Journal of Marine Science and Engineering

Editorial

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2 pages, 156 KiB

Open AccessEditorial

Waves and Ocean Structures

by Jaw-Fang Lee and Ray-Yeng Yang

J. Mar. Sci. Eng. 2021, 9(3), 305; https://doi.org/10.3390/jmse9030305 - 9 Mar 2021

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Abstract

This Special Issue concentrates on the problems of interactions between water waves and ocean structures [...] Full article

(This article belongs to the Special Issue Waves and Ocean Structures)

Research

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18 pages, 7997 KiB

Open AccessArticle

Dynamic Amplification of Gust-Induced Aerodynamic Loads Acting on a Wind Turbine during Typhoons in Taiwan

by Tsung-Yueh Lin, Chun-Yu Yang, Shiu-Wu Chau and Jen-Shiang Kouh

J. Mar. Sci. Eng. 2021, 9(4), 352; https://doi.org/10.3390/jmse9040352 - 24 Mar 2021

Cited by 1 | Viewed by 2680

Abstract

Typhoons, such as Soudelor, which caused the collapse of several onshore wind turbines in 2015, pose a considerable challenge to Taiwan’s wind energy industry. In this study the characteristics of the aerodynamic loads acting on a wind turbine due to wind gusts in [...] Read more.

Typhoons, such as Soudelor, which caused the collapse of several onshore wind turbines in 2015, pose a considerable challenge to Taiwan’s wind energy industry. In this study the characteristics of the aerodynamic loads acting on a wind turbine due to wind gusts in a typhoon are studied with a view to providing a proper definition of the S-Class wind turbine proposed in International Electrotechnical Commission (IEC) 61400-1. Furthermore, based on analysis of wind data during typhoons, as obtained from the meteorological mast in the Zhangbin coastal area, an extreme wind speed and gust model corresponding to the typhoon wind conditions in Taiwan are herein proposed. Finally, the flow fields around a parked wind turbine experiencing both an unsteady gust and a steady extreme wind were simulated by a numerical approach. Numerical results show that the aerodynamic shear force and overturning moment acting on the target wind turbine in a steady wind are significantly lower than those under an unsteady gust. The gust-induced amplification factors for aerodynamic loadings are then deduced from numerical simulations of extreme wind conditions. Full article

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21 pages, 8010 KiB

Open AccessArticle

Study on an Oscillating Water Column Wave Power Converter Installed in an Offshore Jacket Foundation for Wind-Turbine System Part I: Open Sea Wave Energy Converting Efficiency

by Hsien Hua Lee, Guan-Fu Chen and Hsiang-Yu Hsieh

J. Mar. Sci. Eng. 2021, 9(2), 133; https://doi.org/10.3390/jmse9020133 - 28 Jan 2021

Cited by 8 | Viewed by 3802

Abstract

This study is focused on the wave energy converter of an oscillating water column (OWC) system that is integrated with a jacket type infrastructure applied for an offshore wind turbine system. In this way, electricity generation by both wind power and wave power [...] Read more.

This study is focused on the wave energy converter of an oscillating water column (OWC) system that is integrated with a jacket type infrastructure applied for an offshore wind turbine system. In this way, electricity generation by both wind power and wave power can be conducted simultaneously to maximize the utilization of sustainable energy. A numerical analysis was performed in this research to model and simulate the airflow response and evaluate the converting efficiency of wave energy from an OWC system integrated with an offshore template structural system. The performance of the system including the generating airflow velocity, air-pressure in the chamber, generating power and then the converting efficiency of power from waves are all analyzed and discussed in terms of the variations of the OWC system’s geometrical parameters. The parameters under consideration include the exhale orifice-area of airflow, gate-openings of inflow water and the submerged chamber depth. It is found that from the analytical results the performance of the OWC wave energy converter is influenced by the dimensional parameters along with the design conditions of the local environment. After a careful design based on the in-situ conditions including water depth and wave parameters, an open OWC system can be successfully applied to the template structure of offshore wind power infrastructure as a secondary generating system for the multi-purpose utilization of the structure. Full article

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17 pages, 9883 KiB

Open AccessArticle

Visualization Investigation of Energy Dissipation Induced by Eddy Currents for a Solitary-Like Wave Passing over Submerged Breakwater Sets

by Chi-Yu Li, Ruey-Syan Shih and Wen-Kai Weng

J. Mar. Sci. Eng. 2020, 8(11), 834; https://doi.org/10.3390/jmse8110834 - 22 Oct 2020

Cited by 4 | Viewed by 2414

Abstract

Wave attenuation for the purpose of coastal protection has been an important topic in coastal engineering. Wave attenuation in relation to the vortices induced by a solitary-like wave propagating over submerged breakwaters (BWs) is discussed in this paper. A series of hydraulic model [...] Read more.

