This comment addresses the article “Instabilities of rotating inclined buoyancy layers” by Xiao et al. [Phys. Rev. E 108, 025102 (2023)], which presents linear stability results of Prandtl's slope flow subjected to surface cooling and the additional effect of rotation. Our main point of contention concerns the steady base flow used in their work, which the authors claim fulfills all physically plausible boundary conditions, including vanishing temperature difference and upslope velocity at infinite height. While the analytical base flow solution provided in their study satisfies the flow equations and boundary conditions of the standard Prandtl model in a mathematical sense, it suffers from a major physical inadequacy that greatly restricts its applicability to real flows, previously highlighted in literature. This restriction is due to the imposition of an additional (that is, not included in the original Prandtl model) upslope wind forcing term representing an upslope perturbation pressure gradient force. To obtain a steady state, this term must be artificially linked to the slope angle, surface buoyancy, and other governing parameters. Moreover, this term must be imposed externally and becomes infinite for vanishing slope angle, both conditions that are physically unjustifiable. As a second point, we contest the authors' classification of the traveling waves in their study as Tollmien-Schlichting modes, which are characterized by the destabilizing effect of viscosity. Instead, we assert that the nature of the traveling waves—also present in nonrotating Prandtl slope flows as shown in previous literature—are inviscid and should be attributed to an inertial-type Kelvin-Helmholtz instability, amplified by the infinite number of inflection points in the analytical base flow profile.

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• Boundary layer receptivity, stability & separation
• Flow instability
• Rotating geophysical flows
• Stratified geophysical flows
• Thermal convection