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On the stability of plane parallel convective flow

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Summary

The Lyapunov direct method is used to study the nonlinear stability of parallel convective shear flows of an incompressible fluid heated from below with stress-free boundaries. In particular it is showed that plane Couette and plane Poiseuille flows with linear temperature profile are conditionally asymptotically stable, in a stronger norm than the “energy norm”, whenever the Rayleigh number ℛ2 is less than 657.511, independent of the Reynolds numbersR.

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  1. G. Mulone

    Present address: Dipartimento di Matematica, Viale A. Doria 6, I-95125, Catania, Italy

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    1. G. Mulone
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    Mulone, G. On the stability of plane parallel convective flow. Acta Mechanica 87, 153–162 (1991). https://doi.org/10.1007/BF01299792

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