Wave attenuation for the purpose of coastal protection has been an important topic in coastal engineering. Wave attenuation in relation to the vortices induced by a solitary-like wave propagating over submerged breakwaters (BWs) is discussed in this paper. A series of hydraulic model experiments was conducted to investigate the occurrence of eddies, the types and combinations of submerged BWs, and related phenomena of the range expansion of vortices. The microscopic changes in the flow field, the variation of eddies, and the distributions of streamlines were analyzed using the particle image velocimetry (PIV) technique. The measured transmission and reflection coefficients, along with the concept of energy conservation, were also examined to support the results. The results indicate that the attenuated wave energy is related to the induced vortices, and show that the total relative vortex energy for rectangular submerged BWs is larger than that for undulating submerged BWs in both the single and composite sets. The magnitude of the maximum vorticity of the undulating BW sets is larger and more concentrated than that of the rectangular BW sets; however, the total vortex energy is slightly smaller owing to the narrower vortex area range. Full article

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16 pages, 2226 KiB

Open AccessArticle

Dynamic Stability of an Ocean Current Turbine System

by Shueei-Muh Lin, Yang-Yih Chen, Hung-Chu Hsu and Meng-Syue Li

J. Mar. Sci. Eng. 2020, 8(9), 687; https://doi.org/10.3390/jmse8090687 - 6 Sep 2020

Cited by 10 | Viewed by 2228

Abstract

This paper presents a theoretical solution for the dynamic stability of the ocean current turbine system developed in Taiwan. This system is tethered to the sea floor and uses the Kuroshio Current to produce electricity. To maintain the performance of the turbine system [...] Read more.

This paper presents a theoretical solution for the dynamic stability of the ocean current turbine system developed in Taiwan. This system is tethered to the sea floor and uses the Kuroshio Current to produce electricity. To maintain the performance of the turbine system in the presence of the Kuroshio Current, the stability of the surfaced turbine needs to be considered. The proposed system is composed of a turbine, a buoyance platform, a traction rope, and a mooring foundation. The two-dimensional theoretical solutions treat the turbine as a rigid body with a movable structure that is moored with two cables. In this model, the gravity, buoyancy, and drag force generated by the wave on the turbine structure are considered. In addition, an analytical solution is proposed for the general system. Finally, the effects of the wave on the pitch motion and dynamical stability of the ocean current turbine system are investigated. Full article

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12 pages, 4040 KiB

Open AccessArticle

Wave Induced Effects on the Hydrodynamic Coefficients of an Oscillating Heave Plate in Offshore Wind Turbines

by Krish Thiagarajan and Javier Moreno

J. Mar. Sci. Eng. 2020, 8(8), 622; https://doi.org/10.3390/jmse8080622 - 18 Aug 2020

Cited by 18 | Viewed by 3818

Abstract

The research problem discussed in this paper is of relevance to floating offshore wind turbine design, where heave plates are attached to the columns of a semi-submersible in order to improve vertical plane stability and the power output. Because of the shallow draft [...] Read more.

The research problem discussed in this paper is of relevance to floating offshore wind turbine design, where heave plates are attached to the columns of a semi-submersible in order to improve vertical plane stability and the power output. Because of the shallow draft of these structures, the heave plates are proximal to the water surface. When subject to vertical plane motions the flow around a plate is altered by the presence of the free surface, resulting in changes in added mass and damping forces. In this paper, we present the experimental results for the added mass and damping coefficients for circular heave plates attached to a column, when oscillating in heave in the presence of oncoming waves. The results tend to indicate that applying the hydrodynamic coefficients obtained from still water experiments for a structure moving in waves may only be an approximation. For different relative phases of the wave and the motion, large variations could occur. We define a modified Keulegan—Carpenter (

K C

) number that depends on the relative amplitude of motion with respect to the wave. With this definition, the added mass and damping values are seen to be closer to the still water trends. However, at lower

