Navier-stokes problems

当海洋工程和海底技术中的圆柱形结构物暴露在洋流和/或海浪中时，它们可能会经历结构振动。其中之一就是涡流脱落，它会对结构的完整性和疲劳寿命造成严重威胁。这个研究项目主要研究水平圆柱体在没有或存在自由面的情况下的非定常流动，这是流体力学中的一个经典课题。在自然界中，一种特殊类型的流体边界将具有不同物理性质的两种流体(例如地球大气中的水和空气)分隔开来，称为自由表面。具有圆柱形几何形状的典型结构包括拖缆，拖缆可能与自由面成一定角度倾斜：在某些情况下，它们可能与自由面成浅角度，从而接近水平方向。此外，近海平台通常有水平的圆柱形构件。自从60年代海洋工业迅速发展以来，这种流体运动的知识引起了许多在海上油田工作的机械和土木工程师的极大关注。由于旋涡的脱落，流体运动会对浸入其中的结构施加力。由这些力引起的共振振荡可能会破坏海洋中石油生产系统的立管。因此，本文的研究对工程结构的稳定与安全具有重要的现实意义。其目的是提供关于这种类型的流体运动的物理与流体运动对圆柱体的冲击(阻力和升力)之间的关系的有用信息。当然，最终的目标是了解、预测和防止涡流或流动引起的振动。目前的研究方案要求尽可能使用应用数学分析、数值模拟和与实验观测的比较来求解众所周知的Navier-Stokes方程。与实验的比较提供了我们对非常复杂的流动的数值模拟的限度的估计。

When cylindrical structures in ocean engineering and undersea technology are exposed to ocean currents and/or waves, they may experience structural vibrations. One of these instabilities involves vortex shedding, which can cause a serious threat to the integrity and fatigue life of structure. This program of research focuses on the unsteady flow around a horizontal cylindrical body in the absence or presence of a free surface which is a classical topic within hydrodynamics. In nature, a special type of fluid boundary which separates two fluids with different physical properties, for example water and the air in the Earth's atmosphere is known as a free surface. Representative structures having cylindrical geometry include towing cables, which may be inclined at an angle with respect to the free surface: in some cases they may be at a shallow angle with respect to the free surface, thereby approximating a horizontal orientation. Moreover, offshore platforms typically have horizontal, cylindrically shaped members. The knowledge of this kind of fluid motion has attracted considerable attention from many mechanical and civil engineers working in the offshore field, since the rapid expansion of the offshore industry in the 60s. Fluid motion causes forces to be exerted on structures immersed in them due to vortex shedding. Resonant oscillations caused by these forces may destroy riser pipes of an oil production system in the ocean. Thus, the proposed research studies are of considerable and practical importance in the stability and safety of engineering structures. The intent is to produce useful information about the relationship between physics of fluid motion of this type and the impact (drag and lift forces) of the fluid motion on the cylindrical body. The ultimate objective is, of course, the understanding, prediction, and prevention of vortex- or flow-induced vibrations. The present program of research requires the solution of the well known Navier-Stokes equations using applied mathematical analyzes, numerical simulations and comparisons with experimental observations whenever possible. Comparisons with experiments provides an estimate of the limits of our numerical simulations of very complex flows.