Further Modeling of Turbulent Wall Pressure on a Cylinder and Its Scaling with Diameter

摘要

The possible scaling of the axisymmetric component of spectral density of wall pressure in turbulent flow along a slender cylinder is reexamined with use of a formal low-wavenumber expansion in terms of fluctuating Reynolds stresses as sources. A rudimentary model of the sources is formed that conforms to the principle of local similarity near the wall and to probable implications of fluctuating and mean velocity profiles measured in cylindrical boundary layers. To the extent that wall pressure is exclusively due to such a turbulence field, to zero order in wavenumber, at least, it is indicated to scale with cylinder radius (a) and to agree in functional dependence with the current model for this low-wavenumber component. If the turbulence field (despite lack of experimental evidence) involves in addition a weak component that scales with boundary-layer thickness, then at sufficiently low frequencies and wavenumbers the corresponding contribution to wall pressure (when delta/a>>1) may become dominant, and the extrapolation of the current model to very small omega a/U(Infinity) and the associated prediction of diameter dependence may then fail.