Geostrophic Adjustment Within A Rotating, Stratified Fluid

地转调整是将不平衡的流体流场改变为地转平衡的过程。地转平衡是指压力梯度力（由于压力差而使流体运动的力）与科里奥利效应（自转）相平衡的平衡系统。G. Rossby于1938年创立，主要研究领域是基础流体动力学。最终C。C.林在这个问题上引入了坚实的障碍，并证明了开尔文环流定理是成立的。吉尔还将这个问题重新定义为水面上的表面波（海洋不稳定性）。最近T。约翰逊对这个问题有深刻的见解。地形是一组物理对象，如岛屿或海底的形状，可能会影响问题。这项工作主要着眼于形成的环流，这是大规模的流通模式。本文拟建立一个由可移动障碍物限制的地转适应的三维模式。这是为了了解我们期望在我们的实验装置中看到什么，特别是它将帮助我们确定我们期望在特定参数值下看到什么现象。最后，在实验意义上，我们的目标是建立和测试一个旋转台，这样我们就可以将这项工作直接与现实世界的场景联系起来。一旦流体相对于罐壁以相同的速率旋转，它就进入了一种称为固体旋转的状态，这类似于海洋相对于地球自转的运动。一旦进入这种状态，我们就可以移除障碍物，这将导致波浪在水箱周围传播，从而形成漩涡。在最近的分析和数值工作中，理论上认为环流模式有效地记住了这个障碍的位置。最初，我们打算在物理意义上复制这一结果，并最终继续研究地形（即岛屿形状和罐底形状）如何影响环流模式的形成。该项目打算回答哪些问题？除了研究环流的发展，我们还打算评估如何实际应用开尔文环流定理。该定理指出，正压流体的循环，即流体的密度，可以表示为它的压力的函数，围绕一个封闭的曲线，如一个岛或周边的坦克保持恒定的时间。新的科学/工程方法，将在项目的过程中进行。采取联合收割机结合数值和实验方法的惯例。数值组件严重依赖于数学方法，例如求解微分系统或实施时间步长方法，其中这种解决方案是不可能的。此外，它将使我们能够探索更广泛的参数空间。在实验上，我们将开发能够绘制流体密度分布的探针，这包括与电气工程学院合作开发硬件和软件。除此之外，我们还将开发出实用的方法，在旋转和播种流体的同时使罐分层，从而可以分析流动中的大尺度结构。

The key objective and aimsGeostrophic adjustment is the process in which an unbalanced fluid flow field is modified to geostrophic equilibrium. Geostrophic equilibrium is a balanced system in which the pressure gradient force (the force that makes the fluid move due to pressure differences) is balanced by the Coriolis effects (Rotation).Studying atmospheric geostrophic adjustment dates back to C. G. Rossby in 1938, the subject area is fundamental fluid dynamics. Eventually C. C. Lin introduced solid barriers to the problem and showed that Kelvin's circulation theorem would hold, A. Gill also re-purposed the problem in terms surface waves on water (oceanic instabilities). More recently T. Johnson has topography into the problem. Topography is the a collection of physical objects such as islands or the shape of the sea floor which may affect the problem. Mainly this work looks at the formation of gyres, which are large scale circulation patterns. We intend to develop a 3-Dimensional model of geostrophic adjustment confined by impregnable barriers. This is to develop an understanding of what we expect to see within our experimental setup particularly it will help us identify what phenomena we expect to witness for particular parameter values.Finally, within an experimental sense, we aim to set up and test a rotating table so we can relate this work directly to real-world scenarios. Once the fluid is rotating at the same rate with respect to the tank wall it has entered a state called solid body rotation, this is similar to how oceans move with respect to the earth's rotation. Once in this state, we can then remove the barrier which will cause a wave to propagate around the tank causing the gyres to form. In recent analytical and numerical work, it has been theorized that the circulation patterns effectively remember where this barrier was placed. Initially, we intend to replicate this result in a physical sense and eventually go on to study how topography ( i.e. islands shapes and the shape of the tank floor) affect the formation of the circulation patterns.What questions does the project intend to answer?In addition to studying the development of gyres, we intend to assess how we can practically apply Kelvin's circulations theorem. This theorem states that the circulation of a barotropic fluid, i.e. a fluid with a density that can be expressed solely as a function of its pressure, around a closed curve such as an island or the perimeter of the tank remains constant with respect to time.The novel science/engineering methodology that will be carried outduring the course of the project.Taking a combine numeric and experimental approach common practice. The numeric components rely heavily on mathematical methods such as solving differential systems or implementing time step methods where such a solution is not possible. Additionally, it will allow us to explore a broader parameter space to be explored. Experimentally we will develop probes capable of mapping the density profile of our fluid, this includes the development of hardware and software in collaboration with the school of electrical engineering. As well as this, we will develop practical methods of stratifying thetank while it is rotating and seeding the fluid so it is possible to analyse large scale structures within the flow.