This paper presents theoretical analyses of flow fields on an axial pump or compressor, where the main flow enters from one side of the cylindrical casing, whereas an axially reverse and tangentially whirling flow enters from the tip clearance between the casing and the impeller, which sucks in the mixed flow. In this flow field, several secondary vortices exist in the mixing zone across the contact surface between the main and the axially reverse tangentially whirling flow. This type of secondary vortex is called a “backflow vortex.” The backflow vortices are tornado-like, parallel to the casing axis, and periodically distributed on the contact surface; they revolve around the casing axis and rotate around themselves. Regarding the backflow vortices, the relationships between their number (N), revolving diameter (d), revolving angular velocity (ω), and the ratio of the forced vortex region to the distance between the secondary-vortex center and the cylindrical wall (f) were all theoretically investigated. The five major findings are as follows: First, between d, ω, N, and f, any parameter can be determined if the other three are specified. Second, ω decreases, N increases, or f increases when d is increased and the other two are fixed. Third, d decreases, N increases, or f increases when ω is increased and the other two are fixed. Fourth, d increases, ω increases, or f decreases when N is increased and the other two are fixed. Fifth, d increases, ω increases, or N decreases when f is increased and the other two are fixed. To validate these theoretical results, “backflow vortex cavitation,” which occurs around the center of the backflow vortices on a rotating inducer as a representative of axial pumps or compressors, was observed. The backflow vortex cavitation is visible; therefore, d, ω, and N become quantitatively measurable. The test inducer was a triple-threaded helical inducer with a diameter of 65.3 mm and a rotational speed range of 3000–6000 rpm. It was experimentally confirmed that the proposed theoretical analysis is true.