  The paper focuses on applying the octonions to explore the influence of the
external torque on the angular momentum of fluid elements, revealing the
interconnection of the external torque and the vortices of vortex streets. J.
C. Maxwell was the first to introduce the quaternions to study the physical
properties of electromagnetic fields. The contemporary scholars utilize the
quaternions and octonions to investigate the electromagnetic theory,
gravitational theory, quantum mechanics, special relativity, general relativity
and curved spaces and so forth. The paper adopts the octonions to describe the
electromagnetic and gravitational theories, including the octonionic field
potential, field strength, linear momentum, angular momentum, torque and force
and so on. In case the octonion force is equal to zero, it is able to deduce
eight independent equations, including the fluid continuity equation, current
continuity equation, and force equilibrium equation and so forth. Especially,
one of the eight independent equations will uncover the interrelation of the
external torque and angular momentums of fluid elements. One of its inferences
is that the direction, magnitude and frequency of the external torque must
impact the direction and curl of the angular momentum of fluid elements,
altering the frequencies of Karman vortex streets within the fluids. It means
that the external torque is interrelated with the velocity circulation, by
means of the liquid viscosity. The external torque is able to exert an
influence on the direction of downwash flows, improving the lift and drag
characteristics generated by the fluids.
