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Towards better understanding of bridge aerodynamics - turbulence effects

Shuyang Cao State Key Lab for Disaster Reduction in Civil Engineering, Tongji University, Shanghai, China email: [email protected]

ABSTRACT: The importance of aeroelastic performance of bridges is becoming increasingly significant for wind-resistant design, in the trend of variation of cross sections used for long span bridges from truss-stiffened to quasi-streamlined, and then to multiple-box cross section geometries. This paper reviews phenomena of major concern in bridge aerodynamics: VIV, galloping, flutter and buffeting, with a particular attention to turbulence effects. The analytical, wind tunnel and CFD approaches to generate turbulence that are necessary for studying the turbulence effects are discussed also. This paper shows that either qualitative or quantitative understanding of the turbulence effect, particularly the mechanism behind, is surprisingly insufficient. Although turbulence might help the stabilization of long-span bridges and thus it is not a conclusive parameter for wind-resistant design, the turbulence effects on the aerodynamic and aeroelastic behavior of a bridge must be better understood because the interaction between the bridge and the turbulence always exists.

KEY WORDS: Active Wind Tunnel; Buffeting; CFD; Flutter; Galloping; Turbulence Effects; VIV.

1 INTRODUCTION It is really very exciting, however a little bit uneasy, to notice the mass realization of long-span bridges and rapid increase of bridge span in the world in the past several decades. The maximum span of cable-stayed bridge increased from 200-300m in 1950s to more than 1000m recently, represented by the 1088m long Sutong Bridge completed in 2008 in China and 1104m long Russky Bridge completed in 2012 in Russia. Meanwhile, the mid-span of suspension bridge has reached to 1991m in 1998, with the opening of Akashi Kaikyo Bridge in Japan, and the researchers have been planning or proposing to challenge super long bridges with longest span of about 3000-5000m to cross straits, possibly in order to the meet the requirements of globalization. Meanwhile, since the beginning of the years 2000, China has taken a leadership in the realization of an impressive series of long span bridges (Ge and Xiang, 2008). As of 2015, China occupied 6 and 5 seats respectively in the lists of top-ten cable-stayed and top-ten suspension bridges, and these Chinese bridges were completed in this century. Furthermore, the most notable is that the top-ten longest cable-stayed bridges on construction that will be opened in the coming 3-4 years are all in China, and six of the top-ten longest suspension bridges on construction are also in China. It goes without saying that innovations in structure system, design method and construction technique have played important roles in the realization of long span bridges. Every time of growth of bridge span in the past is related to the scientific and technical innovations, among which the contributions from the wind engineering field becomes more and more significant when the bridges becomes more wind-sensitive with increase in bridge span. The collapse of Tacoma Narrows Bridge in 1940 boosted research in the field of bridge aerodynamics - aeroelastics, the study of which had influenced the designs of all the world's great long-span bridges built since 1940. After the failure of Tacoma Narrows Bridge, the wind effects on bridges were enthusiastically investigated by the researchers and engineers involving in bridge aerodynamics, among which the outstanding series work (i.e. Davenport, 1962; Scanlan and Tomko, 1971; Scanlan and Jones, 1990) successfully laid foundations of wind- resistant design of long-span bridges. The Honshu-Shikoku project, which was initiated in 1960s and comprised several long span bridges including the famous Akashi Kaikyo Bridge for which the design against wind load and aeroelastic phenomena was one of the main concerns, accelerated the research of bridge aerodynamics. The Messina Crossing project, the research on which can date back to the 1970s, also stimulated many innovative researches on nonlinear analysis methods of the complex interaction phenomena encountered by long span bridges in turbulent wind (i.e., Argentini et al., 2010; Diana et al., 2013). All the efforts made in the community of wind-resistant design of long-span bridges led to current sophisticated theory and comprehensive and integrated method for wind-resistant design of long-span bridges, which guaranteed the safety and severability of the long span bridges constructed around the world. The significant contribution of aerodynamic research to the realization of long-span bridges can be realized easily from the revolution of bridge deck shape. It is well known that, Humber bridge with a span of 1410m, completed in 1981 in UK, plays an important role in the historical development of suspension bridges because it is characterized by an aerodynamic section, although the first example of long-span bridge with this type of section was the bridge over the River Severn, UK, characterized

