It is well known that there are two typical phase singularities in the fully coherent beams, i.e., the optical vortex and the edge dislocation. Although much of research has explored properties of the fully coherent beams, there are practical uses of the partially coherent beams because they are more resistant to degradation with propagation through turbulent medium than the former. The propagation of the partially coherent beams carrying coherence singularities in oceanic turbulence has attracted much attention due to its application in underwater wireless communication. It is interesting to ask how oceanic turbulence can affect the interaction of coherence vortex and edge dislocation carried by partially coherent beams. Because the Gaussian Schell-model beam is a typical example of partially coherent beams, the interaction of the coherence vortex and edge dislocation carried by the Gaussian Schell-model beams in oceanic turbulence is studied in detail.

By making an analogy with definition of the edge dislocation in coherent beams, the coherence edge dislocation is shown to be in existence in partially coherent beams. Based on the extended Huygens-Fresnel principle, the analytical expression of the cross-spectral density for the Gaussian Schell-model beams carrying the coherence vortex and edge dislocation propagating through oceanic turbulence is derived, which is used to study the interaction of them in oceanic turbulence. The position of correlation singularities of the partially coherent beams at the z plane can be determined by the curves of the real component and imaginary component, as well as phase distribution of the spectral degree of coherence of the Gaussian Schell-model beams.

There should exist another type of coherence singularities, namely the coherence edge dislocation with π-phase jump located along a line in the transverse plane of the correlation function, which is different from the edge dislocation in fully coherent beams (Fig.1), because the transverse edge dislocation with π-phase shift is located along a line in the transverse plane. The coherence edge dislocation is split into two optical vortices by the coherence vortex if the edge dislocation is off-axis, while it is broken into one optical vortex as it is on-axis. The result is similar to the interaction of the phase vortex and edge dislocation in free space. The coherence edge dislocation is translated into one coherence vortex or two vortices with propagation of the beams in oceanic turbulence (Fig.3). The total topological charge is not conserved with propagation of the initial beams with the coherence vortex and off-axis edge dislocation in oceanic turbulence, because appearance or disappearance of a coherent vortex may take place with propagation. The result is different from the interaction of a phase vortex and an off-axis edge dislocation in free space, because the total topological charge is conserved in the latter case. The evolution of the coherence singularities speeds up with increasing the value of the rate of dissipation of mean-square temperature χ_T and the relative strength of salinity and temperature fluctuation_{ω, as well as decreasing the rate of dissipation of turbulent kinetic energy per unit mass ε (Fig.4). The physical reason can be explained by the theoretical expression of the strength of oceanic turbulence. It is seen that the strength of the oceanic turbulence becomes stronger with increasing the rate of dissipation of mean-square temperature and the relative strength of salinity and temperature fluctuation, as well as decreasing the rate of dissipation of turbulent kinetic energy per unit mass. When the initial beam parameters, such as the spatial correlation length δ0, the off-axis distance and the slope of the edge dislocation of the coherence edge dislocation change, the changes of positions and number of coherence singularities in the fields take place with propagation of the beams. It is found that not only creation and annihilation of a pair of coherent vortices, but also appearance and disappearance of a vortex take place with varying the initial beams parameters (Figs.5‒7).}

In the present study, we have firstly introduced the definition of the coherence edge dislocation in accordance with previous researches. Then, the analytical expression of the cross-spectral density for the Gaussian Schell-model beams carrying the coherence vortex and edge dislocation propagating through oceanic turbulence is derived, which is then used to study the interaction of them in oceanic turbulence. It has been shown that the interaction depends on propagation distance, oceanic turbulence parameters, and the beam parameters such as the spatial correlation length and the slope and off-axis distance of the coherent edge dislocation. The creation and annihilation of pairs of coherence vortices occur and the appearance and disappearance of a coherent vortex may also take place by changing these influencing factors. The total topological charge is not generally conserved with propagation of the initial beams. Furthermore, the stronger the oceanic turbulence is, the faster the decrease of the distance for the conservation of the topological charges is.