Geostrophic Adjustment Within A Rotating, Stratified Fluid

旋转分层流体内的地转调整

• 批准号: 2281180
• 金额: --
• 依托单位: Newcastle University
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2281180
• 关键词: Geostrophic; Adjustment; Within; Rotating; Stratified

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.

主要目标和目的地转调整是将不平衡的流体流场修正为地转平衡的过程。地转平衡是一个平衡系统，其中压力梯度力（由于压力差而使流体移动的力）通过科里奥利效应（旋转）来平衡。对大气地转调整的研究可以追溯到1938年C. G. Rossby，主题领域是基础流体动力学。最终，C. C. Lin 为该问题引入了坚实的障碍，并表明开尔文环流定理成立，A. Gill 还根据水面波（海洋不稳定性）重新调整了该问题的用途。最近，T. Johnson 又将地形问题纳入其中。地形是可能影响问题的物理对象的集合，例如岛屿或海底的形状。这项工作主要着眼于环流的形成，环流是大规模的环流模式。我们打算开发一个受坚不可摧的障碍限制的地转调整的三维模型。这是为了了解我们期望在实验设置中看到什么，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，我们的目标是设置和测试一个旋转台，以便我们可以将这项工作直接与现实场景联系起来。一旦流体相对于罐壁以相同的速率旋转，它就进入了称为固体旋转的状态，这类似于海洋相对于地球自转的移动方式。一旦处于这种状态，我们就可以移除障碍物，这将导致波在水箱周围传播，从而形成环流。在最近的分析和数值研究中，理论上认为循环模式有效地记住了该障碍物的位置。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（即岛屿形状和罐底的形状）如何影响环流模式的形成。该项目打算回答什么问题？除了研究环流的发展之外，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（即密度只能以其压力函数表示的流体）围绕封闭曲线（例如岛屿或储罐周长）的循环随时间保持恒定。将在项目过程中实施的新颖的科学/工程方法。采用数值和实验相结合的方法是常见做法。数字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，而这种解决方案是不可能的。此外，它将使我们能够探索更广阔的参数空间。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，我们还将开发在旋转和注入流体时对水箱进行分层的实用方法，以便分析流体中的大规模结构。