The velocity fluctuations at one point of a strongly turbulent air flow, produced by arrays of jets, are analyzed up to eighth order correlations. The odd order correlations show the proportionality factors already found in grid and boundary layer turbulence. Two numerical models are described, which rely on a simple nonlinear process to attempt to explain the observed results. The first model generates a signal where the relations between the phases of the Fourier components are limited to triplets. Except for short range correlations, the agreement with turbulent results is good. However, in the range of small, but still inertial, eddies, significant differences appear. The second model simulates abrupt jumps in velocity. It gives qualitative agreement through the entire range, thus showing that strong coupling of the phases, by occasional discontinuities can produce the same appearance of weak phase relations in the range of medium to large eddies, as well as the short range behavior.