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The paper reports on shape of a three-dimensional coherent structure in a velocity field of a high-swirl turbulent jet with the bubble-type vortex breakdown. A set of the 3D instantenous velocity fields was measured by using the tomographic particle image velocimetry (tomographic PIV) technique and processed by the proper orthogonal decomposition (POD) method. The detected intensive coherent velocity component corresponded to a helical vortex core of the swirling jet and two secondary spiral vortices. The entire coherent structure was rotating around the jet axis in compliance with the direction of the flow swirl. From the 3D data it is concluded that the dynamics of the strsucture can be described by a traveling wave equation: Re[A(y, r)·e ^{i(mθ + ky - ωt)}] with the number of the spiral mode m = +1 for positively defined k and ω.