values obtained from altimetric measurements and other means in French Polynesia.

DIFFERENCES BETWEEN DRY AND WET SUMMER IN THE VERTICAL MOTION ON NORTH SIDE OF QINGHAI-XIZANG PLATEAU AND THE THERMAL IMPACT OF PLATEAU

To better analyse and understand the causes of Northwest China(NW China)arid climate formation,firstly the dry and wet standards were chosen and the yearly dry and wet grades on the north side of Qinghai-Xizang Plateau(hereafter NSQXP)in summers were classified utilizing the rainfall data of five stations over the area in June-August of 1952—1990.Then the differences between the vertical motion over the Qinghai-Xizang Plateau(QXP)and NSQXP in dry and wet summers were comparatively analyzed using the ECMWF's gridded data of June—August of 1979 —1986.Finally the connection between the QXP surface thermal condition and the dry and wet summers on the NSQXP was discussed as well. The main results are the following:(1)the dry and wet standards taking the rainfall standard deviation as criterion are suitable for the arid climate area;(2)the QXP may be,to some extent. responsible for the environment background of Middle Asia,NW China and North China arid climate areas;(3)there are the striking differences between the dominant vertical motion over the QXP and NSQXP in the dry and wet summers of NSQXP:(4)the QXP surface thermal condition is.to a great extent,responsible for the year—to—year variation of NW China arid climate as well.

Numerical Prediction of Added Resistance and Vertical Ship Motions in Regular Head Waves

The numerical prediction of added resistance and vertical ship motions of one ITTC （Intemational Towing Tank Conference） S-175 containership in regular head waves by our own in-house unsteady RANS solver naoe-FOAM-SJTU is presented in this paper. The development of the solver naoe-FOAM-SJTU is based on the open source CFD tool, OpenFOAM. Numerical analysis is focused on the added resistance and vertical ship motions （heave and pitch motions） with four very different wavelengths （ 0.8Lpp 〈 2 〈 1.5L ） in regular head waves. Once the wavelength is near the length of the ship model, the responses of the resistance and ship motions become strongly influenced by nonlinear factors, as a result difficulties within simulations occur. In the paper, a comparison of the experimental results and the nonlinear strip theory was reviewed and based on the findings, the RANS simulations by the solver naoe-FOAM-SJTU were considered competent with the prediction of added resistance and vertical ship motions in a wide range of wave lengths.

Vertical motions of tide gauge stations near the Bohai Sea and Yellow Sea

A modified Gauss-Markov model with weighted constraints was constructed by combining satellite altimeter and tide gauge records. Vertical motion rates of nine tide gauge stations around the Bohal Sea and Yellow Sea are estimated. This is the first time systematic estimates have been derived in this region. Downward trends were seen at the six tide gauge stations located at Tanggu, Longkou, Laohutan, Bayuquan, Xiaochangshan, and Yantai; with vertical motion rates of-1.82±0.50, -1.65±0.46, -0.88±0.42, -0.58±0.62, -0.13±0.43, and -0.01±0.43 mm/yr, respectively. Upward trends were seen at the three tide gauge stations located at Qinhuangdao, Huludao and Chengshantou; with vertical motion rates of 1.12±0.46, 0.55±0.49 and 0.26±0.44 mm/yr, respectively. There was significant subsidence in Tanggu and Longkou, and a rising trend in Qinhuangdao. According to our results, the rate of sea level rise calculated from these tide gauge records can be improved using a more accurate measurement of the land elevation accounting for lifting or subsidence. The model derived can be used to estimate vertical motions of tide gauge stations, and can be widely applied to revise the benchmark levels of tide gauges.

Vertical coherency function model of spatial ground motion

Many studies have focused on horizontal ground motion, resulting in many coherency functions for horizontal ground motion while neglecting related problems arising from vertical ground motion. However, seismic events have demonstrated that the vertical components of ground motion sometimes govern the ultimate failure of structures. In this paper, a vertical coherency function model of spatial ground motion is proposed based on the Hao model and SMART 1 array records, and the validity of the model is demonstrated. The vertical coherency function model of spatial ground motion is also compared with the horizontal coherency function model, indicating that neither model exhibits isotropic characteristics. The value of the vertical coherency function has little correlation with that of the horizontal coherency function. However, the coherence of the vertical ground motion between a pair of stations decreases with their projection distance and the frequency of the ground motion. When the projection distance in the wave direction is greater than 800 meters, the coherency between the two points can be neglected.

