### Abstract

We consider the nonlinear evolution of vortex instabilities in a near-vertical free convection boundary layer in a porous medium. At such inclinations, both small amplitude and strongly nonlinear disturbances may be described within the confines of boundary-layer theory with no further approximations. Steady vortices are induced by placing a thermal disturbance within the boundary layer and by computing their development downstream using a parabolic solver. It is found that the strength of the resulting convection depends not only on the wavelength of the vortex disturbance, but also on the amplitude of the disturbance and its point of introduction into the boundary layer. Whenever vortices grow, they attain a maximum strength before decaying once more. Curiously, there is a specific disturbance amplitude that yields the largest possible response downstream, in the sense that both smaller and larger initial amplitudes yield weaker responses. This unusual phenomenon is shown to be related to the shape of the vortex.

Original language | English |
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Pages (from-to) | 1575-1592 |

Number of pages | 18 |

Journal | Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences |

Volume | 458 |

Issue number | 2023 |

DOIs | |

Publication status | Published - 2002 |