Turbulence phenomena for viscous fluids. Vortices and instability

TL;DR

This paper models turbulence in viscous fluids using Ginzburg-Landau and Navier-Stokes equations, exploring vortex formation, transition mechanisms, and effects of Coriolis force, with applications to tornadoes and water vortices.

Contribution

It introduces a second order phase transition model for turbulence, incorporating rotational effects and thermodynamic compatibility, and explains vortex behavior and formation mechanisms.

Findings

Rotational effects control laminar-turbulent transition.

Weak Coriolis force can reverse vortex rotation.

Model explains vortex origins in water fall and tornadoes.

Abstract

Through the Ginzburg-Landau and the Navier-Stokes equations, we study turbulence phenomena for viscous incompressible and compressible fluids by a second order phase transition. For this model, the velocity is defined by the sum of classical and whirling components. Moreover, the laminar-turbulent transition is controlled by rotational effects of the fluid. Hence, the thermodynamic compatibility of the differential system is proved. The same model is used to understand the origins of tornadoes and their behavior and the birth of the vortices resulting from the fall of water in a vertical tube. Finally, we demonstrate how the weak Coriolis force is able to change the rotation direction of the vortices by modifying the minima of the Ginzburg-Landau equation. Hence, we conclude the paper with the differential system describing the water vorticity and its thermodynamic compatibility.