An Experimental Study on Dynamics Features of Three Side-by-Side Flexible Risers Undergoing Vortex-Induced Vibrations in A Uniform Flow

A vortex-induced vibration (VIV) experiment on three side-by-side risers subjected to a uniform flow was carried out in a combined wave-current flume. The dynamic features of interference effect on three side-by-side risers were investigated by varying fluid velocity and inter-riser spacing. The distributions of dimensionless displacement, dominant frequency, and displacement trajectory of the model risers were measured using mode decomposition and wavelet transform techniques. The coupled interference of inter-riser fluid to adjacent risers at different spacings was disclosed by introducing the “interference ratio” concept. The results show that at spacings smaller than 6.0D, the three model risers display appreciable deviations in their displacement responses in cross-flow or in-line direction, attributable to the strong proximity disturbance and wake interference between the risers. When the spacing is increased to 8.0D, wake interference still makes great difference to the dynamic response of the risers in both directions. As reduced velocity increases, the three risers show higher agreement with an isolated riser in overall dominant vibration frequency in CF direction than that in IL direction at all spacings and the side risers, although symmetrically placed, do not vibrate symmetrically, as a result of the steady deflection of clearance flow within the riser group. Interference effect results in a remarkable unsteady mode competition within the risers; quantitation of the interference levels for the three risers at different spacings with interference ratio revealed that under low flow velocities and large spacing ratios, clearance flow constitutes a non-neglectable interferer for three side-by-side risers.


Introduction
Floating oil production systems (such as tension leg platform (TLP), Spar and FPSO) have become better choices for deepwater development. Slender columnar structures such as risers, steel bars and cables are used as key components of floating oil production systems. In the production of oil and natural gas, multiple risers (cylinders) are usually used, and most of them use "tandem", "side-byside", and "staggered" arrangements, so the interaction of multiple risers under VIV is very complicated, of which, the side-by-side arranged double risers (cylinders) can be regarded as one of the most typical examples of the riser (cylinder) system. In order to better understand the interference effects, some researchers have carried out experimental research and numerical simulations on the dynamic and hydrodynamic characteristics of double risers (cylinders) in side-by-side arrangement (Sumner et al., 1999;Hu and Zhou, 2008;Li and Sumner, 2009;Huera-Huarte and Gharib, 2011;Bao et al., 2013;Xu et al., 2018a;Liu et al., 2019).
Compared with two risers (cylinders) in side-by-side arrangement, three risers (cylinders) in side-by-side arrangement are more common in practical engineering applications (such as a set of risers, a set of cables, and a set of stress bars). It can be inferred that more complex wake and VIV characteristics may be observed when the three risers (cylinders) in side-by-side arrangement vibrate, which cannot be predicted by the knowledge of the two risers (cylinders) in side-by-side arrangement. For the experimental study of three cylinders in side-by-side arrangement, Eastop and Turner (1982) observed quasi-stable behavior of the flow around three cylinders in side-by-side arrangement at S/D=1.375 and Re =0.45×10 4 −1.11×10 5 . In their physical simulations on flow around three side-by-side cylinders for large Reynolds numbers (Re=10000−32000), Kumada et al. (1984) grouped wake patterns into four classes. When Re = 2500, Guillaume and LaRue (1999) found three quasi-stable modes at S/D = 0.338−0.730, one quasi-stable mode at S/D = 0.730−0.850, and one stable mode at S/D =0.850−1.202. Zhou et al. (2000) experimentally studied the complex turbulent wakes generated when three cylinders of equal spacing were in side-by-side arrangement, and the results showed that the lateral distribution of Reynolds normal stress was asymmetric with a smaller ratio of spacing to diameter. On this basis, Zhang and Zhou (2001) experimentally investigated the wake effects behind three side-by-side cylinders with unequal spacings and discovered that at small separation ratios, their flowing behavior turned from symmetric to asymmetric. From physical simulations on three side-by-side cylinders for small Reynolds numbers (Re= 300−1500) and spacing ratio of 1.5, Wang et al. (2002) identified that at equal spacings, the