Synopsis of Vogel-Escudier flow

The topology and the dynamics of Vogel-Escudier flow, which is the flow inside a circular cylinder with a top rotating lid, are presented in this paper. A three-dimensional direct numerical simulation of the Navier-Stokes equations in cylindrical coordinates is used to investigate the flow. Various combinations of Reynolds number and aspect ratio are studied and classified based on the flow topology. The flow is found to exhibit steady axisymmetric, unsteady axisymmetric, rotating azimuthal waves, and weak turbulence regimes. The perturbations found in the system are characteristically different for various flow regimes and are used for the classification of flow. The presence of several modes at high Reynolds number suggests a weak turbulence state, and a Taylor-Gortler type instability wave is found in the sidewall boundary layer.

Automated summary

This paper investigates the topology and dynamics of Vogel-Escudier flow inside a circular cylinder with a rotating lid through direct numerical simulation using Navier-Stokes equations in cylindrical coordinates. Different combinations of Reynolds number and aspect ratio are studied and classified based on flow topology. The presence of various modes at high Reynolds number suggests a weak turbulence state, and a Taylor-Gortler type instability wave is found in the sidewall boundary layer.