### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 2aNS2. An analytical and statistical examination of the low-wave-number
region of the turbulent boundary layer wall pressure.

**Y. F. Hwang
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*Naval Surface Warfare Ctr., Carderock Div., Code 7200, Bethesda, MD 20084
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The underlying physical mechanisms that generate the low-wave-number
pressure components of the turbulent boundary layer wall pressure are examined
based on a solution of linearized Navier-Strokes equations in the viscous
sublayer with no-slip wall condition. The result indicates that the predominant
low-wave-number pressure components are generated by viscous diffusion of shear
stress fluctuations at the no-slip wall. These random pressure components have a
wave-number spectrum spanning from zero wave number to well beyond the
convective wave number. However, their contribution to the convective ridge of
the wall pressure spectrum is negligible compared to those of other sources. In
the low-wave-number limit, we reach the same conclusion reached by Chase [J.
Fluid Mech. 225, 545--555 (1991)], i.e., the wave number spectral density does
not vanish as the streamwise wave number approaches zero. The reasons for
nonvanishing wave-number spectral density as k->0, for both shear stress and
wall pressure, are established analytically. A statistical model is derived
based on a probabilistic area-averaging on an assumed random process which is
capable of producing the measured two-point correlation functions. The result is
a space-time autocorrelation function that yields the experimental
low-wave-number data. [Work supported by NSWC ILIR Program and ONR.]