Phase autocorrelation of random wave fields

The autocorrelation function of the phase of a random gaussian wave field has been measured by computer experiment and found to be in both quantitative and qualitative disagreement with previous calculation of this quantity. A new topological theory for the limiting form of the autocorrelation function for small displacements is developed and shown to be in substantial agreement with the measurements. This topological theory predicts that for extended random wave fields the widths of the phase and field autocorrelation functions both collapse to zero when the net vorticity per unit area differs from zero. Gaussian statistics are used to calculate the full phase autocorrelation function of random wave fields that have zero net vorticity. This new calculation is found to be in good agreement with the data over the whole range of measurement.