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by a main span of 988m, which had been completed in 1966 (Borri et al. 2013). For the design of the Humber Bridge, the depth of the deck was increased by 50% from that of the Severn Bridge, in order to increase the torsional stiffness and then avoid flutter at the design wind speed. The same design concept was followed for the Great Belt East Bridge with a main span of 1624m, built in Denmark in 1998. A streamlined section obtained by optimizing the wind performances by introducing wedge- shaped edge fairings was chosen for the Great Belt East Bridge. As many as 16 different trapezoidal box sections were tested in order to appreciate how modifications to the geometry could influence the aerodynamic stability (Larsen and Gimsing, 1992). A series studies on the aerodynamic performance of twin box girder has been carried out in China in order to meet the continuous need for creating long-span bridges and challenging the span limitation (Yang et al., 2015). A twin box girder solution was also chosen for the design of the 1545m long suspension Kwangyang Bridge in Korea, whose cross sectional shape was optimized by section model tests at three different scales to maximize the aerodynamic stability and minimize the drag force (Kwon et al., 2008). Furthermore, a tri-cellular cross section stiffened by several transverse beams was proposed for the Messina Strait Bridge because the exceptional span of the bridge (main span 3300m long) requires very high aerodynamic and aeroelastic performances. The improved stability brought by this innovative solution was checked with a vast wind tunnel test campaign. Meanwhile, instead of a box solution, a classic truss-stiffened deck configuration with reduced aerodynamic performance was selected for the Akashi Kaikyo Bridge in Japan in order to reach the required performance level for flutter stability (critical wind speed higher than 78m/s) (Miyata et al., 1988), because the mid-span could not exceed 1700m if a closed-box deck solution was chosen, in order to guarantee the required safety level for flutter instability. The options of perforated decks or laterally separated decks were not appropriate either because of the too low torsional stiffness. At the same time, the deck cross sections of almost all long cable-stayed bridges were optimized from an aerodynamic point of view. The cross section of the Sutong Bridge was chosen after various wind tunnel tests associated with aerodynamic instability (Chen et al., 2005). For the design of Stonecutter Bridge, a twin box girder deck with a wide clear separation of 14.3m was adopted, with which stability against flutter both during construction and in-service stages could be anticipated (critical 1-min wind speed higher than 95m/s) (Larose et al., 2003). As shown above, without the improved knowledge of bridge aerodynamics or wind-resistant design methods considering wind-structure interaction mechanism, it is impossible to realize long span bridges. However, it is a little difficult for the author to feel smartness in the process of wind-resistant design of a long span bridge. The modern analytical framework to calculate or predict the wind-induced response of a long-span bridge borrowed the aerodynamic knowledge of aerofoil with a streamline body. However, the shape of many bridge decks is not streamline. Furthermore, with the bridge being more wind sensitive, several assumptions for analyzing bridge vibration such as assumption of small amplitude of vibration do not stand and the nonlinear features of bridge vibration are not ignorable anymore. Changes in stiffness, mass and damping of bridges lead to new requirements in dealing with wind effects. The considerations for wind- resistant design of long bridges have to be adjusted continuously, in the trend of a bridge becoming longer and flexible, by adding more terms or adjusting the values of kinds of parameters in order to describe the complicated and delicate interaction between air and bridge. Currently, the wind-resistant performance of a long-span bridge is investigated mainly by wind tunnel experiments. From well-designed sectional or aeroelastic model tests to identify the static and aerodynamic parameters of bridge sections, safety against winds can be satisfactorily guaranteed. However, we have to admit that the stabilization of vortex induced vibration or flutter of a bridge is sometimes built on trial and error. Also, there are a lot of unknown and uncertain issues when people intend to refine the current methods for gust response analysis. In addition, the mechanisms of cable vibration and vibration control lack sufficient physical understanding. It is believed that more fundamental researches on the wind effects on bridges, in particular bridge aerodynamics, are necessary in order to facilitate the physical understanding of the interaction between wind and bridge, and then make the wind-resistant design more rational and reliable. Among many problems to solve, the Reynolds number effect and turbulence effect are considered as important issues that add uncertainty in applying wind tunnel results to real structures, and turbulence effect is the main concern of this paper. Atmospheric turbulence is irregular air motions characterized by winds that vary in speed and direction. At a height within a few hundred meters from the ground, mechanical effect (velocity shear effect) and temperature effect (buoyancy effect) are the sources of turbulence production of atmospheric flow. Variation of solar heating with time makes the atmospheric boundary layer appear at different metrological conditions, depending on whether both mechanical and convective effects co-exist or either of them dominates. A neutral condition is usually assumed in the case of strong wind because the buoyancy effect is usually weaker than the mechanical effect and can be neglected. Therefore, shear-induced turbulence is mainly targeted when the turbulence effects are concerned in the structural wind engineering field. Turbulence is characterized by chaotic property changes, including low momentum diffusion, high momentum convection, and rapid variation of pressure and flow velocity in space and time, and is thought as the most important unsolved problem of classical physics. Therefore, turbulence problems are normally treated statistically rather than deterministically, although turbulence processes organized dynamic structures. The organized structure of turbulence such as the large-scale bulge of the atmospheric boundary layer that divide the whole turbulent boundary layer into turbulent and non-turbulent regions, longitudinal vortex and other dynamic features were not explicitly considered in the past studies related to wind-structure interaction although there were many tries to simulate numerically the transient features of the wind speed fluctuation (Wang, 2007). In addition to the chaos, the turbulence is characterized by diffusivity, rotationality, three-dimensionality and dissipation. Diffusivity is responsible for the enhanced mixing and increased rates of mass, momentum and energy transports. Rotationality and three-dimensionality are associated with the vortex stretching that is the core mechanism on which the turbulence energy cascade relies. During vortex stretching, unsteady vortices appear on many scales and interact with each other, with an overall tendency that the larger flow structures break down into smaller

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structures and this process continues until the small scale structures are small enough that their kinetic energy can be transformed into heat, that is to say, dissipates. Although turbulence is not a pure random process, the first- and second- order turbulence statistics are often treated as the representative parameters to illustrate the property of turbulence when investigate quantitatively their effects on flow-structure interaction. The vortex shedding from a stationary bluff body is affected by the flow turbulence. Nakamura et al. (1988) and Nakamura (1993) characterized the flow around a bluff body by two basic flow modules: the separation and reattachment of the shear layer and formation of Karman vortex street, and accordingly suggested two representative length scales relevant to the bluff body flow: thickness of the separated shear layer and distance between the two separated shear layers, or simply the body size. The characterization of the turbulence effects should take into account both the intensity of turbulence, , and the longitudinal length scale, . Basu (1986) observed that in the subcritical regime, when / 1, the drag decreases first until 4% and then increases as increases. This behavior has been explained that low turbulence intensities tend to break the coherence of the vortex shedding, while high levels induce earlier transition of the shear layers. According to Surry (1969), small scale turbulence (/ 0.36) likely promotes transition than large scale turbulence (/ 4.3). Blackburn and Melbourne (1996) underlined that high turbulence intensity (up to 18%) with small scale (/ 0.5) increases the postcritical lift force. Nakamura (1993) predicted that the turbulence effects will be negligible if the integral scale of the turbulence is large enough compared with the representative body scale. From the foregoing one may deduce that it is impossible to distinguish the effect of each individual parameter of and . Vickery (1990) suggested that the combined effect of and may be considered / by means of the parameter . ESDU (1980) considered this parameter in the definition of the effective Reynolds number, which allows the assessment of the Reynolds number regime induced by the flow turbulence, in addition to surface roughness. This paper discusses the numerical, wind tunnel and CFD approaches to generate turbulence that are necessary to study the turbulence effects, after a review on the research on the phenomena of major concern in bridge aerodynamics such as VIV, galloping, flutter and buffeting, with a particular attention to turbulence effects. As a specially designed facility to generate “turbulent” flow, an actively-controlled multiple-fan wind tunnel built at Tongji University, is introduced. The simulation of typhoon-induced atmospheric turbulence by using WRF-LES model, and those induced by topography and sea wave by using LES, are introduced also. Satisfactory modeling of the turbulence existing around a bridge will help us study the turbulence effects on a bridge in the future.

