Flows past airplane wings and high-speed ground vehicles have captured the attention of fluid dynamicists, applied mathematicians, and computational scientists and engineers, not only because of their obvious technological significance, but also because of the opportunity they present to perform elegant mathematical analyses and develop realistic and efficient numerical models. Although these flows occur at high Reynolds numbers, and often at transonic or supersonic speeds that are comparable to or even exceed the speed of sound, the effects of viscosity are important in two ways. First, viscous stresses determine the drag force exerted on the moving surfaces, and thus the energy required to sustain the motion; second, viscous stresses are responsible for the production of vorticity which generates circulation and thereby induces lift. A comprehensive analysis of a high-speed flow in aerodynamics incorporates the effects of fluid compresibility and turbulent motion, and accounts for the presence of boundary layers and regions of recirculating flow. In this chapter, we discuss the most basic configuration by neglecting the presence of boundary layers and wakes, and by assuming that the fluid is inviscid and incompressible.
KeywordsLift Force Point Vortex Vortex Sheet Panel Method Vortex Loop
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