K C

values, the added mass coefficients could differ by 30%, which can affect natural frequency estimates. Thus, caution needs to be exerted in the selection of hydrodynamic coefficients for heave plates oscillating in proximity to the free surface. Full article

(This article belongs to the Special Issue Waves and Ocean Structures)

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20 pages, 11985 KiB

Open AccessArticle

Power Prediction of Wind Farms via a Simplified Actuator Disk Model

by Yen-Cheng Chiang, Yu-Cheng Hsu and Shiu-Wu Chau

J. Mar. Sci. Eng. 2020, 8(8), 610; https://doi.org/10.3390/jmse8080610 - 16 Aug 2020

Cited by 3 | Viewed by 2697

Abstract

This paper aims to demonstrate a simplified nonlinear wake model that fills the technical gap between the low-cost and less-accurate linear formulation and the high-cost and high-accuracy large eddy simulation, to offer a suitable balance between the prediction accuracy and the computational cost, [...] Read more.

This paper aims to demonstrate a simplified nonlinear wake model that fills the technical gap between the low-cost and less-accurate linear formulation and the high-cost and high-accuracy large eddy simulation, to offer a suitable balance between the prediction accuracy and the computational cost, and also to establish a robust approach for long-term wind farm power prediction. A simplified actuator disk model based on the momentum theory is proposed to predict the wake interaction among wind turbines along with their power output. The three-dimensional flow field of a wind farm is described by the steady continuity and momentum equation coupled with a k-

ε

turbulence model, where the body force representing the aerodynamic impact of the rotor blade on the airflow is uniformly distributed in the Cartesian cells within the actuator disk. The characteristic wind conditions identified from the data of the supervisory control and data acquisition (SCADA) system were employed to build the power matrix of these typical wind conditions for reducing the computation demands to estimate the yearly power production. The proposed model was favorably validated with the offshore measurement of Horns Rev wind farm, and three Taiwanese onshore wind farms were forecasted for their yearly capacity factors with an average error less than 5%, where the required computational cost is estimated about two orders of magnitude smaller than that of the large eddy simulation. However, the proposed model fails to pronouncedly reproduce the individual power difference among wind turbines in the investigated wind farm due to its time-averaging nature. Full article

(This article belongs to the Special Issue Waves and Ocean Structures)

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20 pages, 4440 KiB

Open AccessArticle

An Experimental and Theoretical Study of Wave Damping due to the Elastic Coating of the Sea Surface

by Igor Shugan, Ray-Yeng Yang and Yang-Yih Chen

J. Mar. Sci. Eng. 2020, 8(8), 571; https://doi.org/10.3390/jmse8080571 - 29 Jul 2020

Cited by 2 | Viewed by 2185

Abstract

Flexible plates or membranes located on the sea surface can be effective for attenuation waves approaching the beach. The most efficient structures should be found through comprehensive research using developed experiments and theory. Our experimental work was focused on the wave propagation and [...] Read more.

Flexible plates or membranes located on the sea surface can be effective for attenuation waves approaching the beach. The most efficient structures should be found through comprehensive research using developed experiments and theory. Our experimental work was focused on the wave propagation and attenuation passing through floating elastic structures. The experiments were conducted at the wave flume of Tainan Hydraulics Laboratory, National Cheng Kung University, Taiwan. The experiment mainly analyzes the reflection coefficient, transmission coefficient and energy loss of the regular wave of intermediate water depth after passing through the elastic structure under different wave steepness and other different wave conditions. Our experiments also explore the comparison of energy dissipation effects and the differences in motion characteristics between different elastic plates and different plate fixing methods. Three elastic materials were tested in the experiments: Latex, cool cotton and polyvinyl chloride (PVC). A model of a thin elastic plate covering the sea surface was used to evaluate the effectiveness of the structure of the wave barrier. The results of experiments carried out in the wave flume were compared with theoretical predictions in a wide range of generated waves. Full article

(This article belongs to the Special Issue Waves and Ocean Structures)

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19 pages, 6150 KiB

Open AccessArticle

Bragg Reflections of Oblique Water Waves by Periodic Surface-Piercing and Submerged Breakwaters

by I-Fan Tseng, Chi-Shian You and Chia-Cheng Tsai

J. Mar. Sci. Eng. 2020, 8(7), 522; https://doi.org/10.3390/jmse8070522 - 16 Jul 2020

Cited by 15 | Viewed by 2786

Abstract

The Bragg reflections of oblique water waves by periodic surface-piercing structures over periodic bottoms are investigated using the eigenfunction matching method (EMM). Based on the assumption of small wave amplitude, the linear wave theory is employed in the solution procedure. In the step [...] Read more.

