Algebraically decaying modes and wave packet pseudo-modes in swept Hiemenz flow

Abstract : The modal structure of the swept Hiemenz flow, a model for the flow near the attachment line of a swept wing, consists of eigenfunctions which exhibit (super-)exponential or algebraic decay as the wall-normal coordinate tends to infinity. The subset of algebraically decaying modes corresponds to parts of the spectrum which are characterized by a significant sensitivity to numerical discretization. Numerical evidence further suggests that a continuous spectrum covering a two-dimensional range of the complex plane exists. We investigate the family of uniform swept Hiemenz modes using eigenvalue computations, numerical simulations and the concept of wave packet pseudo-modes. Three distinct branches of the family of algebraically decaying eigenmodes are identified. They can be superimposed to produce wavefronts propagating towards or away from the boundary layer and standing or travelling wave packets in the free stream. Their role in the exchange of information between the free stream and the attachment-line boundary layer for the swept Hiemenz flow is discussed. The concept of wave packet pseudo-modes has been critical in the analysis of this problem and is expected to lead to further insights into other shear flows in semi- or bi-infinite domains.
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Journal of Fluid Mechanics, Cambridge University Press (CUP), 2010, 643, pp.309-332. 〈10.1017/s0022112009992114〉
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Dominik Obrist, Peter J. Schmid. Algebraically decaying modes and wave packet pseudo-modes in swept Hiemenz flow. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2010, 643, pp.309-332. 〈10.1017/s0022112009992114〉. 〈hal-00998010〉

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