2 MAJOR CONCERN IN BRIDGE AERODYNAMICS 2.1 Vortex-induced Vibration Vortex-induced vibration is a phenomenon triggered by the resonance between the vortex shedding and one of the natural frequencies of the structure, where the vortex shedding frequency is synchronized or locked to the vibration frequency of the structure (Borri, 2013). Large-amplitude but usually non-catastrophic oscillations can occur in a limited range of wind speed. Also both the maximum amplitude of oscillation and the extension of the range of synchronization are dependent on Scruton number or the Skop-Griffin number. The higher the mass-damping parameter is, the lower the response becomes. The well known results include that: a body performing vortex-induced vibrations induces a substantial increase in the wake correlation (e.g. Novak and Tanaka, 1975) and in the drag coefficient (e.g. R. Bishop and Hassan 1964). The wake dynamics changes (Williamson and Roshko, 1988), and the vortex formation length decreases while the base suction increases (Griffin and Ramberg, 1975), among many others. A significant feature of the vortex-induced vibration for a bridge deck section or an elongated rectangular cylinder is that their VIV is often driven by the motion-induced shear layer instability, which is different from that of a circular cylinder, which is often Karman vortex driven. For a bridge, VIV may occur on the cables, the towers or the deck, and may cause either an issue of resistance (fatigue) or serviceability (discomfort), if it occurs at relatively low wind speeds. Moreover, for bridge decks vortex-induced vibrations in a torsional mode are often possible. Vortex-induced vibrations of bridge structures have been observed many times. The first case of VIV for a bridge tower was that of Forth Suspension Bridge, UK (Borri, 2013). Vibrations with amplitude of more than 1m in the fundamental bending mode at erection and freestanding phases were probably due to its reduced mass as compared to similar constructions and required the installation of a peculiar temporary damping system, consisting of an external mass of about 15 tons connected to the top of the tower (Scruton, 1965). Permanent and temporary damping devices (turned-mass and active-mass dampers) were also installed in the towers of the Akashi Kaikyo Bridge, Japan, to restrain the oscillations predicted by wind tunnel tests (Honda et al., 1995). As for the deck oscillation, the Great Belt East Bridge, Denmark, during the final phases of deck erection, showed unacceptable low-frequency vertical oscillations of the main girder, and guide vanes were installed in correspondence of the lower edges of the deck to mitigate the excitation (Larsen et al., 2000). The Deer Isle Bridge, Marine, US, a suspension bridge with a main span of 329m and an H-type cross section, built in 1939 and stiffened after the Tacoma Narrows Bridges, showed significant harmonic vertical bending vibrations at a wind speed about 9m/s (Kumarasena et al., 1991). The Long’s Creek Bridge, Canada, a cable-stayed bridge with a main span of 217m and a steel deck stiffened by two longitudinal beams, was found to vibrate with amplitude of about 20 cm (Wardlaw, 1971). The Second Severn Crossing Bridge, UK, a cable-stayed bridge with a main span of 456m and a deck composed of two longitudinal steel girders, transverse trusses and a reinforced concrete slab, suffered from frequent vertical vibrations, which were not expected from wind tunnel tests, as a result of lower structural damping and different turbulence characteristics (Macdonald et al., 2002). The excitation was suppressed by the installation of baffle plates under the deck. In addition, Li et al. (2011) reported VIV of the Xihoumen suspension bridge with a

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span of 1650m long in China at wind speed of 6-10m/s, which was suppressed by installing barriers. The VIVs were observed not only for cable-supported bridges. The Trans-Tokyo Bay Crossing Bridge, Japan, which is a straight ten-span continuous steel box-girder bridge with a main span of 240m and variable cross-section height, exhibited vibrations exceeding 50cm, occurring for the first vertical mode in the wind speed range 13-18m/s (Fujino and Yoshida, 2002). To reduce the oscillation amplitude several tuned-mass dampers were installed together with 49 cm high vertical plates fastened to the post of crash barriers over the deck. The Volgograd Bridge, Russia, which presents a main span of 155m with a slender steel deck, exhibited vertical vibrations with maximum amplitude of 40cm (Weber at al., 2013). Semi-active tuned-mass dampers were installed to suppress the vibrations in the first three vertical modes. There were several analytical models that tried to simulate the fluid force. In the regime where the body oscillation frequency is synchronized with the periodic vortex wake mode or periodic fluid force, a good approximation to the force and response can be expressed by two harmonic functions with same oscillating frequency but with a phase lag between them. In Feng (1968)’s important classic measurements of response and pressure for an elastically mounted cylinder, it was apparent that there were two amplitude branches, namely the initial branch and the lower branch, with a hysteretic transition between them. Feng (1968) also noted that the jump in response amplitude was reflected by a significant jump in phase of the pressure fluctuation relative to body motion. The jump in the phase of the transverse force in the classical forced vibration study (Bishop and Hassan, 1964) and also the jump in the phase measured in the free-vibration experiments (Feng, 1968) were caused by the changeover of mode from the 2S to 2P mode. If the fluid force is successfully approximated, the equation of motion can be established, with which the response amplitude and frequency may be derived in a straightforward manner. However, the contributes of aerodynamic damping to the fluid force cannot be properly evaluated if a fluid force is expressed by a simple harmonic function, thus the classical harmonic force model cannot predict the maximum amplitude well, even for a vibrating circular or rectangular cylinder, although it is the basis for several offshore design codes. The models based on the coupling between a linear oscillator representing the structure and a nonlinear oscillator representing the wake were studied by many researchers (Hartlen and Currie, 1970; Skop and Griffin, 1973). A van-der-Pol-type equation was utilized to describe the lift force, with several parameters to be fitted. If the parameters are selected appropriately, it is possible to simulate the phenomenon of vortex-induced vibration of a bluff body, including the variation of vibrating amplitude and frequency with velocity. Reproduction of the hysteretic transition was also achieved. In addition, a nonlinear wake oscillator VIV model with variable length of oscillator was proposed for a circular cylinder (Tamura, 1978), where the wake oscillator was the Brikhoff’s type and the effects of the discharged vortices from the wake oscillator were represented by the Magnus effect that determines the relation between lift coefficient and wake angular displacement. The model was shown to be able to capture several complex features of the phenomenon and satisfactory agreement was found with series of experimental and numerical data for various Scruton numbers. The widely utilized VIV models for bridge engineering includes the Scanlan linear model, Scanlan non-linear model, Larson model and Diana model. Scanlan (1975) presented a simpler linear model that split the aerodynamic force in a self-excited term, which introduces negative aerodynamic damping, and a harmonic force term at the Strouhal frequency, which triggers the resonance of the structure. The linear model can predict the maximum amplitude of vibration of a bridge with satisfactory accuracy although the identified aerodynamic damping is not the real one. As commented by Simiu & Scanlan (1986), the linear model is an empirical model that helps simply the nonlinear experimental data that are not fully understood. Ehsan and Scanlan (1990) later presented a single-degree-of-freedom nonlinear model based on a van-der-Pol-type equation. This non-linear model can capture the VIV features as well as the wake oscillator models, with simple procedures to identify the model parameters. Li and He (1995) performed parameter identification of vortex-induced forces on bluff bodies, following the idea of non-linear model of Scanlan. In addition, Larsen (1995) proposed a similar model but with a generalization of the van-der-Pol-type equation, requiring an additional parameter, to better follow the relation between response amplitude and Scruton number. However, the model parameters identified by the non-linear models usually depend on the Scruton number, therefore the experiments need to be performed carefully in order to assure the data obtained in wind tunnel tests applicable to a real bridge. The practical significance of VIV has led to a large number of fundamental researches on the excitation mechanisms on bluff body or bridge sectional models, many of which are discussed in the comprehensive reviews of, for instance, Sarpkaya (1979) and Williamson and Govardhan (2004). Tamura et al. (1993) numerically investigated the aeroelastic instability of an elongated rectangular cylinder and confirmed that the flow structure around the oscillating cylinder becomes two-dimensional in the spanwise direction. Itoh and Tamura (2002) reported that, in the case of the rectangular cylinder with D/B=2.0, the aerodynamic divergent oscillations with a particular dependency of response on dynamic properties occur over the resonant velocity. Such unstable oscillations caused by the motion-induced flow structures affected the large afterbody of the rectangular cylinder. Shiraishi and Matsumoto (1984) classified vortex-induced oscillations with special attention to bridge structures. The role of geometrical shape factor of the section during the interaction with the vortices formed at leading and trailing edges, as well as three excitation mechanisms, were investigated intensively, based on reduced critical wind speed, response amplitude patterns, flow and pressure characteristics. Kobayashi et al. (1988) investigated the instability in the bending mode, highlighting the presence of two mechanisms causing the vortex-induced model response. One was related to the Karman vortices shed in the wake, while the other was associated with occurrence of the motion-induced vortices, which amplified the vibration amplitude. The effects of Reynolds number, Scruton number, oncoming turbulence, non-structural details such as handrails, curbs, flaps, and fairings, among others, on the VIV of bridge deck models have been widely investigated in the bridge wind engineering community. Larose and Auteuil (2006) illustrated the Reynolds number sensitivity of the Ikara Bridge, the IHI Bridge and the

