New Calculations of the Turbulence-Turbulence Contribution to the Wind Noise Pressure Spectra within Homogeneous Anisotropic Turbulence

The turbulence-turbulence interaction and the turbulence-shear interaction are the sources of intrinsic pressure fluctuation for wind noise generated by atmospheric turbulence. In previous research [Yu et al., J. Acoust. Soc. Am. 129(2), 622-632 (2011)], it was shown that the measured turbulent fields outdoors can be realistically modeled with Kraichnan's mirror flow model [Kraichnan, J. Acoust. Soc. Am. 28(3), 378-390 (1956)]. This paper applies Kraichnan's mirror flow idea to develop theory for calculating the turbulence-turbulence interaction wind noise pressure spectra within homogeneous anisotropic turbulence. New calculations of the turbulence-turbulence contribution to the wind noise pressure spectra by incorporating turbulence anisotropy are performed and compared to the result using the same approach but with isotropic input and the result of the turbulence-turbulence interaction pressure spectrum for homogeneous isotropic turbulence using George et al.'s method [George et al., J. Fluid Mech. 148, 155-191 (1984)]. We also evaluated different contributions to the turbulence-turbulence interaction pressure spectra using our approach with both anisotropic and isotropic inputs. Our results indicate that the turbulence anisotropy has small effect on the turbulence-turbulence interaction pressure in source region, but changes the spectral slope in inertial region to about -5/3. The turbulence-turbulence interaction pressure spectrum incorporating turbulence anisotropy is not sensitive to height. The F33F33 term and the F11F11 term are the most dominant contributions to the anisotropic turbulence pressure spectra in the source region and inertial region, respectively.