Abstract
In the present work, a novel stream function satisfying the three-dimensional continuity equation is defined in the form of a single scalar function and proved to represent the streamlines of certain three-dimensional flows. Consequently, the analysis and the results produce a limited counterevidence to the statement about the nonexistence of such function for three-dimensional flows. This new stream function is considered for both incompressible and compressible flows, and the examples of irrotational and rotational flows are discussed in connection with the characteristics of the stream function. In the three-dimensional irrotational incompressible flow considered herein, it is verified that the new stream function satisfies the three-dimensional Laplace equation and is orthogonal to the potential function, as in the case of the Lagrange’s two-dimensional stream function and the corresponding velocity potential. Unsteady incompressible flows are also discussed in this paper.
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