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Stonecutters Bridge with sharp edges. Diana et al. (2007) analyzed the sensitivity of the effects of different aerodynamic devices (trip wire, wings, wind shield) on the behavior of a bridge deck, in terms of stationary aerodynamic coefficients and in terms of vortex shedding excitation. It is interesting to notice that Diana (2003) observed the tendency to excitation, though reduced in magnitude, at yaw angles of 45 degree for the proposed Messina Strait, while Fujino and Yoshida (2002) reported that the synchronization could occur only for winds nearly perpendicular to the bridge axis. Here, a CFD technique that helps simulate the flow around vibrating bodies, the so-called Immersed Boundary Method (1993), is introduced. When performing unsteady simulation of flow past a vibrating bridge deck, it is necessary to apply a body-fitted grid system in order to impose accurately the boundary conditions of velocity on the deck shape, and the grid-system should be regenerated at every time-step to grab updated boundary information. This process inevitably brings huge computational burden. Furthermore, as mentioned above, the non-structural details such as handrails and fairings are often utilized as aerodynamic devices to mitigate the vibration. How to model these non-structural details appropriately while guaranteeing the accuracy of simulating the flow around a bridge deck is a big challenge. The Immersed Boundary Method allows people to use static Cartesian coordinate system to simulate the flow around a static or moving body, by introducing an external force term, , into the Navier-Stokes equations, where and are the parameters to be selected appropriately, is the velocity to be achieved by adding external force at virtual boundary, which can be explicitly imposed when a forced vibration is assumed. Of course, a static body condition can be achieved by imposing 0. Figure 1 presents the lock-in region of the rectangular cylinder with different side ratios B/D under forced vibration, which showed the feasibility of IBM method for VIV studies (Yang and Cao, 2015).

4 3 4

A=0.14D A=0.14D Present Present 3 Stc=0.04~0.5 Stc=0.04~0.5 3 2 A=0.14D Present (Velocity) v Stc=0.04~0.7 Present (Lift) 2 Lock-in region Lock-in recur 2 Stc/Stv Stc/St Stc/Stv Lock-in region Okajima (Lift) 1 Lock-in region 1 1 Stv=Stc Stv=Stc Stv=Stc

0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.2 0.4 0.6 Stc Stc Stc B/D=1 B/D=3 B/D=5 Figure 1. Lock-in region of the rectangular cylinder with different side ratios simulated by IBM

 Turbulence effect There are many experimental and numerical studies on the turbulence effects on VIV phenomenon of a bluff body with a simple body shape, although those on a bridge deck model are comparatively less (Davenport et al., 1971; Miyata et al., 1983; Wardlaw et al., 1983). Novak and Tanaka (1975) showed that the tendency of increase of spanwise correlation of pressure fluctuation around a circular cylinder under forced vibration with the vibration amplitude in uniform flow became ambiguous in turbulent flow. Howell and Novak (1980) reported a decreased aerodynamic force on a circular cylinder under free and forced vibrations in homogeneous and boundary layer turbulent flow. Pasto (2008) presented a suppression of vibration of a freely vibrating circular cylinder in turbulent flow while investigating the role of effective Reynolds number in addition to that of the mass-damping parameter. Zhu and Ding (1990) found that the VIV occurred obviously on a semi-closed box-girder section could be suppressed when the turbulent intensity of oncoming flow reached about 6%. The above results generally led to the conclusion that turbulence has a strong effect on the synchronization mechanism, reducing the oscillation amplitudes and in some instances it is even able to completely inhibit the phenomenon. However, Goswami et al. (1993) showed that the turbulence effect on the response amplitude of a circular cylinder in free vibration was surprisingly negligible, which remained virtually unchanged from the no-grid scenario. More studies on the turbulence effect on VIV seem necessary in order to achieve consistent understanding of the turbulence effect and the mechanism behind. It is noteworthy that Kawatani et al. (1993, 1999) and Kobayashi et al. (1990, 1992) utilized an active gust generator to investigate the effects of turbulence properties including turbulence intensity, turbulence scale, high or low frequency component of turbulence among others on vortex-induced bending or torsional oscillation of two-dimensional rectangular cylinders with different aspect ratios and hexagonal cylinders. It was found that the upstream gust suppressed vortex-induced oscillation of bridge deck section models except for specific section models. In addition, Utsunomiya et al. (2001) tried to explain why several prototype bridges did not exhibit VIV while VIV did appear in wind tunnel test, by investigating the aerodynamic performance of a closed deck section model in slowly fluctuating wind. It was shown that the response of the model depended on the slowly fluctuating wind. 2.2 Galloping Galloping is a one-degree-of-freedom dynamic instability typical of slender structures having special cross sectional shapes such as rectangular sections or D sections, due to cross-flow motion induced forces which produces negative aerodynamic damping. It is characterized by crosswind large oscillations with amplitude growing with the wind speed. A classical example of this kind of instability is the cross-wind large amplitude vibration of power line conductor cables that have received a coating of

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ice. Galloping in the plunging degree-of-freedom is generally not a problem for bridge decks, because it may occur only in the case of very bluff girders, which are usually too stiff to give rise to this type of instability. However, it is an important issue for bridge towers and hangers with noncircular sections. Den Hartog (1956) studied the mechanism of galloping excitation of transmission conductor lines and elaborated a criterion for the critical wind speed on the basis of the slope of the lift coefficient and magnitude of the drag coefficient. The well-known Den Hartog criterion makes the assessment of the tendency of a slender, prismatic structure towards galloping instability available by evaluating it time-averaged section lift and drag coefficients ad assessing the sign of the expression at  0. Parkinson (1963) formulated the non-linear quasi-steady theory to galloping and showed successful qualitative and quantitative agreement with experiment. Interaction between galloping and vortex-induced vibration is an interesting topic. Mannini et al. (2014) studied the combined VIV-galloping instability of a 3:2 rectangular cylinder.

 Turbulence effect Laneville and Parkinson (1971) investigated the influence of isotropic turbulence on the galloping behavior of rectangular cylinders, showing that the quasi-steady theory is still applicable if the static aerodynamic coefficients are measured in a turbulent flow with the same turbulent intensity. Turbulence was found to be able to suppress the galloping of a 2:1 rectangular cylinder with elongated afterbody, but it did not affect the galloping of a square cylinder. However, for a 1:2 rectangular cylinder with short afterbody, the turbulence is found to foster the instability (Laneville and Parkinson, 1971). Miyata et al. (1983) carried out wind tunnel experiments of turbulence effects on the aerodynamic instability of rectangular cylinders with B/D=1-4 under several Scruton numbers, confirming the similar phenomenon on B/D=1 and 2.

