ABSTRACT 



A fully developed turbulent boundary layer with a zero pressure gradient 

 has been studied in a subsonic wind tunnel. The pressure fluctuations on the 

 wall of the wind tunnel were measured by small flush-mounted microphones. 

 Data for the dimensionless spectral density of the pressure fluctuations, 

 P (O/p^ ^0 S*) as a function of the frequency parameter f S*/Uq are presented; 

 P(/)» P? ^0' ^* ^"^ f ^""^ respectively the spectral density, fluid density, free 

 stream velocity, boundary layer displacement thickness, and frequency. Data 

 for the coefficient {v'^)^^^/VipUq are also presented. The transverse cross corre- 

 lation for the pressure fluctuations was studied by using two flush mounted 

 microphones. Rather than the longitudinal cross correlation, the longitudinal 

 cross spectral density was studied, yielding a measure of the coherence of the 

 pressure fluctuations at two points as a function of fx/U^, where x is the longi- 

 tudinal spacing of the two points and U^ is the effective convection velocity of 

 the spatial pattern. 



INTRODUCTION 



Pressure fluctuations necessarily coexist with velocity fluctuations in a turbulent 

 flow. For incompressible flow the pressure and velocity are related by the equation 



d'^u.u- 

 dx-d X- 



which can be obtained by combining the continuity and the Navier-Stokes equations. The 

 solution to this equation is given in terras of an integration over all space and shows that 

 for the case of boundary-layer flow, the vanishing of the velocity fluctuation at the wall does 

 not imply the vanishing of the pressure fluctuations at the wall. 



It is these pressure fluctuations on the wall adjacent to the turbulent boundary layer 

 that are the focus of interest in this study. Some measurements of the characteristics of 

 these pressure fluctuations are reported and the meaning of the measurements are interpreted. 



There are several reasons for being interested in the characteristics of the pressure 

 fluctuations. A direct and immediate need exists for data in the field of noise due. to unsteady 

 flow. When a turbulent boundary layer develops on a flexible wall, the motion of the wall 

 which results from the pressure fluctuations generates a sound field. Some of the noise in 

 aircraft has been attributed to this mechanism. Kraichnan^'^ has given a theoretical 



References are listed on page 12. 



