Crossflow transition prediction based on stationary mode saturation for hypersonic three-dimensional boundary layers

Accurate prediction of crossflow-induced transition in hypersonic boundary layers remains a critical challenge, primarily due to the pronounced nonlinear evolution of stationary crossflow vortices. This study proposes a prediction method that establishes the saturation position of stationary vortices as a transition onset indicator, complemented by a saturation criterion derived from Mack’s linear amplitude. To validate the saturation-transition correlation, direct numerical simulations of the complete transition process were conducted on a hypersonic swept flat plate with two distinct nose radii and wall temperature conditions. Results reveal that despite an order-of-magnitude variation in background disturbance levels, the resultant transition location shift remains constrained within 2-3 nose radii—close to the identified saturation points. Furthermore, the linear amplitude method demonstrates that for given flow conditions, a single threshold value of the linear amplitude reliably determines saturation positions across broad spanwise wavenumbers and initial amplitudes of stationary vortices. This finding validates the effectiveness of linear stability theory based approaches for crossflow transition prediction.