2.3 Flutter Flutter is a dynamic instability basically involving a torsional and a vertical bending vibration mode of the deck. The mechanism through which energy is extracted from the flow and feeds the structural oscillations is related to the variations of modal frequencies, which tend to approach due to flow-structure interaction, and to the phase between the two degrees of freedom (Borri et al., 2013). In case of bluff cross sections the instability may involve only the torsional mode. However, the presence of a vertical bending mode with similar shape and close frequency may cause a reduction of the critical wind speed. Torsional flutter was the reason for the collapse of the Tacoma Narrow Bridge. Flutter causes limit-cycle oscillations of large amplitude that increases with wind speed and can lead to the collapse of a structure. The flutter phenomenon is analytically approached by assuming the so-called “self-excited” forces that stem from the motion of the body. Theodorsen (1934) obtained in closed form the aerodynamic forces on a harmonically oscillating airfoil and calculated the critical flow speed, based on potential flow theory and Kutta condition. Bleich (1948) had first applied Theodorsen’s airfoil theory to bridge decks. Selberg (1965) proposed an empirical formula for the critical wind speed of a flat plate dynamically equivalent to the bridge deck considered, by introducing an experimental coefficient to quantify the actual aerodynamic performance of the deck cross section. Scanlan (1971) reported flutter derivative results for a wide range of bridge deck geometries obtained by free vibration test, which requires simple experimental apparatus only. The flutter derivatives describe the relation of the force components in phase and in quadrature with the structural motion to the displacements and velocities of displacement. The work of Scanlan was a milestone in the history of bridge aerodynamics, which initiated great number of studies towards realization of a better expression of the self-excited force as well as advanced identification algorithm. Scanlan’s original formulation of self-excited forces that neglected the lateral sway of the bridge was further extended into an expression containing the full set of 18 flutter derivations (Singh et al., 1995). In addition, Diana et al. (2008) proposed a time-domain model and an identification procedure, to study the nonlinear character of the aeroelastic forces. Mannini and Bartoli (2015) investigated the aerodynamic uncertainty propagation in bridge flutter analysis. It is noteworthy that Matsumoto et al. (1995) gave a deep insight into the flutter mechanism of rectangular and elliptical sections. The inter-dependence between some flutter derivatives was emphasized and the step by step analysis was proposed as an alternative to complex eigenvalue calculation of critical wind speed, allowing understanding of the role played by each flutter derivative in the instability onset. This work was followed by many similar works (e.g. Chen and Kareem, 2008).

 Turbulence effect Hirai et al. (1967) studied the effects of several parameters (angle of attack, turbulence, frequency ratio and damping) on the flutter critical wind speed for several cross-sectional geometries such as flat plate, truss and H-section, and reported a decrease of critical wind speed in turbulence for classical coupled flutter and no variation or small increase for torsional flutter. Davenport et al. (1971) found that the turbulence raises the critical wind speed for coupled vertical-torsional flutter of flat plate and truss-stiffened decks, although it only marginally postpones the onset of torsional instability for H-shaped plate-girder decks. Scanlan discussed the role of turbulence, assuming that the effect of buffeting forces can be superimposed upon that of self- excited forces measured in turbulent flow. Bucher and Lin (1988) performed analytical time-domain analysis and found that turbulence can play either a destabilizing role if the critical mode is to act alone, or a stabilizing role if it is coupled with other modes, because it foster the vibration energy transfer towards more stable modes. Bartoli et al. (1995) adopts Ito’s differential rule to account for the contribution from oncoming turbulence on the definition of stability threshold for linear and nonlinear structures. Diana et al. (1999) observed a destabilizing effect of turbulence for the Messina Bridge.

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2.4 Buffeting Buffeting in bridge aerodynamics refers to the excitation of a bridge due to the effect of turbulence that naturally present in the atmospheric boundary layer and in the wake of another structure. With respect to the classical problem of response of a system to a multi-correlated random load, it is crucial to account for the effects of self-excited forces, which change the modal frequencies and the damping ratios of the structure and induce a certain degree of coupling between the modes, in particular between vertical bending and torsional modes with similar shapes (Borri et al., 2013). Similar to flutter analysis, the knowledge in the aeronautical field was referred in the initial stage of buffeting analysis for a bridge. Sear (1941) set up the theory of the response of an airfoil to a sinusoidal gust. The obtained functions can be used for the buffeting analysis for wings respectively in the time and frequency domain. The famous approximation to Sear’s function was proposed through the study of the lift force acting on a two-dimensional thin airfoil moving in an isotropic turbulence field (1952). Davenport (1962) published his theory of dynamic response of structures to the random excitation due to turbulence in the atmospheric boundary layer and applied it to a suspension bridge, showing that the fluctuating component has an effect as great or greater than the mean wind and that the vertical vibrations due to the vertical component of turbulence may be as significant as the horizontal action. The response of bridge to turbulence wind is usually calculated by assuming the linear superposition of buffeting and self-excited forces and using the flutter derivatives measured in turbulent flow, although many studies pointed out the necessity of considering coupled oscillation of bending and torsion in order to obtain good agreement with the experimental results. In addition, Holmes (1977) reported that the use of correct aerodynamic damping had an important impact and the quasi-steady theory with an aerodynamic admittance of unity significantly overestimated the response. Chen and Kareem (2000) proposed a time domain approach for predicting the buffeting and flutter responses with aerodynamic nonlinearities. The turbulence field is filtered into low frequency components that alter the self-excited forces through the angle of attack, and high frequency components that possibly influence the deck aerodynamics. Diana et al. (2008) investigated the nonlinear relation between self-excited and buffeting forces and proposed a time-domain rheological model to account for the dependence of aeroelastic forces on reduced wind speed and angle of attack.

