Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second-order adjoint-based sensitivity for hydrodynamic stability and
  control   Adjoint-based sensitivity analysis is routinely used today to assess
efficiently the effect of open-loop control on the linear stability properties
of unstable flows. Sensitivity maps identify regions where small-amplitude
control is the most effective, i.e. yields the largest first-order (linear)
eigenvalue variation. In this study an adjoint method is proposed for computing
a second-order (quadratic) sensitivity operator, and applied to the flow past a
circular cylinder, controlled with a steady body force or a passive device
model. Maps of second-order eigenvalue variations are obtained, without
computing controlled base flows and eigenmodes. For finite control amplitudes,
the second-order analysis improves the accuracy of the first-order prediction,
and informs about its range of validity, and whether it underestimates or
overestimates the actual eigenvalue variation. Regions are identified where
control has little or no first-order effect but a second-order effect. In the
cylinder wake, the effect of a control cylinder tends to be underestimated by
the first-order sensitivity, and including second-order effects yields larger
regions of flow restabilisation. Second-order effects can be decomposed into
two mechanisms: second-order base flow modification, and interaction between
first-order modifications of the base flow and eigenmode. Both contribute
equally in general in sensitive regions of the cylinder wake. Exploiting the
second-order sensitivity operator, the optimal control maximising the total
second-order stabilisation is computed via a quadratic eigenvalue problem. The
approach is applicable to other types of control (e.g. wall blowing/suction and
shape deformation) and other eigenvalue problems (e.g. amplification of
time-harmonic perturbations, or resolvent gain, in stable flows).

29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess