Mathematical methods for boundary layers

当气体或液体高速流过翼型（如飞机机翼或涡轮叶片）时，在翼型表面附近形成高剪切的薄区域，称为边界层。边界层在决定翼型周围的流动中起着至关重要的作用，例如，如果没有边界层，机翼不能产生任何升力，但边界层对机翼的阻力也有很大的贡献。如果边界层变得紊流，这种阻力会急剧增加。如果边界层在前缘附近与机翼分离，升力降低，阻力增加（机翼失速）。这些现象在航空航天工业中是至关重要的，但是当流体高速流过或围绕设备流动时，边界层就会形成。这个暑期学校的目的是向英国的工程博士教授当前研究中使用的数学技术，这些技术可以帮助我们理解，并可能最终控制边界层分离和向湍流的过渡。将探讨解析数学结果和数值结果之间的关系，并确定两者结合的好处。

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.