Optimal perturbations of gravitationally unstable, transient boundary layers in porous media

@article{Daniel2013OptimalPO,
  title={Optimal perturbations of gravitationally unstable, transient boundary layers in porous media},
  author={Don Daniel and Nils Tilton and Amir Riaz},
  journal={Journal of Fluid Mechanics},
  year={2013},
  volume={727},
  pages={456 - 487}
}
Abstract We study the linear stability of gravitationally unstable, transient, diffusive boundary layers in porous media using non-modal stability theory. We first perform a classical optimization procedure, using an adjoint-based method, to obtain the perturbations at the initial time $t= {t}_{p} $ that have a maximum amplification at a final time $t= {t}_{f} $. We then investigate the sensitivity of the optimal perturbations to the initial time, ${t}_{p} $, and the final time, ${t}_{f} $, as… 

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