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Sparsifying the resolvent forcing mode via gradient-based optimisation
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DOI：10.1017/jfm.2022.519.png)
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We consider the use of sparsity-promoting norms in obtaining localised forcing structures from resolvent analysis. By formulating the optimal forcing problem as a Riemannian optimisation, we are able to maximise cost functionals whilst maintaining a unit-energy forcing. Taking the cost functional to be the energy norm of the driven response results in a traditional resolvent analysis and is solvable by a singular value decomposition (SVD). By modifying this cost functional with the L-1-norm, we target spatially localised structures that provide an efficient amplification in the energy of the response. We showcase this optimisation procedure on two flows: plane Poiseuille flow at Reynolds number Re = 4000, and turbulent flow past a NACA 0012 aerofoil at Re = 23 000. In both cases, the optimisation yields sparse forcing modes that maintain important features of the structures arising from an SVD in order to provide a gain in energy. These results showcase the benefits of utilising a sparsity-promoting resolvent formulation to uncover sparse forcings, specifically with a view to using them as actuation locations for flow control.
Keyword:
shear-flow instability
instability control
期刊
IF:
3.9
论文数:
2.0W
被引数:
9.4W
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