wake is symmetric about the flow direction and a narrow-wide-narrow wake pattern is produced. In addition, Zhou (2003) studied the vortex structure of three side-by-side cylindrical turbulent wakes with a spacing of 1.5D. It was reported that the vortex structure in narrow wakes may be generated by the shear layer separation of the upper and lower cylinders. The vortex structure in wide wake may be caused by the instability of the shear layer. Akilli et al. (2004) observed three sideby-side cylindrical asymmetric flow structures with a small spacing ratio (S/D=1.25), and symmetrical flow structures with an intermediate spacing ratio (1.5≤S/D≤2.0). Ozgoren and Dogan (2012) used particle image velocimetry (PIV) to study the instantaneous and time-averaged flow field structure downstream of the three square columns in side-by-side arrangement with different spacing ratios (1.0≤G/D≤3.0) under a uniform flow, and found that when the ratio was smaller than 2.0, an asymmetric and biased wake structure was formed. Furthermore, Xu et al. (2018b) conducted a FIV test study of a 6.0D spacing between three-and four-cylinder systems in side-by-side arrangement, and the results showed that the multi-modal response characteristics of the three-cylinder system arranged side by side were significantly different from those of the four-cylinder system due to the effect of complex wake flow behind the cylinders. Sooraj et al. (2019) analyzed the flow field around three side-by-side cylinders at different sapcing ratios (1.5≤S/D≤4.0) and Reynolds number (90≤ Re≤560). The structure of the instantaneous and time-aver-aged flow field was presented.
Numerical simulation was conducted to study the influence of the spacing between three or more cylinders on the wake structure, force and vortex shedding pattern, and many excellent reports have appeared in recent years. Kang (2004) numerically studied the wake of three side-by-side cylinders at Re = 100 and S/D<6.0. Five wake patterns with different pitch ratios were found in the numerical study. Han et al. (2013a) used a three-step Taylor-characteristicbased-split (3-TCBS) Galerkin finite element (FE) method to study the laminar flow problem of three side-by-side cylinders, systematically classified wakes under different spacing ratios, and gave their relationship with Reynolds number and spacing ratio. In the following year, Han et al. (2013b) carried out a numerical study on the flow around a square cylinder with Re = 200 by a spectral element method, and the numerical results showed that about three wake patterns were related to the spacing ratio. Islam et al. (2018) and Rahman et al. (2018) used the lattice Boltzmann method (LBM) to study the relationship between the flow structure of side-by-side tripartite cylinders and Reynolds number and separation ratio. Alam et al. (2017) numerically simulated the flow around four side-by-side cylinders using the finite volume method (FVM), and systematically studied how wake structure, forces, and vortex shedding patterns depend on the spacing ratio. Islam et al. (2018) numerically simulated the flow of five side-by-side rectangular columns in the range of spacing ratio 0.5−5. In addition to spacing ratio of 0.5, modulation occurred in the time-history analysis of the drag coefficient and lift coefficient in all selected cases.
Compared with rigid cylinders, the dynamic response of flexible risers (cylinders) has many additional complex characteristics, such as modal competition, multi-frequency response, and time-sharing characteristics (Facchinetti et al., 2004;Vandiver et al., 2009). The VIV response of flexible risers (cylinders) is more complicated due to the change in span. Based on the above explanations, although some studies on the side-by-side three risers (cylinders) wake flow field have been published, little attention has been paid to the flexible side-by-side risers VIVs with different spacings, and there is a lack of data on the dynamic response of the side-by-side three risers (cylinders). The coupling mechanism between the dynamic response and the spacing of flexible riser group structures is not clear. The main purpose of this paper is to study the dynamic response of non-linear superposition of multiple wake fields to the structure by changing the multi-stage outflow velocity, riser spacing compared with the dynamic response of isolated analysis, to explore the coupling interference mechanism and dynamic feedback mechanism of the fluid flow between two adjacent risers with three risers arranged side-by-side at different spacings, provide data support for the basic numerical model of riser group, and provide scientific basis for indus-trial design of riser group.
The remainder of this article is arranged as follows: Section 2 elaborates on the test apparatus and experimental details; Section 3 analyzes the root mean square (RMS) dimensionless displacements, dominant frequencies, dominant modes, and displacement trajectories of the three model risers and discusses the experimental results; Section 4 gives some conclusions from the experiment.

Description of the experiment
The experiment was carried out in the combined wavecurrent flume of the Engineering Hydrodynamics Laboratory, Ocean University of China. The flume dimension of 30.0 m×1.2 m×1.0 m (L×W×D), with maximum external flow velocity of 1.0 m/s, can control the flow system to adjust the size of the external flow velocity, so that a uniform flow field with different flow velocities can be produced, and the accuracy of the uniform flow field can meet the requirements of the test. The test apparatus, as illustrated in Fig. 1, consists of a supporting structure, a model riser group, and a top tension system. The supporting structure with the dimension of 3.00 m×0.98 m×2.92 m, designed and developed by the project team members independently and specifically for the experiment, is attached to the flume by high-strength bolts and fasteners to ensure that it works reliably in a uniform flow.
The riser model, 18.0 mm in diameter, has plexiglass tubes (PMMA) with effective length 2.0 m and aspect ratio L/D=111.11. During the experiment, the three model risers stood in side-by-side arrangement, with 40% of the riser length immersed in the flume in a uniform flow (Chaplin et al., 2005;Bearman, 2009a, 2009b;Guo et al., 2006), as shown in Fig. 2. In order to obtain the natural frequency of the riser, the riser model was placed in still water, and applied periodical transient excitations to the riser. After the excitation had been released, we observed how the riser vibration decayed and obtained the strain time histories corresponding to the decay signals. Through FFT transform, we yielded the natural frequency spectrum curve of the riser. The natural frequency of the smooth riser was f 1 =3.30 Hz. Detailed parameters of the model risers are given in Table 1. To ensure identical physical dimensions and mechanical properties between the model risers, the tubes were fabricated to calibration, and sampled for a number of times at the tube mill to our satisfaction.
The model risers are attached to the aluminum alloy fixing plates at the ends of the supporting structure with universal joints, with allowances for hinged boundaries that allow free vibration of the risers in both CF and IL directions. The upper universal joints are connected to a tensiometer, a guide screw, a steel strand, and a self-locking tensioner. To increase the rigidity of the upper fixing structure for the risers and maintain identical top tension between the three risers, two aluminum alloy plates with the same dimensions and hole positions are used and connected to each other on the periphery by high-strength bolts. A tensioner applies tension to the risers by towing the steel strand. When the tensiometer reading arrives at the predefined value, the tensioner is automatically locked. The upper and lower fixing plates are locked by screw lock nuts to doubly ensure that the loads on both ends of the risers are stable in face of violent vibration. The experimental arrangement is shown in Fig. 3. Furthermore, the laser level gauge was multi-directionally calibrated to confine the fiber bragg grating (FBG)   sensors on the risers in the predefined positions and thereby improve the accuracy of the data sampled.
To examine how inter-riser spacing (S) affects the coupled interference within a three-riser group in side-byside arrangement, five spacings, namely, S=3.5D, 4.0D, 5.0D, 6.0D, and 8.0D, were designed for the experiment. As recommended by Zdravkovich (1988), the inter-riser spacings selected herein are those within the interval where there is or is not proximity disturbance. Furthermore, to gain a better insight into whether strong synchronization exists in the vibration amplitude among the three risers with increasing inter-riser spacing (Sanaati and Kato, 2014), a comparative test was conducted on an isolated riser using a larger spacing, S=8.0D, as reference for the riser group tests. The three risers were identified, from the nearer to the farther end, as Riser #1, Riser #2, and Riser #3. In the experiment, Doppler velocimeter was used to measure external flow velocities. This instrument has a measurable flow velocity range of ±0-4 m/s, a precision range of ±0.5%±1 mm/s, a sampling output frequency of 1-200 Hz, a sampling site distance to probe of 0.05m, a diameter of 6 mm, a height of 3-15 mm, an acoustic frequency of 10 MHz, and an intensity range of 25 dB. The experiment was conducted for flow velocities (U) of 0.1−0.6 m/s over ten incremental levels, and corresponding reduced velocities (U r ) of 1.68−10.10. A total of 60 experimental cases were involved. The overall arrangement of the experiment and the experimental cases involved are given in Table 2. FBG sensors were used to measure the coupled vibra-tion behaviors of the three model risers. 24 FBG sensors were used for each model riser and mounted in directions CF1, CF2, IL1, and IL2 (as illustrated in Fig. 4). Six sensors were mounted in each of the two CL directions, marked as G01−G06, to measure the CF vibration of the riser; six were mounted in each of the two IL directions, marked as G07−G12, to measure the IL vibrations of the riser. The coordinates of G01 (G07) and G06 (G12) are 0.25 m and 1.75 m, with four evenly distributed measuring points deployed in between at 0.30 m intervals. With the extremely low bending stiffness of bare optical strings, the FBG measuring points were calibrated immediately before they were passed. A demodulator was attached during the pasting process to measure the oscillograph of these points on real-time basis.

Results and discussion
3.1 Displacement response of three side-by-side risers with different separation distances Fig. 5 shows the RMS dimensionless displacements of the three side-by-side risers in CF and IL directions as a function of reduced velocity. To facilitate comparison, the experimental data of the isolated riser are also indicated in the diagrams. First, in CF direction, as can be observed from Figs. 5a−5c, at S=3.5D, the RMS displacement of Riser #1 was lower than that of the isolated riser across all reduced velocities tested; the same happened in IL direction, too. Within the S=4.0D−6.0D interval, under U r ≤7.58, the RMS displacement of Riser #1 varied in roughly the same way; as  LIU Yu et al. China Ocean Eng., 2020, Vol. 34, No. 4, P. 500-512 503 reduced velocity further increased, within the 8.42≤U r ≤ 10.10 interval, the three risers displayed obviously divergent displacement variations at all spacing levels. Under U r =10.10, in particular, the RMS displacement of Riser #1 dropped abruptly at S=4.0D and S=5.0D; the same happened to Riser #2 and Riser #3. These decreases are helpful for further transformation of the risers' vibration mode. At S=8.0D, the RMS displacement under U r ≤4.20 was obviously higher than that of the isolated riser at any other spacing. This indicates that at large spacings, instead of reducing the displacement response of Riser #1, the interference effect between the three risers further increased its displacement. This is different from the displacement response mechanisms observed by Xu et al. (2018c) from a two-cylinder system. Furthermore, as can be observed, while Riser #1 and Riser #3 were symmetric in structural space, their displacement responses were asymmetric within the spacing interval tested. These differences are possibly attributable to the interference of clearance flow between the three risers, which led to an instability in the vortex shear layer behind the risers and produced wakes of varying widths behind the risers Alam et al., 2003) that disrupted the vibration displacement symmetry between the side risers (Riser #1 and Riser #3). For Riser #2, which was exposed to clearance flow from both Riser #1 and Riser #3, within the 4.20≤U r ≤7.58 interval, its RMS displacement was higher than that of the isolated riser for all spacings. This is attributable to the normal superimposition of wake vortex shedding behind Riser #1 and Riser #3 with that behind Riser #2. Within this reduced velocity interval, at S=3.5D, the RMS displacement of Riser #2 was higher than that at other spacings; within the S=4.0D−8.0D interval, the displacement distribution of this riser varied in roughly the same manner. As shown in Figs. 5e−5f, the RMS displacements were more discrete in IL direction than those in CF direction for all spacings tested; Riser #1 and Riser #3 reached their displacement peaks 0.38D and 0.36D, respectively, under U r =9.26, whereas Riser #2 reached its displacement peak 0.37D under U r =8.42. This indicates that the three risers almost shared the same maximum displacement amplitude in IL direction. For the isolated riser, however, its peak displacement under U r =10.10 was 0.33D. Moreover, a displacement asymmetry is also observed between Riser #1 and Riser #3, which is attributable to the same reason explained for what happened in CF direction. As analyzed above, interference effect from the three side-by-side risers can increase their displacement responses in CF direction but reduce their displacement responses in IL direction.
