MATH3101: FLUID MECHANICS III

• (Dynamics I (MATH1607) AND Analysis in Many Variables II (MATH2031) AND 20 additional credits of Level 2 mathematics modules) OR (Analysis in Many Variables II (MATH2031) AND Analysis I (MATH1051) (if taken in Year 2) AND Dynamics I (if taken in Year 2)) OR (Foundations of Physics I (PHYS1122) AND Analysis in Many Variables II (MATH2031) AND 20 additional credits of Level 2 mathematics modules.)

• One 20 credit Level 3 mathematics module.

• 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 specialised mathematical skills in the following areas which can be used with minimal guidance: Modelling.
• They will be able to formulate and use mathematical models in various situations.

Key Skills:

• 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 predictable and unpredictable problems.

Eight written 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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