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It is proved that in any vortex flow of a liquid or a gas the vorticity evolution can be considered as the displacement of vortex tubes at a certain velocity U which generally is not the same as the fluid velocity. For a viscous incompressible fluid a technique of calculating U from the fluid velocity field is proposed.

For the general case of a spatial isoenergetic flow of ideal gas, Helmholtz's theorems are generalized and the speed with which vortex tubes move is found, keeping the intensity. It is shown that along the streamline without stagnation point, vorticity either is equal to zero everywhere, or it is non zero at all. The pattern of vortex lines behind the three-dimensional detached bow shock wave is specified.

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