Stability of a temporally evolving natural convection boundary layer on an isothermal wall. (2nd September 2019)

• Record Type: Journal Article
• Authors: Ke, Junhao; Williamson, N.; Armfield, S. W.; McBain, G. D.; Norris, S. E.
• Is Part Of: Journal of fluid mechanics. Volume 877(2019)
• Page Start: 1163
• Page End: 1185
• Publication Date: 2019-09-02
• Subjects: boundary layer stability, -- absolute/convective instability; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2019.639
• Languages: English
• ISSNs: 0022-1120

Abstract

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.