Artificial eigenmodes in truncated flow domains
Whenever linear eigenmodes of open flows are computed on a numerical domain that is truncated in the streamwise direction, artificial boundary conditions may give rise to spurious pressure signals that are capable of providing unwanted perturbation feedback to upstream locations. The manifestation of such feedback in the eigenmode spectrum is analysed here for two simple configurations. First, explicitly prescribed feedback in a Ginzburg–Landau model is shown to produce a spurious eigenmode branch, named the ‘arc branch’, that strongly resembles a characteristic family of eigenmodes typically present in open shear flow calculations. Second, corresponding mode branches in the global spectrum of an incompressible parallel jet in a truncated domain are examined. It is demonstrated that these eigenmodes of the numerical model depend on the presence of spurious forcing of a local \(k^+\) instability wave at the inflow, caused by pressure signals that appear to be generated at the outflow. Multiple local \(k^+\) branches result in multiple global eigenmode branches. For the particular boundary treatment chosen here, the strength of the pressure feedback from the outflow towards the inflow boundary is found to decay with the cube of the numerical domain length. It is concluded that arc branch eigenmodes are artefacts of domain truncation, with limited value for physical analysis. It is demonstrated, for the example of a non-parallel jet, how spurious feedback may be reduced by an absorbing layer near the outflow boundary.
KeywordsGlobal instability Non-reflecting boundary conditions Jets
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Discussions with Xavier Garnaud and Wilfried Coenen greatly helped shape the ideas presented in this paper. The study was supported by the Agence Nationale de la Recherche under the Cool Jazz project, Grant Number ANR-12-BS09-0024.
- 2.Buell, J.C., Huerre, P.: Inflow/outflow boundary conditions and global dynamics of spatial mixing layers. In: Proceedings of 2nd Summer Program, Stanford University. Center Turbulence Research, pp. 19–27 (1988)Google Scholar
- 14.Huerre, P.: Open shear flow instabilities. In: Batchelor, G.K., Moffatt, H.K., Worster, M.G. (eds.) Perspectives in Fluid Dynamics, pp. 159–229. Cambridge University Press, Cambridge (2000)Google Scholar
- 25.Trefethen, L. N., Embree, M.: Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators. Princeton University Press (2005). See also http://www.cs.ox.ac.uk/projects/pseudospectra/