Beyond secondary instability: on the emergence of finite-amplitude waves in Görtler vortices

Görtler vortices developing over a concave wall support rapidly oscillating wavelike disturbances through secondary instabilities. Although experiments indicate that the finite-amplitude evolution of these waves acts as a precursor to turbulence transition, accurate and efficient prediction has remained out of reach. We overcome this limitation by using the parabolised coherent structures (PCS) method of Song & Deguchi (2025 J. Fluid Mech. , vol. 1025, A42), which incorporates the nonlinear vortex-wave interaction into a standard spatial-marching approach. Our computational results agree well with the wave amplitude and displacement thickness observed in the widely known experiments of Swearingen & Blackwelder (1987 J. Fluid Mech. , vol. 182, pp. 255–290).