Extended Taylor frozen-flow hypothesis and statistics of optical phase in aero-optics

We present an extended Taylor frozen-flow model for the statistics of the spatiotemporal disturbances of the index of refraction of air and the phase of an optical beam propagated through the turbulent boundary and shear layers in a high-Reynolds-number flow. By incorporating rapid random fluctuations of the flow velocity about a mean convection velocity and an anisotropic spatial power spectrum for the index of refraction, we calculate both the short-delay temporal structure function and the power spectral density of these disturbances. We discuss the predicted scaling behaviors for these quantities in the context of existing experimental observations, showing specifically the agreement of these predictions with some optical phase data obtained by the Airborne Aero-Optical Laboratory.