From the above analysis, it can be seen that in the CF direction, when S=3.5D, the displacement amplitude of both side risers remains low, while the displacement amplitude of the intermediate riser is high at this spacing. When S= 4.0D, 5.0D and 6.0D, with increasing spacing, the three risers all showed a similar variation trend, except that the displacement amplitudes of Riser #1 and #2 are higher than that of Riser #3. When S=8.0D, the interference effect still exists. The displacement amplitudes of both sides of risers are higher than those of the remaining spacings, and the displacement amplitude of the intermediate riser is less differ- ent from that of the remaining spacings. In the IL direction, when S= 3.5D, the displacement amplitude of Riser #1 remains low, and the displacement amplitudes of Risers #2 and #3 are approximate to those of S= 4.0D, 5.0D and 6.0D, with a relatively consistent change trend. When S = 8.0D, compared with other spacings, the displacement amplitudes of both sides risers varied around the isolated riser, while the displacement amplitude of the intermediate riser is higher than that of the isolated riser. At high reduced velocity, the vibration displacement of the three risers at different spacings decreases to different degrees in the two directions. In addition, it is found that the three risers in side-by-side arrangement can enhance the displacement response in the CF direction and weaken the displacement response in the IL direction under the interference effect.

Coupling effect of Riser #2
In practical marine engineering application, even more complicated phenomena will be found in the fluid flow of three side-by-side risers, whereas Riser #2, as the intermediate riser, can arouse even large proximity disturbance to the side risers at small spacings. Next, the paper is going to look at the dynamic responses of Riser #2. Here, Fig. 6 and Fig.  7 compare the dynamic responses of Riser #2 under U r =9.26 with those of the isolated riser for typical spacing at S=3.5D, wherein the black dotted line denotes the RMS displacement and the red dash-dotted line denotes the maximum displacement. In CF direction, the dominant mode of both the isolated riser and Riser #2 of the three-riser group was first order, with the modal weights correspond to the maximum values being 1.10D and 1.50D, respectively. This suggests that under U r =9.26, proximity disturbance from the LIU Yu et al. China Ocean Eng., 2020, Vol. 34, No. 4, P. 500-512 505 side risers added to the vibration of Riser #2. Besides, we can see that the isolated riser had a fairly high first and second modal weight, with obvious second vibration pattern. Mode switching occurred at this point as a result of intense first and second mode competition. The displacement time histories at measuring points z/L=0.125, 0.575, 0.725, and 0.875 are "bimodal", as marked by the elliptical boxes in Fig. 6, and the displacement amplitudes at all measuring points remained fairly stable across the timescale. When we look back at Riser #2 of the three-riser group, we will see an irregularity and non-periodicity in its modal weight and dimensionless displacement in the same time domains, as marked by the elliptical boxes in Fig. 7. The first mode had a higher participation than that observed for the isolated riser, with maximum modal weight being as high as 1.5D. At smaller spacings, affected by clearance flow, the strong interaction between the three risers changed the vortex shedding pattern in the wake region for Riser #2, causing the vortices produced in the farther downstream region to combine into a separate wake under an in-phase effect. The strong interactive flow structure at that time was primarily an in-phase structure (Islam et al., 2018). This explains why no "bimodal" pattern is observed from the displacement time histories of Riser #2 at any measuring point and its vibration trajectory was stronger than the first vibration mode and weaker than the second vibration mode of the isolated riser.