Engineering characteristics of near-fault vertical ground motions and their effect on the seismic response of bridges

A wide variety of near-fault strong ground motion records were collected from various tectonic environments worldwide and were used to study the peak value ratio and response spectrum ratio of the vertical to horizontal component of ground motion, focusing on the effect of earthquake magnitude, site conditions, pulse duration, and statistical component. The results show that both the peak value ratio and response spectrum ratio are larger than the 2/3 value prescribed in existing seismic codes, and the relationship between the vertical and horizontal ground motions is comparatively intricate. In addition, the effect of the near-fault ground motions on bridge performance is analyzed, considering both the material nonlinear characteristics and the P-A effect.

Seismic Design Loads of Truss Arch Frames with Ceilings subjected to Vertical and Horizontal Earthquake Motions

Spatial structures such as a gymnasium and an exhibition hall often use ceilings because of enhancing sound effects and reducing heating bills. Although the ceiling members fell down on a large scale due to the seismic motion according to the past great earthquake disaster reports, structural engineers particularly do not carry out the seismic design. The study gives structural engineers the equivalent static loads for the design of the earthquake-proof design of the ceiling system. In particular, it is significant to investigate the dynamic behavior and the applied seismic loads for the complicated vibration of the long span arch building structures with RC columns.

Effect of seawater on incident plane P and SV waves at ocean bottom and engineering characteristics of offshore ground motion records off the coast of southern California, USA

The effect of seawater on vertical ground motions is studied via a theoretical method and then actual offshore ground motion records are analyzed using a statistical method. A theoretical analysis of the effect of seawater on incident plane P and SV waves at ocean bottom indicate that on one hand, the affected frequency range of vertical ground motions is prominent due to P wave resonance in the water layer if the impedance ratio between the seawater and the underlying medium is large, but it is greatly suppressed if the impedance ratio is small; on the other hand, for the ocean bottom interface model selected herein, vertical ground motions consisting of mostly P waves are more easily affected by seawater than those dominated by SV waves. The statistical analysis of engineering parameters of offshore ground motion records indicate that:(1) Under the infl uence of softer surface soil at the seafl oor, both horizontal and vertical spectral accelerations of offshore motions are exaggerated at long period components, which leads to the peak spectral values moving to a longer period.(2) The spectral ratios(V/H) of offshore ground motions are much smaller than onshore ground motions near the P wave resonant frequencies in the water layer; and as the period becomes larger, the effect of seawater becomes smaller, which leads to a similar V/H at intermediate periods(near 2 s). These results are consistent with the conclusions of Boore and Smith(1999), but the V/H of offshore motion may be smaller than the onshore ground motions at longer periods(more than 5 s).

Impacts of the MJO on Winter Rainfall and Circulation in China

Impacts of the MJO on winter rainfall and circulation in China are investigated using a real-time multivariate MJO index.Composite results using the daily rainfall anomalies and "rainy day" anomalies according to eight different MJO phases show that the MJO has considerable influence on winter rainfall in China. Rainfall anomalies show systematic and substantial changes(enhanced/suppressed) in the Yangtze River Basin and South China with the eastward propagation of the MJO convective center from the Indian Ocean to the western Pacific.When the MJO is in phase 2 and 3(MJO convective center is located over the Indian Ocean),rainfall probability is significantly enhanced.While in phase 6 and 7(MJO convective center is over the western Pacific),rainfall probability is significantly reduced. MJO in winter influences the rainfall in China mainly through modulating the circulation in the subtropics and mid-high latitudes.For the subtropics,MJO influences the northward moisture transport coming from the Bay of Bengal and the South China Sea by modulating the southern trough of the Bay of Bengal and the western Pacific subtropical high.For the mid-high latitudes,the propagation of the low frequency perturbations associated with the eastward-propagating MJO convection modulate the circulation in the mid-high latitudes,e.g.the East Asian winter monsoon and the low trough over central Asia.

