Laminar-turbulent transition in Taylor-Couette flow from a molecule dependent transport equation

Abstract

Abstract In this Letter, a previously utilized higher-order momentum transport equation obtained using a projection-perturbation formalism from the most general equation of classical transport for the N-particle distribution function, the Liouville equation, is applied to the Taylor-Couette flow, e.g. fluid flow enclosed between two concentric cylinders where the inner cylinder is rotating with some constant speed and the outer cylinder is stationary. The results of the numerical simulation of azimuthal velocity profiles are analyzed to see how an initial laminar velocity profile evolves in time into a velocity profile characteristic for turbulent flow. Although the experiments were not very accurate, they all point to the near uniformity of the velocity profiles in turbulent regime in the central region of the annulus. Using the time evolution of the velocity profiles, we further investigate possibility of observing double phase transition from a laminar to turbulent regime.