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The trace of vertical vortex flow at hydraulic intakes is of the shape of spiral lines, which was observed in the presented experiments with the tracer technique. It represents the fluid particles flow spirally from the water surface to the underwater and rotate around the vortex-axis multi-cycle. This process is similar to the movement of screw. To describe the multi-circle spiral characteristics under the axisymmetric condition, the vertical vortex would change not only in the radial direction but also in the axial direction. The improved formulae for three velocity components for the vertical vortex flow were deduced by using the method of separation of variables in this article. In the improved formulae, the velocity components are the functions of the radial and axial coordinates, so the multi-circle spiral flow of vertical vortex could be simulated. The calculated and measured results for the vertical vortex flow were compared and the causes of errors were analyzed.