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Advanced Topics in Fluid Mechanics of Climate - Mathematical Tripos - Paper

Exams, Mathematics

Post: February 27th, 2013
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This is the Past Paper of Mathematical Tripos which includes Combinatorics, Kruska Katona Theorem, Vertex Boundary, Harper’s Inequality, Usual Compression Operator, Construction of Cellular Homology, Intersection Pairing, Differentiable Map etc. Key important points are: Advanced Topics in Fluid Mechanics of Climate, Rossby Waves, Coriolis Parameter, Free Surface Elevation, Water Potential Vorticity, Uniform Density Fluid, Plane-Wave Solutions, Dispersion Relation
This is the Past Paper of Mathematical Tripos which includes Combinatorics, Kruska Katona Theorem, Vertex Boundary, Harper’s Inequality, Usual Compression Operator, Construction of Cellular Homology, Intersection Pairing, Differentiable Map etc. Key important points are: Advanced Topics in Fluid Mechanics of Climate, Rossby Waves, Coriolis Parameter, Free Surface Elevation, Water Potential Vorticity, Uniform Density Fluid, Plane-Wave Solutions, Dispersion Relation
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Contents
MATHEMATICAL TRIPOS Tuesday, 12 June, 2012 1:30 pm to 4:30 pm Part III PAPER 79 ADVANCED TOPICS IN FLUID MECHANICS OF CLIMATE You may attempt ALL questions, although full marks can be achieved by good answers to THREE questions. Completed answers are preferred to fragments. There are FOUR questions in total. The questions carry equal weight. STATIONERY REQUIREMENTS Cover sheet Treasury Tag Script paper SPECIAL REQUIREMENTS None You may not start to read the questions printed on the subsequent pages until instructed to do so by the Invigilator. 2 1 Rossby waves on a zonal jet Rossby waves can be supported by variations in the rotation rate or bottom topography. In some cases, these waves can also be supported by a large-scale mean flow. To show this, consider a steady mean flow, u = U0 sin πy in geostrophic balance. L [Assume that the Coriolis parameter f = f0 , and the bottom depth, H = H0 are constant.] What is the corresponding free surface elevation, η , in a uniform ..

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