The analytical expression for the root-mean-square (Rms) beam width of the radial Gaussian beam array propagating in oceanic turbulence is derived, where the coherent combination is considered. Meanwhile, the analytical expression for effect of the turbulence on the beam F is also obtained. Giving a comparison of results of F calculated by the analytical expression and the previously integrating one, it can be seen that the two results are in agreement with each other exactly. Further, the influences of the rate of dissipation of mean-squared temperatureχ(T), the rate of dissipation of kinetic energy per unit mass of seawater εand the ratio of temperature to salinity contribution to the refractive index spectrum w are investigated. The results indicate that the Rms beam width increases as χ(T) increases, εdecreases and the salinity-induced turbulence dominates. Moreover, the changings of effective radius of curvature with mentioned above parameters are studied. The strength of turbulence determines the value of effective radius of curvature, and which decreases asχ(T) and w increases, and εdecreases.
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