The action principle for generalized fluid motion including gyroviscosity

• Method for constructing action principles for a diverse class of fluids with gyroscopic momentum transport is described.
• General criteria for the conservation of momentum and angular momentum via Noether's theorem are obtained.
• Fluids with intrinsic angular momentum are built as an illustration of the method.

A general set of fluid equations that allow for energy-conserving momentum transport by gyroscopic motion of fluid elements is obtained. The equations are produced by a class of action principles that yield a large subset of the known fluid and magnetofluid models, including gyroviscosity. Analysis of the action principle yields broad, model-independent results regarding the conservation laws of energy and linear and angular momenta. The formalism is illustrated by studying fluid models with intrinsic angular momentum that may appear in the contexts of condensed matter, biological, and other areas of physics.