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Unconditional nonlinear stability for convection in a porous medium with vertical throughflow

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Summary

Linear and nonlinear stability analyses of vertical throughflow in a fluid saturated porous layer, which is modelled using a cubic Forchheimer model, are studied. To ensure unconditional nonlinear results are obtainable, and to avoid the loss of key terms, a weighted functional is used in the energy analysis. The linear instability and nonlinear stability thresholds show considerable agreement when the vertical throughflow is small, although there is substantial deterioration of this agreement as the vertical throughflow increases.

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  1. Department of Mathematical Sciences, University of Durham, Durham, DH1 3LE, UK

    A. A. Hill

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  1. A. A. Hill
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Correspondence to A. A. Hill.

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Hill, A.A. Unconditional nonlinear stability for convection in a porous medium with vertical throughflow. Acta Mechanica 193, 197–206 (2007). https://doi.org/10.1007/s00707-007-0473-5

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  • DOI: https://doi.org/10.1007/s00707-007-0473-5

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