A Diagnostic Study of the Asymmetric Distribution of Rainfall during the Landfall of Typhoon Haitang(2005)

The precipitation during landfall of typhoon Haitang （2005） showed asymmetric structures （left side/right side of the track）. Analysis of Weather Research and Forecasting model simulation data showed that rainfall on the right side was more than 15 times stronger than on the left side. The causes were analyzed by focusing on comparing the water vapor flux, stability and upward motion between the two sides. The major results were as follows： （1） Relative humidity on both sides was over 80%, whereas the convergence of water vapor flux in the lower troposphere was about 10 times larger on the right side than on the left side. （2） Both sides featured conditional symmetric instability [MPV （moist potential vorticity） 〈0], but the right side was more unstable than the left side. （3） Strong （weak） upward motion occurred throughout the troposphere on the right （left） side. The Q vector diagnosis suggested that large-scale and mesoscale forcing accounted for the difference in vertical velocity. Orographic lift and surface friction forced the development of the asymmetric precipitation pattern. On the right side, strong upward motion from the forcing of different scale weather systems and topography caused a substantial release of unstable energy and the transportation of water vapor from the lower to the upper troposphere, which produced torrential rainfall. However, the above conditions on the left side were all much weaker, which led to weaker rainfall. This may have been the cause of the asymmetric distribution of rainfall during the landfall of typhoon Haitang.

New Evidence for Improving Omega Estimation by Explicitly Considering Horizontal Divergence

It is well known that the quasi-geostrophic （QG） omega equation with only two contributors respectively associated with vorticity advection （VA） and temperature advection is derived for midlatitude synoptic-scale systems only.Based on reliable reanalysis data,new evidence revealed by cyclonic and anticyclonic cases indicates that forecasters might sometimes experience problems by paying too much attention to the 500-hPa VA when estimating vertical motions not only in subtropical systems but also in systems meeting all the assumptions of the QG omega equation.Our investigations also showed that explicitly considering the vertical profiles of horizontal divergence could allow for better interpretation of vertical motions and weather in these real cases,suggesting that this equation might not be sufficient due to the presence of only two horizontaldivergence-related （HDR） mechanisms and the absence of other HDR mechanisms,e.g.,frictional force,mountain barriers,diabatic/adiabatic processes,and acceleration/deceleration of air flows.

Acomparative study between China and U.S.on seismic design philosophy and practice of a long span arch bridge

This paper presents the first of a series of case studies on the seismic design of long span bridges （cable-stayed bridges, suspension bridges and arch bridges） under a cooperative research project on seismic behavior and design of highway bridges between the State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University and the Multidisciplinary Center for Earthquake Engineering Research, University at Buffalo. The objective of this series of case studies is to examine the differences and similarities on the seismic design practice of long span bridges in China and the U.S., to identify research needs and to develop design guidelines beneficial to bridge engineers in both countries. Unlike short to medium span bridges, long span bridges are not included in most seismic design specifications, mainly because they are location dependent and structurally unique. In this paper, an available model of a steel tied half through arch bridge with a main span of 550m in China is discussed. Analysis is focused on comparisons of the seismic responses due to different ground motions. Seismic design criteria and seismic performance requirements for long span bridges in both countries were first introduced and compared, and then three near field earthquake records with large vertical components were selected as the excitations to examine the seismic behavior and seismic vulnerability of the bridge. Results show that （1） the selected near field ground motions cause larger responses to key components （critical sections） of the bridge （such as arch rib ends） with a maximum increase of more than twice those caused by the site specific ground motions; （2） piers, longitudinal girders and arch crowns are more vulnerable to vertical motions, especially their axial forces; and （3） large vertical components of near field ground motions may not significantly affect the bridge＇s internal forces provided that their peak acceleration spectra ordinates only appear at periods of less than 0.2s. However, they may have more influence on the longitudinal displacements of sliding bearings due to their large displacement spectra ordinates at the fundamental period of the bridge.

Interannual Variability of the Hadley Circulation Associated with Tropical Pacific SST Anomaly

The seasonal and interannual variability of zonal mean Hadley circulation are analyzed, and the important effects of sea surface temperature(SST), especially the tropical Pacific SST, on the meridional circulation are discussed. Following results are obtained: 1) the Hadley circulation presents a single clockwise(anticlockwise) cross-equator circulation in the Northern(Southern) Hemisphere winter,while it is a double-ring-shaped circulation quasi-symmetric about the equator in spring and autumn. The annual mean state just indicates the residual of the Hadley cell in winter and summer. 2) The first mode of interannual anomalies shows a single cell crossing the equator like the climatology in winter and summer but with narrower width. The second mode shows a double ring-shaped cell quasi-symmetric about the equator which is similar to the Hadley cell in spring or autumn. 3) Vertical motion of the Hadley circulation is driven by sea surface temperature(SST) through latent and sensible heat in the tropics, and the interannual anomalies are mainly driven by the SST anomaly(SSTa) in the tropical Pacific. 4) The meridional gradient of SSTa is well consistent with the lower meridional wind of Hadley circulation in the interannual part. For the spatial distribution, the meridional gradient of SSTa in the Pacific plays a major role for the first two modes while the effects of the Indian Ocean and the Atlantic Ocean can be ignored.

