A phenomenon called thermal striping, consisting of quasiperiodic temperature oscillations, is of significant concern in liquid-metal-cooled nuclear reactors. While it is believed to be caused by a shear-flow instability, the physical mechanism is not fully understood, and is thus difficult to predict. We consider plane Poiseuille flow with stable density stratification in the wall-normal direction as a model for hydrodynamic instability in a heated, wall-bounded shear flow characteristic of thermal striping scenarios. The temporal linear stability eigenvalue problem is then solved, and the neutral curves are calculated for different stratification levels. Excellent collapse of the neutral curves is observed in the limit of small Péclet number, $\text{Pe}\lesssim 1$, when curves are shown as a function of a modified Richardson number, $\mathcal{R}=\text{Ri}·\text{Pe}$. Furthermore, the normal modes are stable for all Reynolds numbers when $\mathcal{R}$, is greater than some critical value ${\mathcal{R}}^{*}$, with ${\mathcal{R}}^{*}\doteq 0.3338$. We further develop a perturbation solution of the low-Péclet-number equations (LPNE) of Lignières [Astron. Astrophys 348, 933 (1999)], which contains $\mathcal{R}$ as the natural parameter controlling buoyancy forces. The perturbation eigenvalue problem is solved to $\mathcal{O}\left(\mathcal{R}\right)$. The perturbation of the growth rate is negative, indicating stratification has a strictly stabilizing effect. An analytical solution in the infinite Re limit is developed for the perturbation system, which also confirms stratification's stabilizing effect. The relevance of the results to thermal striping in liquid-metal-cooled nuclear reactors is also discussed.

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• Flow instability
• Perturbative methods