Spiral waves in three-dimensional helical viscous flows

A study is made of an unbounded viscous incompressible flow in the case in which the vortex lines of the absolute motion coincide with the streamlines of the relative motion; after Joukowsky, this flow is called helical flow. The vector potential of the flow is constructed and the notion of the stream function is generalized to include three-dimensional uniform helical flows in an arbitrary orthogonal coordinate system. It is shown that both axisymmetric and asymmetric waves may propagate in a rotating fluid; the amplitude of these waves decays exponentially with time, the decrement being proportional to the square of the rotational velocity of the fluid and the kinematic viscosity and inversely proportional to the square of the phase velocity.