Characteristic parameters of optical wave and short-term beam spreading in oceanic turbulence

In 2000, Nikishov et al. presented an analytical model for the power spectrum of oceanic turbulence, in which the stable stratification of seawater is assumed, i.e., the eddy diffusivity of temperature is equal to that of salinity, and the eddy diffusivity ratio is equal to unity. Until now, all previous studies on the light propagation through oceanic turbulence were based on the Nikishov's power spectrum model. However, the eddy diffusivity of temperature and eddy diffusivity of salt are different from each other in most of underwater environments. Very recently, Elamassie et al. established a more reasonable power spectrum model of underwater turbulent fluctuations as an explicit function of eddy diffusivity ratio. The characteristic parameters such as the spatial coherence length of optical wave in turbulent medium play an important role in characterizing the strength of turbulence, the phase correction techniques in light propagation, etc. In the present paper, based on the Elamassie's power spectrum model of oceanic turbulence, the analytical formulae of the wave structure function, the spatial coherence length of optical wave and the Fried parameter in oceanic turbulence are derived, and the correctness of each of these formulae is verified. It is shown numerically that the results obtained by using the Elamassie's power spectrum model are quite different from those obtained by using the Nikishov's power spectrum model. If the Nikishov's power spectrum model is adopted, the strength of turbulence is underestimated when oceanic turbulence is dominated by the temperature fluctuations, while the strength of turbulence is overestimated when oceanic turbulence is dominated by the salinity fluctuations. If the Elamassie's power spectrum model is adopted, it is shown that the Kolmogorov five-thirds power law of the wave structure function is also valid for oceanic turbulence in the inertial range, and 2.1 times the spatial coherence length of optical wave is the Fried parameter, which are in agreement with those in atmospheric turbulence. In addition, based on the Elamassie's power spectrum model, the semi-analytical formula of the short-term beam spreading of Gaussian beams is derived in this paper, and its correctness is also verified. It is shown that the difference in short-term beam spreading is very large, whether the stable stratification of seawater is assumed or not. The results obtained in this paper are very useful for applications in optical communication, imaging and sensing systems involving turbulent underwater channels.