3 TURBULENCE GENERATION 3.1 Mathematical methods A fast Fourier transform (FFT) based mathematical method is often employed to transform signals between time (or spatial) domain and frequency domain, which has many applications in physics and engineering. One of the most important parts of the mathematical simulation methodology is the generation of the stochastic processes, fields and waves involved in the problem. The generated sample functions must accurately describe the probabilistic characteristics of the corresponding stochastic processes, fields or waves that may be either stationary or non-stationary, homogeneous or non-homogeneous, one-dimensional or multi-dimensional, univariate or multi-variate, Gaussian or non-Gaussian (Shinozuka and Jan, 1972; Shinozuka and Deodatis, 1996). Traditionally, the method based on the summation of trigonometric series with random phase angles has been the most popular, perhaps due to its simplicity. The multivariate processes are generated by implementing a stochastic decomposition scheme that exploits the concept of decomposing a set of correlated processes into a number of component processes. When the cross-spectral density matrix of an n-variate process is specified, its component processes can be simulated as the sum of cosine functions with random frequencies and random phase angles. Meanwhile, simulation of multivariate processes based on digital filtering was accomplished by first simulating a family of uncorrelated processes and subsequently imposing the appropriate correlation structure by a transformation (Li and Kareem, 1993). More developments in digital filtering techniques include state space modeling, autoregressive (AR), moving average (MA), and the combination autoregressive and moving averages (ARMA) models (Kareem, 1987, Reed and Scanlan, 1984, Li and Kareem, 1993). In addition, the wavelet transform, Hilbert transform and POD analysis have been incorporated into the mathematical approaches, which make the simulation of evolutionary characteristics of transient winds possible (Kitagawa and Nomura, 2003; Wang, 2007). Although the above techniques vary in their applicability, complexity, computer storage requirement, and computing time, many simulated data show excellent agreement with the specified wind features, including the target spectral characteristics of the wind that makes the mathematical method very suitable to wind engineering application. The mathematical technique has immediate applications to the simulation of real-time processes, e.g., simulate the evolutionary characteristics of transient winds in order to explore the non-stationary thunderstorm wind loading on structures (Wang et al., 2013). Meanwhile, the time- dependent velocity fluctuations modeled by mathematical approach are often utilized as the inlet flow boundary condition for the CFD approach. However, the movement of wind flow in the ABL is determined by the governing equations of the fluids, thus the atmospheric turbulence is not a pure random process. It contains organized turbulence structures as other turbulent boundary layers. Anyway, with more wind speed features considered in the process of mathematical simulation, it may be able to expect that the simulated flow field approaches to the real one and is suitable to some wind engineering applications. 3.2 Wind tunnel modeling The model test in a wind tunnel is considered the most reliable approach to study the wind effects on structures. The current wind load codes/standards are formulated under the premise that wind loads on structures are simulated in wind tunnels. The pioneer researchers in the wind engineering field had established the experimental technique related to the boundary layer wind tunnel test while creating the framework of wind resistant design of structures (Daveport and Isyumov, 1967; Cermak and Cochran, 1992). In short, wind tunnel simulation of ABL is a well established practice, and the boundary layer wind tunnel has

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become a necessary tool for wind resistance design. In order to investigate the wind effects on structures realistically, the model tests should be conducted in wind tunnel flows with characteristics similar to those of natural wind. The natural atmospheric boundary layer over various ground conditions are categorized into a limited number of terrain categories, which can be modeled in the boundary layer wind tunnels by different combinations of passive devices including spires, barriers and roughness blocks. Based on the assumption that velocity fluctuations can be adequately modeled by stationary mean and turbulent flow properties, attempts to simulate an atmospheric flow in a wind tunnel have so far been confined to the reproduction of the statistical characteristics, including power spectrum, vertical profiles of mean velocity and turbulence intensity and sometimes coherence. The well-known technique to create isotropic turbulence is utilizing turbulence grids, with which a homogeneous turbulence field can be anticipated (Simons and Salter, 1934). The classic knowledge of turbulence was mainly obtained based on the intensive research on grid turbulence. Currently the most frequently used device to study the turbulence effects of aerodynamics of a bluff body is still the turbulence grid. However, the inertia region in the spectrum of grid turbulence is usually too narrow compared with atmospheric turbulence or even does not exist. The turbulence Reynolds number is too small also. Modeling a high turbulence Reynolds number flow by adding actuated devices in the tunnel have been tried by many researchers, because utilizing very large wind tunnels is usually impossible for the majority of the researchers. The specially designed devices that stimulate the flow intentionally help increase the turbulence Reynolds number, or help modeling some particular features of the atmospheric turbulence. Makita (1991) developed a turbulence generator to model homogeneous flow field with high turbulence Reynolds number. Kobayashi (1994) developed an active gust generator with arrays of plates and airfoils, which were controlled respectively to control the velocity fluctuations in the longitudinal and vertical directions. Diana et al. (2002) utilized an active turbulence generator to study the complex aerodynamic admittance role in buffeting response of a bridge deck. Nishi and Miyagi (1993) considered that the simulation of wind velocity history was of equal importance with the reproduction of the statistics. If the “raw” wind velocity history can be reproduced, on which the wind effects on structures are investigated, the obtained results would be more convincible. The longitudinal wind velocity is modeled by controlling the rotational speed of fans, while the vertical component is modeled by controlling the attack angle of the blades. Figure 2a illustrates the actively controlled multiple-fan (99 fans) wind tunnel installed at Miyazaki University, Japan. Figure 2b is a photo of a multi-fan (120 fans) wind tunnel of Tongji University, China, whose design concept followed that of the tunnel at Miyazaki University, Japan, but the dynamic performance (frequency response) of the fans is improved aiming at modeling the high- frequency turbulence including the transient wind. The 120 fans are arranged in a 12×10 matrix, and the test section size is 1.8m×1.5m. Figure 3 compares the time histories of longitudinal and vertical velocity components set as the target and those

(a) Miyazaki tunnel (99 fans) (b) Tongji tunnel (120 fans) Figure 2 Multiple-fan wind tunnels

1 6 Target [m/s] [m/s] 5 u 0 v 4 3 u v -1 0 10 20 t [s]

1 6 Measured [m/s] 5 [m/s] u 0 v 4 3 u v -1 0 10 20 t [s] Figure 3 Comparison of the target and reproduced wind speed fluctuations

