Estimating local instabilities for irregular flows in the differentially heated rotating annulus
In stable flows, transient growth of ’non-normal’ modes can lead to turbulence. Usually, non-normal modes are computed from linearized model equations . However, for some problems the proper set of equations is unknown, or unhandy for the purpose of finding non-normal modes. Therefore it is proposed to estimate non-normal modes from data alone, without using the model equations. Crucial for such an estimation is a good guess of the linear system matrix for the flow under consideration. Such a guess can be obtained following the approach by  discussed in the context of climate analysis. In the present paper a simple test case will be presented that demonstrates the suitability of the approach. Subsequently, the method is applied to temperature data from a differentially heated rotating annulus, a laboratory model that covers features of the large-scale atmospheric circulation . The method proposed might help to gain insight into the spatial structures of local instability in annulus flows.
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