15 October 2019

Dr Ian Griffiths, University of Oxford

iPhones, Dysons and Cheerios: using fluid dynamics to aid technology

As technology continues to advance, new strategies involving a range of scientific disciplines are required. Mathematicians can provide frameworks to predict operating regimes and manufacture techniques. In this talk we show how mathematics can be used to help in the fabrication of precision glass, for smartphones and new flexible devices; the development of superior filters for vacuum cleaners; and the manufacture of unusual cereal shapes (like Nestlé Alphabet cereals).

8 October 2019

Prof Jonathan Healey, Keel University

Fractal neutral curves in the linear stability of shear flows

Rayleigh showed that the linear stability properties of inviscid shear
layers are described by a second order linear ODE, and the effects of
buoyancy due to fluid density variations were included by Taylor and
Goldstein in 1931, resulting in one additional linear term in
Rayleigh's equation (for weakly varying density). Rayleigh's inflexion
point theorem no longer applies and Taylor gave an example where
stable stratification (density increasing with depth) destabilizes an
inflexionless flow. The Taylor-Goldstein equation is widely used in
many geophysical and astrophysical flow applications. In this talk we
show that this linear ODE can produce neutral curves (separating
stable from unstable regimes) with fractal properties, and discuss
possible implications for nonlinear dynamics.