Geostrophic Adjustment Within A Rotating, Stratified Fluid

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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.