Torques and angular momenta of fluid elements in the octonion spaces

- Zi-Hua Weng

## Abstract

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.10 Aug 2021Submitted to *Mathematical Methods in the Applied Sciences* 11 Aug 2021Submission Checks Completed

11 Aug 2021Assigned to Editor

25 Aug 2021Reviewer(s) Assigned

10 Dec 2021Review(s) Completed, Editorial Evaluation Pending

11 Dec 2021Editorial Decision: Revise Major

11 Jan 20221st Revision Received

12 Jan 2022Submission Checks Completed

12 Jan 2022Assigned to Editor

14 Jan 2022Reviewer(s) Assigned

28 Oct 2022Review(s) Completed, Editorial Evaluation Pending

30 Oct 2022Editorial Decision: Accept