Correction Functions for the Pressure Fluctuation Field

In this chapter, we shall use the general results of Chapter Three together with the field models presented in the last chapter to construct correction functions that take into account the effect of the size of the receiving surface of the transducer on the measured spectral characteristics of the turbulent pressure field near a wall. We begin with the correction functions for the power spectrum. The relationship between the size of the receiving surface of a pressure transducer and the size of the smallest eddies in the boundary layer is such that the measured power spectrum is sensitive to the transducer size in a broad frequency range, and the distortion of the spectrum at high frequencies may amount to several orders of magnitude. It is then frequently impossible to use the uncorrected measurements directly. Since the pressure field at each point in space is determined by the velocity field within a certain volume of the fluid (theoretically, in the entire volume of the turbulent fluid), the pressure field is less “rigid” than the velocity field. The measured power spectra and the correction functions are, therefore, often given as functions of the frequency and not of the wavenumber (as in the case of the velocity fluctuations considered in Section 3.4).