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Stability of a temporally evolving natural convection boundary layer on an isothermal wall

  • Junhao Ke (a1), N. Williamson (a1), S. W. Armfield (a1), G. D. McBain (a2) and S. E. Norris (a3)...

Abstract

The stability properties of a natural convection boundary layer adjacent to an isothermally heated vertical wall, with Prandtl number 0.71, are numerically investigated in the configuration of a temporally evolving parallel flow. The instantaneous linear stability of the flow is first investigated by solving the eigenvalue problem with a quasi-steady assumption, whereby the unsteady base flow is frozen in time. Temporal responses of the discrete perturbation modes are numerically obtained by solving the two-dimensional linearized disturbance equations using a ‘frozen’ base flow as an initial-value problem at various $Gr_{\unicode[STIX]{x1D6FF}}$ , where $Gr_{\unicode[STIX]{x1D6FF}}$ is the Grashof number based on the velocity integral boundary layer thickness $\unicode[STIX]{x1D6FF}$ . The resultant amplification rates of the discrete modes are compared with the quasi-steady eigenvalue analysis, and both two-dimensional and three-dimensional direct numerical simulations (DNS) of the temporally evolving flow. The amplification rate predicted by the linear theory compares well with the result of direct numerical simulation up to a transition point. The extent of the linear regime where the perturbations linearly interact with the base flow is thus identified. The value of the transition $Gr_{\unicode[STIX]{x1D6FF}}$ , according to the three-dimensional DNS results, is dependent on the initial perturbation amplitude. Beyond the transition point, the DNS results diverge from the linear stability predictions as nonlinear mechanisms become important.

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Corresponding author

Email address for correspondence: junhao.ke@sydney.edu.au

References

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Stability of a temporally evolving natural convection boundary layer on an isothermal wall

  • Junhao Ke (a1), N. Williamson (a1), S. W. Armfield (a1), G. D. McBain (a2) and S. E. Norris (a3)...

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