An analytical connection between temporal and spatio-temporal growth rates in linear stability analysis

Details An analytical connection between temporal and spatio-temporal growth rates in linear stability analysis An analytical connection between temporal and spatio-temporal growth rates in linear stability analysis

2012-03-08

arxiv.org/abs/1203.1797v1

Physics

Fluid Dynamics

7 pages, 2 figures

Scientific paper

We derive an exact formula for the complex frequency in spatio-temporal stability analysis that is valid for arbitrary complex wave numbers. The usefulness of the formula lies in the fact that it depends only on purely temporal quantities, which are easily calculated. We apply the formula to two model dispersion relations: the linearized complex Ginzburg-Landau equation, and a model of wake instability. In the first case, a quadratic truncation of the exact formula applies; in the second, the same quadratic truncation yields an estimate of the parameter values at which the transition to absolute instability occurs.

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