A note on the hydrodynamics of viscous fluids

The cross-product of the velocity and the vorticity in a viscous incompressible fluid is formulated and its properties investigated. When the cross-product is identically null, either the flow is vortex-free, or the velocity and the vorticity are parallel to each other. The second case yields the following important result for three-dimensional flows: if the velocity and the vorticity are related by a position-independent scalar function, that function must be time-independent as well. (English translation of the seventy-five-years old Czech text — Trkal V.: asopis pro pstování mathematiky a fysiky48 (1919) 302–311.)The paper has been translated (by I. Gregora) from Czech original which appeared in asopis pro pstování mathematiky a fysiky, Vol. 48 (1919), pp. 302–311; see a contextualizing account in the preceding paper in this issue, p. 89. The reprints are available on request from the Editorial Office.I express my warm gratitude to Prof. Dr. F. Závika for his valuable comments.