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.

This research proposes the design of a mooring system that allows the floating platform to stably dive deep enough to prevent damage induced by typhoon waves. The design principle of the mechanism is that the submarined floating platform with negative buoyancy is connected to a pontoon with positive buoyancy. The diving depth of the floating platform is determined by the rope length. If the static equilibrium of the two forces is satisfied, the diving depth will be kept. If the diving depth of the floating platform is enough, the platform will not be directly damaged by the wave impact. In reality, the system will be greatly subjected to the typhoon wave and the ocean current. The stability of the system and the dynamic tension of the rope must be significantly concerned. In this study, the linear elastic model of the mooring system composed of a floater platform, towed parachute, pontoon, traction rope, and mooring foundation is derived. The theoretical solution of the static and dynamic stability analysis of the mooring system is proposed. The dynamic behaviors of the floating platform and pontoon, and the tension of the rope under the effects of waves and ocean currents, are investigated. It is discovered that the buffer spring helps reduce the tension of the rope. The proposed protection procedure can avoid the damage of the floating platform and the mooring line, due to Typhoon wave impact.

This research proposes a mooring design which keeps the turbine ocean current, static, balanced, and fixed at a predetermined depth under water, to ensure that the ocean current generator can effectively use current to generate electricity, and that the water pressure remains adequate value before critical pressure damage occurs. In this design, the turbine generator, which withstands the force of ocean currents, is mounted in front of a floating platform by ropes, and the platform is anchored to the deep seabed with light-weight high-strength PE ropes. In addition, a pontoon is connected to the ocean current generator with a rope. The balance is reached by the ocean current generator weight, floating pontoon, and the tension of the ropes which are connected between the generator and floating platform. Therefore, both horizontal and vertical forces become static and the depth can be determined by the length of the rope. Because the floating platform and pontoons on the water surface are significantly affected by waves, the two devices subjected to the wave exciting forces are further affected by the movement of the platform, pontoons, turbines, and the tensions of the ropes. Among them, the exciting forces depend on the operating volume of the two devices. Moreover, there is a phase difference between the floating platform and the pontoon under the action of the waves. In this study, the linear elastic model is used to simulate the motion equation of the overall mooring system. A theoretical solution of the static and dynamic stability analysis of the mooring system is proposed. The dynamic behaviors of the turbine, the floating platform, the pontoon, and the tension of the rope under the effects of waves and ocean currents are investigated. The study found the relationship of the phase difference and the direction difference of waves and ocean currents, the wavelength, and the length of the rope between the carrier and the turbine. It was found that the phase difference has a great influence on the dynamic behaviors of the system. The length of the rope can be adjusted to avoid resonance and reduce the rope tension. In addition, a buffer spring can be used to reduce the dynamic tension of the rope significantly to ensure the safety and life of the rope.

The theory of surface wave generation, in viscous flows, is modified by replacing the linear-logarithmic shear velocity profile, in the air, with a model which links smoothly the linear and logarithmic layers through the buffer layer. This profile includes the effects of air flow turbulence using a damped mixing-length model. In the water, an exponential shear velocity profile is used. It is shown that this modified and coupled shear-velocity profile gives a better agreement with experimental data than the coupled linear-logarithmic, non smooth profile, (in the air)–exponential profile (in the water), widely used in the literature. We also give new insights on retrograde modes that are Doppler shifted by the surface velocity at the air-sea interface, namely on the threshold value of the surface current for the occurrence of a second unstable mode.

This paper provides a simple relationship to theoretically estimate the wave friction factor in various flow regimes in porous media based on the slip factor formula. The theoretical formula shows that the wave friction factor varies inversely with the relative bed roughness, A/ks, over a rough bed and that it can be conveniently determined if wave conditions and sediment parameters are known without using a specific regression formula deduced from experiments. A laboratory experiment that directly measures the wave-driven bed shear stress dominant in the turbulent regime with a permeable bed is used to examine the newly derived relationship. In the laminar regime, the comparison demonstrates that the theoretical results determined by the proposed formula are in good agreement with existing measurements. In the turbulent-rough regime, the influence of eddy viscosity is considered in the slip factor formula and the zero-equation model is used in estimating the average eddy viscosity. The theoretica...

A permanent gravity wave propagating on deep water is a classic mathematical problem. However, the Fourier series approximation (FSA) based on the physical plane was examined to be valid for almost waves at all depths. The accuracy of the FSA for almost-limiting gravity waves remains unevaluated, which is the purpose of this study. We calculate some physical properties of almost-limiting waves on deep water using the FSA and compare them with other studies on the complex plane. The comparison results show that the closer the wave is, the greater the difference. We find that the main reason for this difference is that the wave profile in the FSA retains an original implicit form and is not represented by Fourier series. Therefore, the kinematic and dynamic conditions of the free surface around the wave crest cannot be satisfied at the same time.