Turbulence phenomena for viscous fluids: Vortices and instability

摘要

By means of the Ginzburg–Landau and the Navier–Stokes equations, we study turbulence phenomena for viscous incompressible and compressible fluids viewed as a second order phase transition. For this model, the velocity is defined as the sum of classical and whirling components. Moreover, the laminar-turbulent transition is controlled by rotational effects in the fluid. Compatibility of the differential system with thermodynamics is proved.The same model is used to understand the origins of tornadoes and their behavior; and also 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. We conclude with the differential system describing water vorticity and its compatibility with thermodynamics.