Research in Wave Propagation and Scattering

Waves are important in the broad field of continuous media because they are the fundamental mechanism by which all information is transmitted. Two examples which illustrate the consequences of this fact are (i) shock waves, which form around a supersonic jet fighter, and (ii) tsunami waves, which are the first indication at a shoreline that there has been a distant underwater earthquake or upheaval. Waves in one-dimension, such as on strings, can be studied using classical methods of Fourier analysis etc., but how do we analyse the propagation and scattering of waves in two or three dimensions? The waves group at Manchester is concerned with a largely analytical investigation into the propagation of waves in complex media of many types, and the work has many applications ranging from phenomenological issues to answering basic questions in engineering.

Research investigation continues into acoustic, electromagnetic and water wave scattering by complicated shaped bodies, and propagation and scattering in inhomogeneous media. Examples include:

• Refraction of sound waves by shear layers (with application to aerojet noise).
• Propagation through composite and dielectric materials (for microwave and elastic wave propagation).
• Propagation along fibre optic cables (to determine energy losses and signal errors).
• Non-uniqueness in water wave models.
• Rossby wave diffraction and propagation in oceans.
• Fluid-structure interaction (vehicle noise).

Mathematically, problems in wave scattering or propagation usually reduce to solving a partial differential equation subject to various boundary conditions. Analytical approaches such as integral-equation methods and the Wiener-Hopf technique, as well as asymptotic techniques, are often used to find these solutions.

The group has collaborations with a number of industrial contacts, and has been fortunate in receiving funding from EPSRC, NERC and other funding bodies in recent years.

Members of staff involved