Measurement of the gradient field of a turbulent free surface

We study the free surface above a turbulent channel flow. We describe a laser scanning technique that can be used to measure the space–time turbulent surface gradient field along a line. A harmonically swiveling laser beam is focused on the surface and its angle of refraction is measured using a position sensing device. The registered signals can be converted easily to the desired gradient field, and spectra and correlations can be measured. Examples of measured spectra and correlation functions of the surface above a turbulent channel flow (Reynolds number R _λ ≈ 250) demonstrate the viability of the technique. We further assess the validity of Taylor’s frozen turbulence hypothesis that implies that time-dependent signals measured along a line that is oriented perpendicularly to the mean channel velocity can be interpreted as 2D measurements of the surface slope. While Taylor’s hypothesis works for a turbulent velocity field, it does not work for its free surface.

Willem van de WaterEmail: