As a widespread meso-scale phenomena among deep-sea environment, meso-scale eddy greatly affect marine thermohaline structure, thereby modify underwater sound propagation characteristics，and until now it has not yet fully and clearly understand the relevant acoustic signal fluctuation and perturbation under such sophisticated marine enviornment, otherwise there are still many difficulty to monitor the variation of meso-scale eddy efficiently by applying acoustic method. In addition to some traditional ways such as acoustic transmitting time perturbation, now some researchers has focused on applying some acoustic variables, such as waveguide invariant, based on analyzing and describing sound propagation characteristics under meso-scale eddy environment. By considering the equivalent between ray theory and normal mode theory, deep-sea sound propagation characteristics is analyzed by applying ray stability parameter and waveguide invariant, considering the equivalent between period of horizontal interference of normal mode and ray horizontal span. The equivalent between ray stability parameter and scattering matrix of normal mode is also discussed. The temporal variation of ray stability parameter under cold eddy environment in the South China Sea is analyzed by applying acoustic propagation simulation data with data assimilation result of ocean model. When the cold eddy pass the acoustic section slowly, the according results show that the variability of ray stability parameter is more stable compared with those of waveguide invariants, when sound propagate in environment consisting of a range-independent background on which a weak range-dependent perturbation is superimposed. The variation of ray stability parameter present the temporal-spatial characteristics of marine environment more clearly, therefore there are great potentiality for applying ray stability parameter in the deep-sea acoustic monitoring.