Görtler vortices evolve in boundary layers over concave surfaces as a result of the imbalance between centrifugal effects an radial pressure gradients. Depending on various geometrical and flow conditions, these instabilities may lead to secondary instabilities and further downstream to premature precursors to turbulence. In this paper, the growth of Görtler vortices excited by distributed roughness elements is analyzed using the solution to nonlinear boundary region equations with upstream boundary conditions derived previously via an asymptotic analysis applied in the vicinity of the roughness elements. Generalized Rayleigh pressure equation derived for the transverse flow is used to determine the growth rates associated with the secondary instabilities. Within the analysis, the roughness shape, height and diameter, as well as the spanwise separation between the roughness elements are varied in the linear regime, while keeping the same Görtler number. Among other various results, it is found that hill type shape distributed roughness elements are more likely to excite the Görtler instabilities than sharp edge type (e.g., cylindrical) roughness elements, and by increasing the roughness diameter, the size of Görtler vortices associated with the hill type roughness are increasing as expected, but the size of Görtler vortices associated with cylindrical elements are decreasing.

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