## 1 Introduction  
Submerged self-resonating waterjet is a simple means with strong self-oscillating cavitation characteristics [1; 2], which have been widely applied in the industries of cutting of solid materials, cleaning and burry removal of complicated mechanical products [3; 4; 5]. Over the past few years, deep-sea resources have attracted worldwide attention, and self-resonating waterjet also has broad applications in the exploitation of deep-sea mineral resources. The deep-sea environment is so complex, and the mineral resources have a changeable outlook when facing different erosion materials and cavitation behaviors, the confining pressure and the velocity of the flow decision on the oscillation characteristics of self-resonating waterjet. Although the modulation mechanisms of oscillation characteristics are a key technology in a complex deep-sea environment, it still not perfect.  
Thus far, many experimental studies on submerged self-resonating waterjet have been done with the driving pump pressure [6], structure and size of the nozzle [7], cavitation erosion [8], etc., which, evaluated by the losing mass of the specimen, have the disadvantage of long erosion time [9]. Additionally, by contrast images, one or two cycles from the high-speed visualization in the article [10], the research of the cavitation cloud is defective for the influence of the unsteady pressure.  
Moreover, in recent years, many researchers have focused on the mathematical modeling of oscillation characteristics of submerged self-resonating waterjets. [PERSON] [11] studied the critical cavitation number and the vortex shedding by various liquid pressures and several jet exit velocities under the submerged conditions. They suggestedthe empirical formula of the force ratio at different cavitation numbers. [PERSON] [12] established a numerical finite-difference solution for simulating the process of cavitation bubbles form, collapse, rebound and travel along the jet. They combined the computational fluid dynamics results and the modified Euler and Runge-Kutta-Fehlber, and successfully solved more wide range results of Rayleigh-Plesset formula solutions. In this research [13], we had pointed out that the resonance frequency of the nozzle played an important role in modulating the oscillation characteristics. According to the \"triad resonance\" theory, the frequencies bands of the self-resonating waterjet had acquired.  
Furthermore, with the development of CFD, numerical studies for submerged self-resonating waterjet have seen flourishing development, for prediction cavitation erosion [14], bubble dynamics [15], aided design [16], etc. However, the systematically specialized research on submerged self-resonating waterjet velocity, pressure, and cavitation distribution characteristics is not enough.  
For the investigation of the modulation mechanisms of the submerged self-resonating waterjet, the present study has started from the resonance frequency of the self-oscillating jet, based on mixture multiphase models, coupling realizable turbulence model and Schnerr-Sauer cavitation model, a two-phase flow model of submerged self-resonating waterjet is developed. Define and adjust model parameters, cater to the \"triad resonance\" theory--the fundamental frequency, the nature frequency, the resonance frequency are almost equal [17], and comparison of frequency distribution characteristics of numerical simulations against experimental data of the pressure oscillation is done. Based on this, the structural characteristics of the flow field at the nozzle exit are systematically studied.