MATH31620: Fluid Mechanics

• Dynamics and Analysis in Many Variables.

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• To introduce a mathematical description of fluid flow and other continuous media to familiarise students with the successful applications of mathematics in this area of modelling.
• to prepare students for future study of advanced topics.

• Kinematics: Eulerian and Lagrangian pictures, velocity field, streamlines and stream functions.
• Compressibility, vorticity and circulation, integrals over material domains.
• Dynamics of ideal fluids: derivation of the incompressible Euler equations, energy, vorticity dynamics, circulation and rotating frames.
• Water waves: free-surface boundaries, linearisation, travelling and standing waves.
• Compressible flow: barotropic fluids, sound waves, nonlinearity.
• Hydrodynamic stability: normal mode analysis, Rayleigh-Taylor and Kelvin-Helmholtz instabilities.
• Dynamics of viscous fluids: Newtonian fluids, derivation of the Navier-Stokes equations, exact solutions, dynamical similarity, boundary layers.

Subject-specific Knowledge:

• By the end of the module students will: be able to solve novel and/or complex problems in Fluid Mechanics.
• Have a systematic and coherent understanding of theoretical mathematics in the field of Fluid Mechanics.
• Have acquired coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas:
• Kinematics and dynamics of fluid flows, compressible flow, hydrodynamic stability and dynamics of viscous fluids.
• Equations of motion and their derivation for fluids.

Subject-specific Skills:

• In addition students will have highly specialised and advanced mathematical skills in the following areas: Modelling.
• They will be able to formulate and use mathematical models in various situations.

Key Skills:

• Students will be able to study independently to further their knowledge of an advanced topic.

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
• Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
• The end-of-year examination assesses the knowledge acquired and the ability to solve complex and specialised problems.

Eight written or electronic assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

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