Sedeonic generalization of hydrodynamic equations. Vortex models of plane turbulent walls-bounded flows

Abstract: We discuss a generalization of hydrodynamic equations based on the anticommutative spacetime algebra of 16-component sedeons. A symmetric system of Maxwell-type equations is obtained, which describes the longitudinal motion and rotation of vortex tubes. Based on these equations, a simple model of a plane, fully developed turbulent flow is proposed. As examples, we consider turbulent near-wall flows, as well as Couette and Poiseuille flows in rectangular channels.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemsfluid dynamics

Audience: researchers in the topic

Mathematical models and integration methods