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This paper investigates the effects of surface roughness on the convective stability behavior of boundary-layer flow over a rotating disk. An enforced axial flow and the Miklavčič and Wang (MW) model of roughness are applied to this flow. The effects of both anisotropic and isotropic surface roughness on the distinct instability properties of the boundary-layer flow over a rotating disk will also be examined for this model. It is possible to implement these types of roughness on this geometric shape while considering an axial flow. This approach requires a modification for the no-slip condition and that the current boundary conditions are partial-slip conditions. The Navier–Stokes equations are used to obtain the steady mean-flow system, and linear stability equations are then formulated to obtain neutral stability curves while investigating the convective instability behavior for stationary modes. The stability analysis results are then confirmed by the linear convective growth rates for stationary disturbances and the energy analysis. The stability characteristics of the inviscid type I (or cross-flow) instability and the viscous type II instability are examined over a rough, rotating disk within the boundary layer at all axial flow rates considered. Our findings indicate that the radial grooves have a strong destabilizing effect on the type II mode as the axial flow is increased, whereas the concentric grooves and isotropic surface roughness stabilize the boundary-layer flow for the type I mode. It is worth noting that the flows over a concentrically grooved disk with increasing enforced axial flow strength are the most stable for the inviscid type I instability.
Al-Malki et al. (Fri,) studied this question.