Mathematical Sciences: Some Mathematical Problems in Transonic Aerodynamics & in Flows with Vorticity

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Numerical and asymptotic techniques will be used to investigate transonic flow about aircraft wings and flows with distributed vorticity. Specific transonic problems to be analyzed are design of optimum critical axisymmetric bodies, flows about lifting, not-so-slender transonic wings and the transonic area rule, and wind tunnel flows. Some use will be made of the transonic small disturbance formulation. The investigations of the vortical flow problem will involve development and clarification of theories integrating nonlinear and viscous effects. Both the transonic and vortical flow problems require interaction between numerical and asymptotic treatments in order to deal with complex nonlinearities. Present day commercial aircraft cruise in the transonic regime. In this regime drag (the force opposing forward motion) rises rapidly hence there is interest in understanding transonic flows and in the design of reduced drag wings. The study of flows with distributed vorticity (a certain distribution of whirl-like motion in the environment of interest) is both of a fundamental nature in fluid mechanics, but also of considerable interest in specific applications. One example of such an application is the prediction of aerodynamic losses and heat loads in turbo-machinery. The investigators will use modern methods of applied mathematics to deal with the complexities of the problems in the areas of research proposed.