Abstract: In this paper, based on the idea of the multi-temperature model, the characteristic information of distribution of vibrational levels is phenomenologically analyzed and the vibration-dissociation coupling characteristics of diatomic molecules in nonequilibrium relaxing process are also investigated. It is found that the lower and higher vibrational levels of diatomic molecule could reach an independently quasi-equilibrium relatively fast, but the relative population density difference between the vibrational levels, which caused by the partially dissociation of the higher levels, could lead to the redistribution of all vibrational levels. And this redistribution process is also a cumulating energy process for dissociation in which the molecules of the lower levels would be excited to the higher levels through the mid-vibrational levels by vibrational-vibrational and translational-vibrational energy exchange in sequence. By modifying the Hammerling hypothesis, the vibrational temperature are redefined by the distribution of mid-levels of vibration, and a new correlated vibrational and translational temperatures model of diatomic molecular vibrational levels population distribution in thermodynamic nonequilibrium states is built. The simulation results of the nonequilibrium nitrogen species relaxation process behind a shock wave show that this model can predict the incubation period and the relaxation time characteristic of average vibrational energy and vibrational temperature.

Key words: nonequilibrium flow, distribution functions of vibrational level, vibration-dissociation coupling, vibrational temperature, incubation period