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reproduced in the test section, the correlation of which is about 94%, implying a good modeling of the target velocity fluctuations. 3.3 CFD approach Computational Fluid Dynamics (CFD) is basically a numerical approach to simulating or predicting phenomena and quantities of a flow by solving the equations of motion of the fluid at a discrete set of points. It has wide applications in flow- related engineering fields including aeronautical, mechanical and civil/architectural fields, although the difficulties in applying it to particular problems in these fields are different. The structural CWE usually involves the combination of problems of bluff body aerodynamics, inflow turbulence, wake turbulence, grid generation and high Reynolds number (up to the order of 107 to 108). All these problems require special attention in numerical simulation. Unsteady calculation is usually necessary in order to investigate the turbulence effects on the aerodynamics of a bridge, which requires to impose the velocity field, the so-called inflow turbulence, on the inlet of the computational domain, at every computation step. Of course, the time-dependent inflow turbulence data is necessary to possess the required statistical values. The methods developed till now for generating inflow turbulence can generally be classified into two types. The first is the analytical method, which artificially generates time series of velocity fluctuations by performing an inverse Fourier transformation-based simulation as mentioned in Section 3.1. The stochastic nature of inflow turbulence generated by the analytical method may satisfy the prescribed requirements of the turbulence statistics at one point or sometimes correlated multiple points. However, if it is not generated from the governing equations of the fluid, the velocity fluctuations cannot have the organized structures of a turbulent ABL. Thus, the wind-induced response of a structure obtained for this kind of “turbulent” flow is questionable. To partly resolve this problem, Kondo et al. (1997) proposed to conduct a divergence-free relaxation operation on the analytically generated fluctuation. Huang et al. (2010) proposed a new inflow turbulence generator not only rigorously satisfying the divergence-free condition but also suitable for parallel computation. The other is the CFD method, which directly conducts numerical simulation of a turbulent boundary layer using a CFD approach. In order to achieve a fully developed turbulent boundary layer, the re-scaling technique proposed by Lund et al. (1998) was widely utilized, whose points was to rescale the velocity field at a downstream station, and re-introduce it as a boundary condition at the inlet, to allow for the calculation of spatially developing boundary layer in conjunction with pseudo-periodic boundary conditions applied in the streamwise direction. With the CFD method, it is possible to simulate a fully-developed or spatially-developing turbulent boundary layer whose turbulent flow field at one location can be extracted and utilized as the time-dependent inflow data for other calculations. The CFD method has recently achieved great success in generating inflow turbulence (Nozawa and Tamura, 2002; Kataoka and Mizuno, 2002). Although a CFD method avoids the problems caused by the analytical method, it requires a large computational load. The resolution of the flow field is basically dependent on grid size, so a very fine grid is necessary to simulate the high-frequency component of turbulence. For instance, Kaneda et al. (2003) performed a very large-scale simulation with a total grid number of 20483 to demonstrate the existence of Kolmogorov’s -5/3 power law at the turbulence spectra by utilizing the Earth Simulator, Japan, which was the fastest supercomputer at that time. It is predicted that even after several decades, it’s still impossible for general users to perform a complete simulation of turbulence that sufficiently resolves the whole wave number range of turbulence. Besides using more grid cells, another approach to increasing the high-frequency component of turbulence is to use high-order algorithms to express the derivative. It is difficult for traditional numerical algorithms such as FDM, FVM and FEM to reproduce the high-frequency component because they are inherently low-order methods. On the other hand, the traditional high-order methods used in numerical simulation of turbulence, such as compact finite difference, spectral and spectral element methods, are difficult to utilize in CWE applications due to their complexity and non-universality. One high-order algorithm, the Differential Quadrature Method (DQM) was tried to model inflow turbulence (Wang et al., 2013), with the aid of the recycling technique.

20

+ y CS7 US8  = 3 + u / CS5 US6 u

rms CS3 US4 w

 .5  Del Alamo &

+ 5 u 2

+ / [118] + (y ) Jimenez u 10 5ln + 2. CS7 US8 rms = v u CS5 US6   u CS3 US4 / 1 rms

Del Alamo & u Jimenez [118] 0 0 100 101 102 0 50 100 150 (a) y+ (b) y+ Mean-velocity rms of velocity fluctuations. Figure 4. Numerical results of local DQM for channel flow at Reτ=uτb/ν=180

The local DQM is verified through a three dimensional turbulence simulation in channel flow at Reτ=uτb/ν=180, where uτ is friction velocity, ν is kinematic viscosity coefficient and b is half width of the channel. The traditional fractional step method is applied to coupling the NS equations and mass conservation equation. The local DQM is used to discretize the convection terms in space when calculating the intermediate velocities, and the viscous terms are spatially discretized by the second-order central

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difference scheme. The first-order explicit Euler scheme is used for the unsteady terms. The second-order Adams-Bashforth scheme and the Crank-Nicolson scheme are utilized for the convection and the viscous terms, respectively. The computational domain is 2π×2×π in the longitudinal (streamwise), vertical (wall-normal) and spanwise directions, respectively, with a coarse + + mesh of 65×65×65. A uniform grid is used in both the streamwise (x =Δx×uτ/ν=8.8) and spanwise (z =Δz×uτ/ν=17.6) directions. + The grid size stretches in the vertical direction with a minimum value of y =Δy×uτ/ν=0.9 near the wall and a maximum value of y+=11.5 at the center of the channel. For the boundary conditions, a periodic condition is imposed for velocity and pressure in the streamwise and spanwise directions while a non-slip boundary condition is utilized on the upper and bottom boundaries. Figure 4 shows that the mean velocity and root-mean-square (rms) of velocity fluctuations obtained by the local DQM agree well with the numerical data of Del Alamo and Jimenez (2003), which were obtained by DNS based on spectral method at the same Reynolds number, although the present simulation uses a coarse grid. Generally, it can be concluded that local DQM yields satisfactory results and are thus applicable to turbulence simulation. Figure 5 comprare the power spectral densities of the along-wind velocity fluctuation obtained by DQM with the Karman spectrum. In Figure 5 (Re~1020), the power spectrum follows the Karman spectrum until ⁄ 0.8 at US4, until ⁄ 1.5 at US6 and until ⁄ 2.4 at US8. The improvement of high-frequency energy in high-order schemes is obvious.

Figure 5. Compraison of the power spectral densities of the along-wind velocity fluctuation

3.4 Simulation of atmospheric turbulence by WRF-LES The CFD and wind tunnel approaches to model the air turbulence described above are applicable to idealized homogeneous air circumstance. However, the wind speed characteristics at a location to build a large bridge are usually influenced by topography or islands and local climate. Meso-scale meteorological model that simulates realistic air movement within a definite space and time range is tried to simulate atmospheric turbulence. Take WRF model (Weather Research and Forecast) for an example, based on atmospheric dynamic equations and proper physical schemes, it predicts meteorological phenomena ranging from tens of kilometers to hundreds of meters, thus the obtained atmospheric features would be more realistic than those modeled by common wind tunnel experiments or theoretical inflow CFD model. Even though the basic equations are similar between the CFD and meso-scale models, the objectives and methods are significantly different to each other. One of the significant differences between them is the scale of fluid in interest. Schlunzen (2011) depicts the methods to study the atmosphere phenomena with different scales. For the scale of 10km to 1km, local atmospheric phenomena take an important role. The strong vertical convection appears and the purpose of land use becomes a representative factor to parameterize the effects of land surface and near-ground boundary. For the scale from 1km to 10m, local terrain effect should be included. Turbulence effect is also important for this scale, requiring an effective way to include the subgrid effect. When the scale is shrinking into hundreds of meters or less, the subgrid effect on airflow is indispensible. Recently, 3D Smagorinsky turbulence closure and prognostic turbulent kinetic energy (TKE) closure schemes for subgrid scale (SGS) were added into WRF. These schemes are widely used in micro-scale meteorology and LES scale applications (2007). However, the research on the atmospheric turbulence of a real region by using LES-based meteorological model is still very few. Bou-Zeid at al. (2004) developed a scale-dependent dynamic model to help improving the subgrid turbulence effect for ideal conditions. Talbot et al. (2012) investigated the performance of WRF-LES in real cases and reported that WRF-LES had no more advantages in studying the subgrid turbulence when the scale is smaller than 50 meters. To explore the multi-scale atmospheric turbulence phenomenon, Typhoon Kai-tak that hit China in 2012 is simulated with WRF-LES. This typhoon is selected because it passed an observational tower. The simulated typhoon track and wind history are compared with observational data. For typhoon simulation, five nested domains are calculated, the inner two of which have higher spatial and temporal resolution. Table1 provides a summary of computational domain, the number and size of the grid and time step. Only the inner two domains are calculated with WRF-LES model, in order to investigate the behavior of WRF- LES model in modeling the atmosphere turbulence. Figure 6 compares the typhoon route between the simulation and

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observation. Nudging technique is applied for the beginning several hours in order to track the typhoon route well. However, nudging technique is not utilized later because it is not a physical method. Figure 7 compares the simulated velocity history during the passing of Typhoon kai-tak and the observation. Note the observation is ten-minute mean data. Although the simulated velocity trend generally follows the measurement, there is an abrupt velocity drop related to the passing of typhoon eye in the simulation results, which does not exist in the observation. This discrepancy is a direct result of the non-perfect prediction of typhoon route, which shows that a good simulation of typhoon route plays key roles in calculating the velocity at a particular point close to the typhoon eye. Other results show that WRF-LES simulation with 3D Smagorinsky closure has limitations for simulating high frequency component. The contributions to the turbulence energy from local complex terrain or other instabilities should be included.

