Low-dimensional subspace and local dynamical equilibrium in transonic buffet

The transonic buffet phenomenon over the ONERA OAT15A supercritical airfoil is investigated using two-dimensional unsteady Reynolds-averaged Navier–Stokes simulations with Reynolds Stress Model turbulence closure at M∞=0.73 and α=3.5°. The simulations reproduce the characteristic self-sustained shock oscillation, shock–boundary layer interaction, and periodic aerodynamic response, with a dominant buffet frequency of 166.5 Hz corresponding to St=0.070, consistent with available experimental measurements. Proper Orthogonal Decomposition identifies a dominant conjugate modal pair containing approximately 83% of the total modal energy, highlighting the low-dimensional organization of the principal buffet dynamics. A two-dimensional Koopman representation is subsequently employed to assess the dynamical closure of the dominant modal coordinates, establishing a coherent reduced temporal description of the buffet cycle. Building on this reduced dynamics, a theoretical and mathematical formulation is introduced to interpret the dominant shock-associated motion as a local dynamical equilibrium of the evolving flow state. The formulation provides a complementary description of the established shock–boundary layer feedback by organizing its collective effect through inertial, restoring, and non-conservative contributions. Finally, a two-mode lower-order reconstruction reproduces the dominant flow evolution with a mean normalized error of 4.67%, while the reconstructed lift and drag histories achieve correlation coefficients of 0.998 and 0.976, respectively. The results connect the established low-dimensional structure of transonic buffet with its dynamical closure and a local dynamical-equilibrium interpretation, while demonstrating the effectiveness of the resulting reduced representation.