AI 中文总结
该研究针对振荡水柱这一波浪能转换器，构建两种浅水动力学模型，证明其局部适定性，明确水柱有效浮力周期由附加质量与弹簧力刚度的竞争决定。
AI 中文摘要
我们研究振荡水柱的动力学，振荡水柱是一种波浪能转换器，其中水波与固定的部分浸没结构及气室相互作用。考虑浅水区域，流体运动由一维非线性浅水方程或Boussinesq-Abbott方程控制，而气室内的气压变化对流体起到弹簧力的作用。结构和气室的存在为流体方程引入了约束。在不存在结构阻尼的情况下，假设流体-弹性总能量守恒，我们将约束方程重新表述为开阔水域与气室之间的传输问题，并证明其局部适定性。我们还考虑了另一种建模方法，即气室内流体的上部被视为可在下部流体上方垂直自由移动的刚性层（水柱）。对于该构型，我们将动力学重新表述为波-弹簧-质量系统，其中水柱的运动由气室外的浅水波驱动。我们确立了其局部适定性，并表明水柱运动的有效浮力周期由附加质量与弹簧力刚度之间的竞争决定。
英文摘要
We investigate the dynamics of an oscillating water column, which is a wave energy converter where water waves interact with a fixed partially immersed structure and an air chamber. Considering the shallow water regime, the fluid motion is governed by either the one-dimensional nonlinear shallow water equations or the Boussinesq-Abbott equations, while the air pressure variation in the chamber acts as a spring force on the fluid. The presence of the structure and the air chamber introduces constraints into the fluid equations. Assuming conservation of the total fluid-elastic energy in the absence of structural damping, we reformulate the constrained equations as transmission problems between the open water and the chamber and show their local well-posedness. We also consider a different modeling approach in which the upper part of the fluid in the chamber is treated as a rigid layer (water column) free to move vertically above the lower fluid. For this configuration, we reformulate the dynamics as wave-spring-mass systems, where the motion of the water column is driven by the shallow water waves outside the chamber. We establish their local well-posedness and show that the effective buoyancy period of the water column motion is determined by the competition between the added mass and the stiffness of the spring force.