Table 1 Details of computation domains Domain Grids Area Grid size Time step Model 1 180*144*61 1611km*1287 km 9 km 18 s Without 2 150*142*61 447km*423 km 3 km 6 s LES 3 145*124*61 144km*123 km 1 km 2 s 4 121*121*61 40km*40 km 1/3 km 1 s With LES 5 100*100*61 11km*11 km 1/9 km 1/3 s

Figure 6 Typhoon route

Figure 7 Comparison of wind speed during the passage of a typhoon

 Turbulence induced by air-sea surface interaction Sea waves play aerodynamic roles as surface roughness when a turbulent boundary layer is developing over the sea surface. Unlike roughness on land, a wave’s aerodynamic performance is not fixed because it moves and its shape changes continuously even during a single wind event, which makes the turbuelent structure over a sea wave very complicated. The air-sea interface is a complex system of interacting waves and atmospheric turbulence over a wide variety of spatial and temporal scales. The exchange of momentum and energy across the sea surface, for the most part, occurs on a molecular scale, involving both turbulent and laminar processes modified by wave breaking, surface tension, the structure of the wind boundary layer, and the ocean mixed layer, among other effects. In order to better parameterize sea-air interaction, several numerical studies that idealizes or simplifies the flow configuration by assuming the sea surface to be two-dimensional and non-evolving are carried out to study the influence of imposed sinusoidal wave motion on the upper flow field while neglecting the effects of other factors such as wave breaking and wave evolvement. The wave surface elevation h is assumed to be a function of both the x coordinate value and time t, and is expressed as hxt(,) a sin(- kxct ), where a is wave amplitude, k is wave number ( k  2/, where  is wavelength), and c is phase speed of the wave. The sea wave was non-evolving, so all wave parameters including wave amplitude, wavelength and phase velocity did not change with time. In addition to wave amplitude, another important parameter discussed is wave age, which is defined as

  cU/ b , where U b is a representative velocity of the air. Wave age describes the evolution state of a sea wave. Take the sea at a location experiencing a typhoon as an example to explain the meaning of wave age. A sea wave emerges and grows under the stimulation of strong wind with 01 (wave follows wind), and gradually gains phase speed until it finally turns into a mature sea with large phase speed. When the typhoon eye approaches, the wave may move faster than the wind due to the reduction of wind speed, i.e.   1 (wind follows wave). It is also possible for the wind direction to reverse after passage of the typhoon eye and yield negative wave age   0 (wave opposes wind). Figure 8a decipits the instantaneous turbulence structure, expressed by a indicator of vortex structure 2 , over a stationary wave. Comprared with Figure 8a, it can be found that the

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(a) c/Ub = 0.0 (b) c/Ub = 1.0 (wave follows wind)

(c) c/Ub = 1.5 (wind follows wave) (d) c/Ub = -1.0 (wave against wind) Figure 8. Instantaneous turbulent structure over simplified sea surface (a/ = 0.05)

ξ=0.025 ξ=0.025 4.0 0.6 ξ=0.050 ξ=0.050 ξ=0.075 ξ=0.075 3.5

0.4 g h

α 3.0

0.2 2.5

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 β β (a) Power law index (b) Gradient height Figure 9. Variations of power law index and gradient height with wave age

0.20 0.30 ξ=0.025 ξ=0.025 ξ=0.050 ξ=0.050 0.15 ξ=0.075 ξ=0.075 0.20 * 0 0.10 u h 0.10

0.05 0.00

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 β β (a) Roughness length (b) Friction velocity Figure 10. Variations of roughness length and friction velocity with wave age turbulence structures are surpressed when wave follows wind, as shown in Figure 8b, but it is enriched when wind follows wave (Figure 8c) and developed to higher locations when wave moves against wind as shown in Figure 8d. Meanwhile, the change of gradient height and power law index, and the change of roughness length and friction velocity with wave age at different wave amplitudes, are illustrated in Figure 9 and Figure 10, respectively. Figure 9a shows that, for all three investigated wave amplitudes, the power law index exhibits a smallest value at around  =0.75, rather than at  =0 (static waves). When the wave moves downstream slower ( 01 ) or a little faster than air (11.5   ), the power law index is smaller than that of a static wave. When the wave moves downstream much faster than air (   1.5 ) or moves against wind (   0 ), the power law index is greater than that of a static wave and increases with increase in the absolute value of wave age. It is also shown in Figure 9a that the power law index increases with increase in wave amplitude when the wave age is fixed. As for the results of the gradient height, Figure 9b shows that the lowest gradient height appears at around  =0.75 also at all three investigated wave amplitudes. The gradient height increases when the wave age becomes smaller or greater than 0.75, and increases with increase in wave amplitude. The variations of power law index and gradient height with wave age consistently show that, when the velocity difference between the wave and air is small, the wave plays a lesser aerodynamic role as surface roughness than a static wave in determining the structure of the boundary layer. However, the wave plays a greater aerodynamic role when the velocity difference becomes more obvious. This aerodynamic behavior of moving waves is also indicated in Figures 10a and 10b, in which the roughness length and friction velocity possess smallest values at around  =0.5.

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4. CONCLUSION This paper reviews phenomena of major concern in bridge aerodynamics: VIV, galloping, flutter and buffeting, with a particular attention to turbulence effects. The analytical, wind tunnel and CFD approaches to generate turbulence that are necessary for studying the turbulence effects are discussed also. This paper shows that either qualitative or quantitative understanding of the turbulence effect, particularly the mechanism behind, is surprisingly insufficient. Although turbulence might help the stabilization of long-span bridges and thus it is not a conclusive parameter for wind-resistant design, the turbulence effects on the aerodynamic and aeroelastic behavior of a bridge must be better understood because the interaction between the bridge and the turbulence always exists. Advanced modelling, both physical and numerical, of the turbuelnce are being performed in Tongji University, but unfortunately, the interaction between the generated turbulence with the bridge have not been conducted, which will be an emphasis of the future work.

ACKNOWLEDGMENTS The author gratefully acknowledge the support of National Key Basic Research Program of China (i.e.973 Program) (2013CB036300), and the National Natural Science Foundation of China (91215302 and 51323013).

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14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015