The acoustic receptivity of Tollmien–Schlichting (TS) waves due to two-dimensional sharp-edged rectangular bumps and gaps in a compressible boundary layer was investigated by direct numerical simulations. The conclusions were based on a new procedure proposed for obtaining the receptivity amplitudes which appeared to be more robust and accurate than previous ones. The procedure is particularly important for the correct evaluation of the receptivity of gaps. The receptivity amplitudes for gaps were smaller than those for bumps, except for the nominally zero height/depth roughness element, where, consistent with a linear behaviour, they had the same absolute value. The procedure also revealed in detail the behaviour in the region downstream of the roughness element where the TS wave is formed (the formation region). This region extends for approximately $50\delta ^*_{b}$ , regardless of bump height or gap depth. For bumps, the receptivity scaled superlinearly with bump height while for the gaps it scaled sublinear with depth. This behaviour is associated with the different velocity profiles caused by bumps and gaps in the formation region. We also discussed issues regarding comparison with experiments. Investigation of the effect of compressibility confirmed that, in the subsonic regime, the receptivity reduces with Mach number. Finally, we addressed the receptivity scaling with the acoustic wave amplitude. It was found that the receptivity scales linearly with the acoustic wave amplitude in a range for which experiments available in the literature indicated a superlinearly scaling. Reasons for these conflicting results are discussed.

We develop and implement a neural operator (NOp) to predict the evolution of waves on the surface of water. The NOp uses a graph neural network (GNN) to connect randomly sampled points on the water surface and exchange information between them to make the prediction. Our main contribution is adding physical knowledge to the implementation, which allows the model to be more general and able to be used in domains of different geometries with no retraining. Our implementation also takes advantage of the fact that the governing equations are independent of rotation and translation to make training easier. In this work, the model is trained with data from a single domain with fixed dimensions and evaluated in domains of different dimensions with little impact to performance.