| The vertical vortex frequently occurs at hydraulic intakes such as diversion pipeline, diversion tunnel, spillway and pumping station. Its'existence can worsen the flow pattern of intakes, cause discharge reduction, decrease the generating capacity, increase the fluctuation of hydraulic structure, and cause cavitations damage. The research for hydraulic characteristics of vertical vortex is the base of knowing and avoiding it. It is a regret that the research results cannot satisfy the demand of engineering design now. The experimental investigations mainly pay attention to the actual projects and the anti-vortex measures. It is lack of the theory research for the vertical vortex and the numerical calculation is on the initial step. Therefore it is urgent to study the hydraulic phenomenon about the vertical vortex.The key hydraulic characteristics of vertical vortex are the multi-circle spiral flow and funnel-shaped free water surface, which are studied by theory, experimental investigation, and numerical simulation in this paper. The main contents of the studies and achievements are as follows:1. The key idea of the separation of variables is introduced for the mathematical analysis of the vertical vortex in this paper, which no...
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