Wave and phase structure functions of plane and spherical waves in particle-free natural turbulent waters

The expressions for the wave and the phase structure functions of a plane wave and a spherical wave propagating in the natural water turbulence characterized by the recently developed spatial power spectrum (Yao et al., 2020) are evaluated in general and in the limits of large and small separations. The spatial coherence radius for both plane and spherical waves is then deduced. The angle-of-arrival variance of these wavefronts at the collecting lens of the receiving system is also evaluated. In-depth numerical illustrations of the dependence of these quantities on the average temperature/salinity, temperature/energy dissipation rates, and the temperature-salinity gradient ratio are included. Our results are of utmost importance for underwater imaging and sensing technologies.