The Bragg reflections of oblique water waves by periodic surface-piercing structures over periodic bottoms are investigated using the eigenfunction matching method (EMM). Based on the assumption of small wave amplitude, the linear wave theory is employed in the solution procedure. In the step approximation, the surface-piercing structures and the bottom profiles are sliced into shelves separated by abrupt steps. For each shelf, the solution is composed of eigenfunctions with unknown coefficients representing the wave amplitudes. Upon applying the conservations of mass and momentum, a system of linear equations is obtained and is then solved by a sparse-matrix solver. The proposed EMM is validated by several examples in the literature. Then, the method is applied to solve Bragg reflections of oblique water waves by various surface-piercing structures over periodic bottoms. From the numerical experiments, Bragg’s law of oblique waves was used to predict the occurrences of Bragg resonance. Full article

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18 pages, 8817 KiB

Open AccessArticle

Structural Safety Analysis for an Oscillating Water Column Wave Power Conversion System Installed in Caisson Structure

by Hsien Hua Lee, Thung-Yeh Wu, Chung-You Lin and Yung-Fang Chiu

J. Mar. Sci. Eng. 2020, 8(7), 506; https://doi.org/10.3390/jmse8070506 - 9 Jul 2020

Cited by 5 | Viewed by 2634

Abstract

In this study, an alternative way, a so called caisson based type of oscillating water column (OWC) wave energy converting system was proposed to capture and convert wave energy. Since the caisson structure is constructed to protect the coastal line or ports, it [...] Read more.

In this study, an alternative way, a so called caisson based type of oscillating water column (OWC) wave energy converting system was proposed to capture and convert wave energy. Since the caisson structure is constructed to protect the coastal line or ports, it is important to know if a built-in associated OWC system will be a burden to affect the safety of the structure or it is safe enough to work appropriately. In this study, three steps of structural analysis were performed: firstly, the analysis for the structural safety of the whole caisson structure; secondly, performing the mechanic analysis for the chamber of the associated OWC system; and finally, performing the analysis for the wave induced air-pressure in the chamber under the design conditions of a local location during the wave-converting operation. For the structural safety analysis, a typical structural model associated with caisson breakwater was built and analyzed while the shape of the structure, material applied to the construction, and associated boundary conditions were all set-up according to the wave and structures. The motion and the strain distribution of the caisson structure subjected to designated waves of 50-year return period were evaluated and compared to the safety requirement by the code. For the analysis of the energy converting performance, a numerical method by using a theorem of unsteady Navier–Stokes equations in conservation form was used to analyze the proposed OWC model when the structure subjected to an incident wave of a 10-year return period. Full article

(This article belongs to the Special Issue Waves and Ocean Structures)

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27 pages, 15596 KiB

Open AccessFeature PaperArticle

Multiple TLDs on Motion Reduction Control of the Offshore Wind Turbines

by Po-Hung Yeh, Shao-Hua Chung and Bang-Fuh Chen

J. Mar. Sci. Eng. 2020, 8(6), 470; https://doi.org/10.3390/jmse8060470 - 24 Jun 2020

Cited by 12 | Viewed by 3814

Abstract

This study explores the damping effects of tuned liquid dampers (TLDs) on a monopile offshore wind turbine (OWT). The fluid–solid coupling of ANSYS was used to simulate the damping effect of a TLD on the structures. The environmental conditions refer to the IEC-61400-3 [...] Read more.

This study explores the damping effects of tuned liquid dampers (TLDs) on a monopile offshore wind turbine (OWT). The fluid–solid coupling of ANSYS was used to simulate the damping effect of a TLD on the structures. The environmental conditions refer to the IEC-61400-3 and the Design Load Case (DLC) 1.2 for the annual average environmental conditions and DLC 6.2 for the 50-year regression period, and the extreme environmental conditions were used in the study. The turbulent wind field simulation was performed by TurbSim, and the load of wind waves on structures was generated by FAST, which were all developed by the NREL (National Renewable Energy Laboratory). In addition to wind and waves, the seismic force was also considered. The cylindrical TLD was located above the rotor nacelle assembly (RNA). A TLD has different damping effects when acting under wind, wave, and earthquake loads, respectively. The effect of the TLD regarding motion reduction on the OWT under coupled wind, wave, and seismic loads was studied. This study also designed a simple experiment to verify the correctness of the numerical simulation results. Fatigue analysis shows that multi-layer TLDs can extend the fatigue life (37%) of an OWT. In addition, under extreme environmental load conditions, multi-layer TLDs have a better vibration damping performance than single-layer TLDs. The study demonstrates that multi-layer TLDs can be considered as a vibration reduction damper for OWTs. Full article

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18 pages, 4496 KiB

Open AccessArticle

Propagation of Solitary Waves over a Submerged Slotted Barrier

by Yun-Ta Wu and Shih-Chun Hsiao

J. Mar. Sci. Eng. 2020, 8(6), 419; https://doi.org/10.3390/jmse8060419 - 9 Jun 2020

Cited by 5 | Viewed by 2396

Abstract

In this article, the interaction of solitary waves and a submerged slotted barrier is investigated in which the slotted barrier consists of three impermeable elements and its porosity can be determined by the distance between the two neighboring elements. A new experiment is [...] Read more.

In this article, the interaction of solitary waves and a submerged slotted barrier is investigated in which the slotted barrier consists of three impermeable elements and its porosity can be determined by the distance between the two neighboring elements. A new experiment is conducted to measure free surface elevation, velocity, and turbulent kinetic energy. Numerical simulation is performed using a two-dimensional model based on the Reynolds-Averaged Navier-Stokes equations and the non-linear k-ɛ turbulence model. A detailed flow pattern is illustrated by a flow visualization technique. A laboratory observation indicates that flow separations occur at each element of the slotted barrier and the vortex shedding process is then triggered due to the complicated interaction of those induced vortices that further create a complex flow pattern. During the vortex shedding process, seeding particles that are initially accumulated near the seafloor are suspended by an upward jet formed by vortices interacting. Model-data comparisons are carried out to examine the accuracy of the model. Overall model-data comparisons are in satisfactory agreement, but modeled results sometimes fail to predict the positions of the induced vortices. Since the measured data is unique in terms of velocity and turbulence, the dataset can be used for further improvement of numerical modeling. Full article

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20 pages, 5315 KiB

Open AccessArticle

Numerical Study of the Influence of Fishnet Mesh Size on a Floating Platform

by Hung-Jie Tang, Chai-Cheng Huang and Ray-Yeng Yang

J. Mar. Sci. Eng. 2020, 8(5), 343; https://doi.org/10.3390/jmse8050343 - 12 May 2020

Cited by 1 | Viewed by 2802

Abstract

This study aims to investigate the influence of fishnet mesh size on a floating platform. A self-developed, time-domain numerical model was used for the evaluation. This model is based on potential flow theory, uses the boundary element method (BEM) to solve nonlinear wave-body [...] Read more.

This study aims to investigate the influence of fishnet mesh size on a floating platform. A self-developed, time-domain numerical model was used for the evaluation. This model is based on potential flow theory, uses the boundary element method (BEM) to solve nonlinear wave-body interactions, and applies the Morison equation to calculate the hydrodynamic forces exerted on fishnets. The mooring system is treated as a linear and symmetric spring. The results near the resonant frequency of the platform indicate that the smaller the fishnet mesh size, the lower the heave, pitch, and sea-side tension response amplitude operators (RAOs), but the higher the reflection coefficient. The results in the lower frequency region reveal that the smaller the fishnet mesh size, the lower the surge and heave RAOs, but the higher the pitch and tension RAOs. Meanwhile, the time-domain results at the resonant frequency of heave motion are shown to indicate the influences of a platform with various fishnets mesh sizes on the rigid body motion, mooring line tension, and transmitted wave heights. In addition, a comparison of nonlinear effects indicates that, after reducing the fishnet mesh size, the second-order RAOs of heave, pitch, and sea-side tension decrease, but the changes are minor against the first-order results. Full article

(This article belongs to the Special Issue Waves and Ocean Structures)

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18 pages, 3859 KiB

Open AccessFeature PaperArticle

Mooring Drag Effects in Interaction Problems of Waves and Moored Underwater Floating Structures

by Cheng-Tsung Chen, Jaw-Fang Lee and Chun-Han Lo

J. Mar. Sci. Eng. 2020, 8(3), 146; https://doi.org/10.3390/jmse8030146 - 25 Feb 2020

Cited by 3 | Viewed by 2394

Abstract

In contrast to either considering structures with full degrees of freedom but with wave force on mooring lines neglected or with wave scattering and radiation neglected, in this paper, a new analytic solution is presented for wave interaction with moored structures of full [...] Read more.