To obtain a better insight into the coupled vibration responses of the intermediate riser in CF and IL directions, Fig. 8 compares the spatial displacement trajectories of the  isolated riser with those of Riser #2 at different spacings, across the reduced velocities tested, as U r =1.68, the vibration amplitude of the riser is extremely small (≤0.005D). The space displacement trajectory of the riser at this flow velocity is not given herein. For the isolated riser, as illustrated in Fig. 8a, within the U r ≤3.36 interval, its displacement trajectories were quite small and looked like a "crescent". As reduced velocity increased, within the 4.20≤U r ≤ 10.10 interval, affected by the strong nonlinear coupling of lift force in CF direction with drag force in IL direction, its vibration trajectories grew into regular "8-shaped", which is similar to the x-y trajectory behavior observed by Vandiver et al. (2009) in their VIV tests on slender flexible risers. Existence of interference effect led to a deflection in the riser's trajectory and the reduced velocity under which a "8shaped" trajectory appeared for Riser #2 came later than that for the isolated riser at all spacings. Moreover, as can be observed, at S=5.0D, the "8-shaped" displacement trajectory for Riser #2 first appeared under U r =7.58 and these figures are symmetric about spacing S=5.0D, as marked by the dotted line in Figs. 8b−8f. As reduced velocity further increased, within the 9.26≤U r ≤10.10 interval, Riser #2 displayed an irregular "rod" or "crescent" vibration pattern at all spacings. The unsteady coupling of the vibration frequency of Riser #2 in CF with that in IL directions (Kheirkhah et al., 2012) under these velocities disrupted the two-fold relationship. More detailed analysis is presented in Section 3.3. From the displacement trajectories, at S=6.0D and S=8.0D, Riser #2 had still maintained the strong interference effect from Riser #1 and Riser #3 across the reduced velocities tested, especially when reduced velocities were high. This indicates that under large spacings and high velocities, the intermediate riser was still exposed to multiple high-order harmonic components.
3.3 Dominant frequencies and dominant modes with respect to displacement Fig. 9 compares the dimensionless dominant frequency f s /f 1 of the isolated riser and the three risers in CF and IL directions as a function of reduced velocity. It is noted that dominant frequency f s is deemed as the frequency corresponding to the maximum peak in the power spectral density diagram yielded from FFT (Xu et al., 2018a). In CF direction, the dimensionless dominant frequency f s /f 1 of the isolated riser became approximately linear with increasing reduced velocity. As can be detected from Figs. 9a, 9c, and 9e, in the presence of interference effect, when clearance flow passed the riser, the input of high-momentum fluid enhanced the pressure behind the riser, resulting in an unsteady vibration frequency for Riser #1, Riser #2, and Riser #3 at S=3.5D and 4.0D; S=3.5D, 4.0D and 8.0D; and S=3.5D, 4.0D, 5.0D, and 8.0D, respectively. Interestingly, at S=6.0D, the dominant vibration frequencies of the three risers became highly consistent with that of the isolated riser. This suggests that at this spacing, inter-riser clearance flow did not make much difference to the vortex shedding frequency behind the risers. In IL direction, as illustrated in Figs. 9b, 9d, and 9f, irregular frequency variations can be observed in Riser #1 relative to the isolated riser at all spacings tested, especially at S=3.5D and 8.0D. The same happened to Riser #2 at S=5.0D. As to Riser #3, its dominant frequency variation was approximately linear as a function of reduced velocity at all spacings and the trend remained stable. Fig. 10 shows the first four modal weights in the CF and IL directions of the isolated riser and the three-riser group at S=3.5D, and the ordinates are the modal weights of 1, 2, 3, and 4, respectively. It should be noted that the magnitude of Fig. 9. Dimensionless dominant frequencies in both the CF and IL directions versus relative reduced velocity for risers with different cases. the ordinate of the third and fourth order modal weights is reduced in Fig. 10 to increase the visibility of higher-order modal weights.
