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The eN method is widely used in engineering for transition prediction. When it is applied to three-dimensional boundary layers, one has to choose the direction along which the growth rate of the disturbance is to be integrated. The direction determined on the base of saddle point method is mathematically most reasonable. However, unlike in the case of water wave, in problems of hydrodynamic stability, its physical meaning is not so obvious, as the frequency and wave number may be complex. And even more, on some occasions, one may not be able to find the direction on the base of continuously varying the frequency and wave number. In this paper, these problems are clarified by investigating the evolution of a wave packet through DNS. Suggestions for how to do transition prediction are also provided for the case of discontinuity of direction set by saddle point method.
Author(s):
Caihong SU
Tianjin University
China