In contrast to either considering structures with full degrees of freedom but with wave force on mooring lines neglected or with wave scattering and radiation neglected, in this paper, a new analytic solution is presented for wave interaction with moored structures of full degrees of freedom and with wave forces acting on mooring lines considered. The linear potential wave theory is applied to solve the wave problem. The wave fields are expressed as superposition of scattering and radiation waves. Wave forces acting on the mooring lines are calculated using the Morison equation with relative motions. A coupling formulation among water waves, underwater floating structure, and mooring lines are presented. The principle of energy conservation, as well as numerical results, are used to verify the present solution. With complete considerations of interactions among waves and moored structures, the characteristics of motions of the structure, the wave fields, and the wave forces acting on the mooring lines are investigated. Full article

(This article belongs to the Special Issue Waves and Ocean Structures)

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19 pages, 11283 KiB

Open AccessArticle

Estimation of the Motion Performance of a Light Buoy Adopting Ecofriendly and Lightweight Materials in Waves

by Se-Min Jeong, Bo-Hun Son and Chang-Yull Lee

J. Mar. Sci. Eng. 2020, 8(2), 139; https://doi.org/10.3390/jmse8020139 - 20 Feb 2020

Cited by 8 | Viewed by 4162

Abstract

In this study, the methods and results of numerical simulations to estimate the motion performance of a newly developed lightweight light buoy in waves and to check the effect of conceptually developed appendages on that performance were introduced. The results from a potential-based [...] Read more.

In this study, the methods and results of numerical simulations to estimate the motion performance of a newly developed lightweight light buoy in waves and to check the effect of conceptually developed appendages on that performance were introduced. The results from a potential-based motion analysis with viscous damping coefficients obtained from free decay tests using computational fluid dynamics (CFD) and those obtained from wave motion simulation using CFD were compared. From these results, it was confirmed that viscous damping should be considered when the frequency of an incoming wave is close to the natural frequency of the buoy. It was estimated that the pitch and heave motions of the light buoy became smaller when the developed appendages were adopted. Although the quantitative superiority of the appendages was different, the qualitative superiority was similar between both results. Full article

(This article belongs to the Special Issue Waves and Ocean Structures)

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14 pages, 4151 KiB

Open AccessArticle

Effect of Top Tension on Vortex-Induced Vibration of Deep-Sea Risers

by Jie Zhang, He Guo, Yougang Tang and Yulong Li

J. Mar. Sci. Eng. 2020, 8(2), 121; https://doi.org/10.3390/jmse8020121 - 15 Feb 2020

Cited by 9 | Viewed by 3266

Abstract

With the increase of water depth, the design and use of the top-tensioned risers (TTR) are facing more and more challenges. This research presents the effect of top tension on dynamic behavior of deep-sea risers by means of numerical simulations and experiments. First, [...] Read more.

With the increase of water depth, the design and use of the top-tensioned risers (TTR) are facing more and more challenges. This research presents the effect of top tension on dynamic behavior of deep-sea risers by means of numerical simulations and experiments. First, the governing equation of vortex-induced vibration (VIV) of TTR based on Euler-Bernoulli theory and Van der Pol wake-oscillator model was established, and the effect of top tension on natural vibration of TTR was discussed. Then, the dynamic response of TTR in shear current was calculated numerically by finite difference method. The displacement, bending stress and vibration frequency of TTR with the variation of top tension were investigated. Finally, a VIV experiment of a 5 m long flexible top-tensioned model was carried out at the towing tank of Tianjin University. The results show that the vibration displacement of TTR increases and the bending stress decreases as the top tension increases. The dominant frequency of VIV of TTR is controlled by the current velocity and is barely influenced by the top tension. With the increase of top tension, the natural frequency of TTR increases, the lower order modes are excited in the same current. Full article

(This article belongs to the Special Issue Waves and Ocean Structures)

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