The wall pressure statistics
The random forces resulting from pressure fluctuations in the turbulent boundary layer over structural surfaces cause vibration. This surface motion becomes a source of noise which must be considered in the design of a vehicle. Therefore, the development of methods aimed at predicting interior noise levels, pressure fluctuations, and structural loading has become important in the design for instance of commercial aircraft, payload-carrying aerospace launchers, high speed trains. As pointed out by Graham (1996), in order to take into account this aspect in the design phase, there is a need for simple models capable of enhancing our physical understanding of the noise generation process and to provide relatively simple predictive formula to be utilized in the design process.
The methods of modeling and predicting sound and vibrations from a structure subject to a random pressure load, presume that the forcing function for the surface has been estimated. It can be shown [see e. g. Blake (1986) and Graham (1997)] that the excitation term is directly related to the boundary layer wavenumber-frequency spectrum that, therefore, has become the subject of many investigations. In the present discussion, we
do not enter into the details of the structural aspects, but we limit ourselves to reviewing the main features concerning the wavenumber-frequency spectrum analysis, modeling and prediction.