By comparing the CF and IL directions, it is found that the change trend of the first-order modal weight of each riser is very close to that of the riser displacement response, which better reveals the first-order modal dominants of the riser vibration. The modal weights of the three-riser group in the CF direction show different trends with the reduced velocity. Among them, the weight change of Riser #3 and the isolated riser is more consistent, and Riser #2 and Riser #1 have a larger deviation. This is because when S=3.5D, Fig. 10. First four modal weights of the three-riser group in CF (a, b, c, d) and IL direction (e, f, g, h).
LIU Yu et al. China Ocean Eng., 2020, Vol. 34, No. 4, P. 500-512 509 the interference effect between the three-riser group causes an unstable wide and narrow wake inside, which further illustrates the asymmetry of the vibration displacement of Risers #1 and #3. In addition, it can be found that when 6.73 ≤U r ≤ 10.10, the second-order to fourth-order modal weights are more discrete, which can be attributed to the interference effect that causes the riser to have obvious unstable modal competition. In the IL direction, the first-order modal weights of the three-riser group are highly discrete, and their peaks appear at U r =8.42, which are 0.19D, 0.31D, and 0.26D, respectively. When 1.68≤U r ≤8.42, the secondorder modal weights of the three-riser group present a similar trend with the isolated riser, while when 9.26≤U r ≤ 10.10, different change trends occur, especially when the weight value of Riser #2 exceeds that of the isolated riser.
The third-to fourth-order modes of the three-riser group have low participation in the entire reduced velocity experimental interval, and their weight change trends are stable.
3.4 Interference ratio of three side-by-side risers with different separation distances To further quantify the proximity disturbance between the three risers at different spacings, an "interference ratio" concept was introduced herein. Here, interference ratio (I) is defined as the ratio of the RMS dimensionless displacement of individual risers of the three-riser group in CF or IL direction and the RMS of the dimensionless displacement of the isolated riser at the corresponding reduced velocity to the RMS dimensionless displacement of an isolated riser under the same reduced velocity. Fig. 11 compares the interference ratios of the three risers in CF and IL directions over the reduced velocity interval tested for different spacings. Under U r ≤3.36, the interference ratio of Riser #1, Riser #2, and Riser #3 were higher than 100% at some particular spacings, which largely enhanced the vibration displacement of the risers, and all maximums of the risers occurred at S=8.0D. This indicates that under low velocities, inter-riser fluid imposes greater interference effect on the adjacent risers; under low velocities and large spacings, the interference effect of clearance flow on riser groups is therefore never neglectable. Within this reduced velocity interval, the discretization under low velocity effect in IL direction is higher than that in CF direction, as marked by the red rectangular boxes in Fig. 11. Within the 4.20≤U r ≤6.73 interval, as the reduced velocity increased, the interference ratios of the three risers in CF direction at different spacings continued to concentrate from the sides toward the center; that of Riser #2 remained relatively high at S=3.5D. When 7.58≤U r ≤9.26, as can be observed, Riser #1 behaved much differently at S=3.5D from that at other spacings. Fig. 11. Interference ratio of the three-riser system in the CF (a) and IL (b) directions versus the reduced velocity.
Within the three-riser group, existence of wide and narrow wakes behind Riser #1 and Riser #2 deteriorated the displacement amplitude of Riser #1. Under U r =10.10, interference I remained in the reduced-vibration region for all risers at all spacings except Riser #2 at S=8.0D.
