Boundary Layer Noise: The Relationship between Turbulent Shear Stress and the Turbulent Wall Pressure Field

Abstract

This paper presents a recently developed model of wall turbulence that provides a new interpretation of the turbulent wall pressure field and hence a new approach to related acoustical and vibrational problems. The theory suggests that the turbulent transfer of momentum is effected by a moving array of horse-shoe vortex structures that are generated and maintained by a spatio-temporal instability of the sublayer flow. As a result of the interaction between these vortex systems and the basic flow, a characteristic pressure signature is generated on the wall directly beneath each vortex structure, the shape and average strength of the signature being related to the local turbulent shear stress distribution. The turbulent wall pressure field is attributed to the motion of the resultant pattern of pressure signatures over the wall, and is seen as an integral and essential part of the turbulent shear stress mechanism. A new “pulse amplitude modulated” model of the pressure field is accordingly proposed in which the pressure at a fixed point on the wall is generated essentially at a single, characteristic frequency (related to local wall shear stress) by the regular or near regular passage of pressure pulses whose amplitudes vary randomly over a range determined by the ratio of boundary layer to sublayer thickness (i.e., over several orders of magnitude).