Potential vorticity analysis of quasi-biweekly rainfall events over the Yangtze Basin in summer 2014

A series of heavy rainfall events occurred over the Yangtze River Valley(YRV)in summer 2014,which were modulated by the 10-20-day quasi-biweekly oscillation(QBWO).Thus,the strongest QBWO cycle for the period 10-24 July was used as a representative case to reveal the dynamical mechanism for the QBWO of the YRV rainfall from the potential vorticity(PV)perspective and based on MERRA-2 reanalysis data.The quasi-biweekly YRV rainfall was found to depend closely on the QBWO of the upper-tropospheric South Asian high(SAH),with the SAH configuration modified by the southward-intruding midlatitude high PV stream along with southwestward-advected high PV,altering the divergent condition over the YRV.Quantitative diagnoses for the anomalous vertical motion demonstrated that,in the wet phase of the QBWO cycle,the upper-tropospheric southward-intruding high PV stream acted as a positive PV advection,while negative PV advection was generated due to the lower-tropospheric southerlies,thereby forming a positive vertical gradient of horizontal PV advection to induce evident isentropic-displacement ascending motion.On the other hand,the southward-intruding high PV stream extended downward to the middle troposphere,causing the isentropic surfaces to become more sloping,thus producing a strong isentropic-gliding ascending component.Subsequently,the stronger diabatic heating-related ascending motion was induced to generate positive rainfall anomalies over the YRV.The opposite situation arose in the dry phase,with weak descending motion in magnitude.

ANALYSIS OF THE WESTWARD EXTENSION OF WESTERN PACIFIC SUBTROPICAL HIGH DURING A HEAVY RAIN PERIOD OVER SOUTHERN CHINA IN JUNE 2005

The NCEP/NCAR II daily mean reanalysis data and observed precipitation data are employed to investigate the westward extension of the western Pacific subtropical high (WPSH) during the heavy rain period over the southern China in June 2005. Results show that there may exist a relationship between the east-west shift of the WPSH and the process of a southern China heavy rain. The analysis indicates that the vertical motion in the WPSH area is mainly caused by the latent heat release of monsoon rain belts on its northern and southern sides. The vertical motion could cause the accumulation of air mass in the center and west of the WPSH, which leads to its strengthening. The appearance of the northern and southern monsoon rain belts could not only enhance the WPSH by strengthening the descending draft, but also excite the development of positive vorticity and restrict the WPSH's movement in the north-south direction. Moreover, the Indian monsoon rainfall to the west of the WPSH may excite the development of anticyclonic vorticity on its eastern side, which leads to the westward extension of the WPSH.

Numerical Modeling of an Advanced Semi-SWATH Hull in Calm Water and Regular Head Wave

A small waterplane area twin hull(SWATH)has excellent seakeeping performance and low wave-making resistance,and it has been applied to small working craft,pleasure boats,and unmanned surface vehicles.However,with the increase in speed,the hydrodynamic resistance of SWATH will increase exponentially because of its large wet surface,followed by the uncomfortable situation of the hull underwater part relative to the water level and in terms of high trim by stern and high sinkage.A way to improve this situation is to reduce the depth of the draft at high speeds to ensure that all or a part of the volume of the submerged bodies is above the water level.Based on this idea,a new type of semi-SWATH hull form was analyzed in this paper.The two submerged bodies of the SWATH have a catamaran boat shape.This paper employed Sie-mens PLM Star-CCM+to study the hydrodynamic performance of an advanced semi-SWATH model.Bare-hull resistance was estimated for both SWATH and CAT(CATAMARAN)modes in calm water.Moreover,the efect of fxed stabilizing fns with diferent angles on the vertical motions of the vessel in regular head waves was investigated with an overset mesh approach.The vertical motion responses were estimated at diferent wave encounter frequencies,and the present numerical method results have been verifed by already published experimental data.