Geostrophic Adjustment Within A Rotating, Stratified Fluid

地转调整的主要目标和目的是将不平衡的流场修正到地转平衡的过程。地转平衡是一个平衡系统，其中压力梯度力(由于压差而使流体运动的力)被科里奥利效应(旋转)平衡。大气地转调节的研究可以追溯到1938年C.G.Rossby，其主题领域是基础流体动力学。最后，C.C.Lin引入了固体屏障来解决这个问题，并证明了开尔文环流定理是成立的，A.Gill还用水面波(海洋不稳定性)的术语重新讨论了这个问题。最近，T·约翰逊对这一问题进行了地形研究。地形是可能影响问题的物理物体的集合，如岛屿或海底的形状。这项工作主要着眼于环流的形成，这是一种大规模的环流模式。我们打算开发一个受坚不可摧的障碍限制的地转调节的三维模式。这是为了加深对我们在实验设置中预期看到的内容的理解，特别是它将帮助我们确定对于特定参数值我们预计会看到什么现象。最后，在实验意义上，我们的目标是建立和测试一个旋转工作台，以便我们可以将这项工作直接与真实世界的场景相关联。一旦流体相对于罐壁以相同的速度旋转，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，我们就可以移除势垒，该势垒将导致波在水箱周围传播，从而形成回旋。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屏障被放置在哪里。首先，我们打算在物理意义上复制这一结果，并最终研究地形(即岛屿形状和罐底形状)如何影响环流模式的形成。该项目打算回答什么问题？除了研究涡旋的发展，我们还打算评估如何实际应用开尔文环流定理。这个定理指出，正压流体，即密度可以仅表示为其压力的函数的流体，围绕闭合曲线(如岛屿或储罐周长)的循环在时间上保持不变。将在项目过程中实施的新的科学/工程方法。采取数值和实验相结合的方法。数值部分在很大程度上依赖于数学方法，例如求解微分系统或在不可能实现这种解决方案的情况下实施时间步长方法。此外，它将允许我们探索更广阔的参数空间。在实验方面，我们将开发能够绘制流体密度分布的探测器，这包括与电气工程学院合作开发硬件和软件。除此之外，我们还将开发实用的方法，在罐旋转和播撒流体时对罐进行分层，以便有可能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.