Mathematics of Fluids and Plasmas 1: Fluid Dynamics

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Credits

15

Module code

MA41006

About the module

This module provides an introduction to the Mathematics of Fluids and Plasmas, focusing on Fluid Dynamics. This module is mandatory for students taking the BSc or MMath in Mathematics or the BSc or MSci in Mathematics and Physics, and is optional for students taking any other Mathematics combined degrees. If you have questions about this module or the possible combinations, please contact your Advisor of Studies.

Prerequisites

Students taking this module must have achieved a pass mark in each of the modules MA31002 and either MA31007 or MA32002, or equivalents.

Indicative Content

  • Fundamentals

    Fields, flux, potentials. Representation of fields: fieldlines/streamlines, contours, flux surfaces. Gauss' and Stokes' theorems.

  • Conservation laws

    Conservation of mass, conservation of momentum, Euler’s equation, energy equation, equation of state.

  • Common approximations

    Incompressible, irrotational, potential flows, Bernoulli’s theorem. Laplace’s equation, boundary conditions, uniqueness theorem, separable solutions.

  • Vorticity

    Vorticity and circulation, Kelvin's circulation theorem, vorticity evolution.

  • The solar wind

    Introduction to solar features, Parker's solar wind solution.

  • Waves

    Sound waves, linearisation, dispersion relations, wave properties.

  • Viscous flow

    Stress tensor, viscous stresses, viscosity, energy dissipation, the Reynolds number.

  • Turbulence and Chaos

     

Delivery and Assessment

The module is delivered in the form of lectures and workshops/tutorials and assessed via an exam (80%) and coursework (20%).

Credit Rating

This module is a Scottish Higher Education Level 4 or SCQF level 10 module and is rated as 15 SCOTCAT credits or 7.5 ECTS credits.