In IL direction, as illustrated in Fig. 11b, it is observed that under U r ≤3.36, low velocity effect also occurred to interference ratio. As the reduced velocity increased, the interference ratio distribution was different from that in CF direction within the 4.20≤U r ≤10.10 interval and remained in the reduced vibration region for the majority of the cases. This further verifies the differential displacement responses of the inter-riser fluid within the three-riser group between the two directions. At S=3.5D, the interference ratio of Riser #1 stayed at a relatively low level within the 5.05≤U r ≤ 9.26 interval, especially under U r ≤9.26, when the interference ratio of this riser dropped to −68.79%. Combination of the effects from both Riser #2 and Riser #3 limited the uprolling of the separated shear layer of Riser #1, preventing it from producing strong vortex shedding. This flow phenomenon was kept over a fairly long reduced velocity interval. Under U r =10.10, roughly the same happened to the interference ratio in IL direction.

Conclusions
A VIV experiment on a three-riser group in side-by-side arrangement was carried out in a combined wave-current flume for five different spacings. The effects of fluid velocity and inter-riser spacing on the vibration responses of risers were investigated by comparing the dominant frequencies, RMS dimensionless displacements and displacement trajectories of the three risers at different spacings. Based on the experimental results, the following conclusions can be drawn.
(1) The vibration responses of a three-riser group in CF and IL directions are different from those of an isolated riser. At spacings smaller than 6.0D, obvious proximity disturbance exists in CF direction, especially at 3.5D, when normal superimposition of wake vortex shedding from the side risers causes the displacement amplitude ratio of the intermediate riser in CF direction to remain higher than those of the side risers under all reduced velocities. At S=8.0D, a strong coupling still exists within the three-riser group in both directions. The side-by-side arrangement of the threeriser group results in obvious disturbance to the flow field, increasing the displacement in CF direction but reducing that in IL direction.
(2) As the reduced velocity increases, the input of highmomentum fluid enhances the pressure behind the risers, causing the dominant frequencies of the three risers no longer stable at particular spacings. The overall variation of dominant vibration frequency of a three side-by-side risers group is more consistent with that of an isolated riser in CF direction than in IL direction. Because of the interference of the riser wake on the two sides of the three risers on the intermediate riser, the intermediate riser entered the lock-in region at a reduced velocity later than that for the isolated riser.
(3) Existence of double interference from the side risers causes the displacement trajectory of the intermediate riser to deflect at all spacings; the "8-shaped" trajectory occurs at a later reduced velocity than that for an isolated riser. Furthermore, under high velocities and small spacings, interference effect can cause the vortex shear layer behind the riser to become unstable and produce wakes of varying widths. This results in an irregularity and non-periodicity in the modal weight and dimensionless displacement in the corresponding time domain. The vibration trajectory is stronger than the first vibration pattern but weaker than the second vibration pattern for an isolated riser. This gives rise to a mode competition that locally constrains self-excitation.
(4) An "interference ratio" concept is used to quantify the degree of proximity disturbance within the three-riser group for different spacings. At reduced velocities smaller than 3.36, the vibration displacements of the three risers in CF direction largely increase and all maximums appear at S=8.0D; the same low velocity effect also occurs in IL direction. Hence, with low velocities and large spacings, the interference effect of clearance flow is never neglectable. Within the 4.20≤U r ≤6.73 interval, the interference ratios of the three risers in CF direction continue to concentrate from the sides toward the center; as the reduced velocity further increases, the interference ratio continues to decline. In IL direction, the interference ratio distributions are different from those in CF direction within the 4.20≤U r ≤10.10 interval and the three risers stay in the reduced vibration region for most of the cases.
(5) Steady deflection of clearance flow within the riser group results in an asymmetry in the vibration responses between the symmetrically placed side risers at all spacings. Within the asymmetric vibration region, the vibration difference between the side risers is considerable and the displacement amount is remarkably different between the two risers. More importantly, this difference exists across a very wide range of the reduced velocity. This observation would be of reference value to practical engineering applications such as load calculation and collision protection design for marine riser bundles.