Overview

There is much active mathematical research into aeroacoustics (the study of sound in aircraft engines).  This field is closely followed, and often contributed to (sometimes helpfully) by engineers in both academia and industry (e.g. Airbus, Boeing, NASA, etc).  The aim of this course is to give an overview of the mathematical techniques needed to understand the current research problems, and read current papers in the area.  This could lead on to several possible PhD projects, including in asymptotics, numerical analysis, and stability theory.

Aims

The application of wave theory to problems involving the generation, propagation and scattering of acoustic and other waves is of considerable relevance in many practical situations. These include, for example, underwater sound propagation, aircraft noise, remote sensing, the effect of noise in built-up areas, and a variety of medical diagnostic applications. This course would aim to provide the basic theory of wave generation, propagation and scattering, and an overview of the mathematical methods and approximations used to tackle these problems, with emphasis on applications to aeroacoustics.  The ultimate aim is for students to understand the underlying mathematical tools of acoustics sufficiently to read current research publications on acoustics, and to be able to apply these techniques to current research questions within mathematics, engineering and industry.

Learning Outcomes

• Reproduce standard models and arguments for sound generation and propagation.
  
• Apply mathematical techniques to model sound generation and propagation in simple systems.
• Understand and apply Wiener-Hopf factorisation in the scalar case.
  

Approximate Syllabus

• Some general acoustic theory.
• Sound generation by turbulence and moving bodies (including the Lighthill and Ffowcs Williams Hawkings acoustic analogies).
• Scattering (including the scalar Wiener-Hopf technique applied to the Sommerfeld problem of scattering by a sharp edge)
• Long-distance sound propagation including nonlinear and viscous effects.
• Wave-guides.
• High frequencies and Ray Tracing.

Reading List

• D.G. Crighton, A.P. Dowling, J.E. Ffowcs Williams, et al, "Modern Methods in Analyticial Acoustics", Springer 1992.
• M. Howe, "Acoustics & Aerodynamic Sound", Cambridge 2015 (available online through Warwick Library).
  
• S.W. Rienstra & A. Hirschberg, "An Introduction to Acoustics", (available online).