Mathematical methods for boundary layers

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When a gas or liquid flows at high speed past an aerofoil (like an aeroplane wing, or a turbine blade) thin regions of high shear form close to the aerofoil surface, which are called boundary layers. Boundary layers play a crucial role in determining the flow around the aerofoil, e.g. if there were no boundary layers, a wing could not generate any lift, but the boundary layers also contribute significantly to the drag on the wing. This drag increases sharply if the boundary layer becomes turbulent. If the boundary layers separate from the aerofoil near the leading edge the lift reduces and the drag increases (the wing stalls). These phenomena are of central importance in the aerospace industries, but boundary layers can form whenever fluid flows through, or around, a device at speed. This summer school is concerned with teaching UK based engineering PhD students about the mathematical techniques used in current research that help us to understand, and perhaps ultimately control, boundary layer separation and transition to turbulence. The relation between analytical mathematical results and numerical results will be explored, and the benefits of combining the two identified.