Measurement of spatiotemporal phase statistics in turbulent air flow using high-speed digital holographic interferometry.

We describe a method of measuring spatiotemporal (ST) structure and covariance functions of the phase fluctuations in a collimated light beam propagated through a region of refractive index turbulence. The measurements are performed in a small wind tunnel, in which a turbulent temperature field is created using heated wires at the inlet of the test section. A collimated sheet of light is sent through the channel, and the phase fluctuations across the sheet are measured. The spatial phase structure function can be estimated from a series of images captured at an arbitrary frame rate by spatial phase unwrapping, whereas the ST structure function requires a time resolved measurement and a full three-dimensional unwrapping. The measured spatial phase structure function shows agreement with the Kolmogorov theory with a pronounced inertial subrange, which is taken as a validation of the method. Because of turbulent mixing in the boundary layers close to the walls of the channel, the flow will not obey the Taylor hypothesis of frozen turbulence. This can be clearly seen in the ST structure function calculated in a coordinate system that moves along with the bulk flow. At zero spatial separation, this function should always be zero according to the Taylor hypothesis, but due to the mixing effect there will be a growth in the structure function with increasing time difference depending on the rate of mixing.