Simplified model of underwater electrical discharge

A model of the underwater discharge with initiating wire is presented. The model reveals the nature of similarity parameters which have been phenomenologically introduced in earlier experimental research in order to predict behavior of different discharges. It is shown that these parameters naturally appear as a result of the normalization of differential equations, which determines the process of underwater wire initiated discharge. In these equations the energy conservation law for wire material evaporation and the dependence of plasma conductivity on the energy dissipated in the discharge are implied to calculate the time varying resistance of the discharge gap. The comparison of calculations with the experimental results shows that good agreement is achieved when modification of these parameters is introduced. These new similarity parameters are functions of the original similarity parameters, hence the law of the similarity of underwater electrical discharge is preserved.