Boundary-Layer and Interior Separations in the Taylor--Couette--Poiseuille Flow

TL;DR

This paper rigorously characterizes boundary-layer and interior separations in Taylor-Couette-Poiseuille flow, revealing that propagating Taylor vortices emerge only after a specific structural bifurcation at higher Taylor numbers.

Contribution

It provides a new rigorous analysis of flow separations and clarifies the conditions for the emergence of propagating Taylor vortices in TCP flow.

Findings

PTV do not appear after the first bifurcation

PTV emerge only after a structural bifurcation

Flow separations are linked to boundary-layer and interior bifurcations

Abstract

In this article, we derive a rigorous characterization of the boundary-layer and interior separations in the Taylor-Couette-Poiseuille (TCP) flow. The results obtained provide a rigorous characterization on how, when and where the propagating Taylor vortices (PTV) are generated. In particular, contrary to what is commonly believed, we show that the PTV do not appear after the first dynamical bifurcation, and they appear only when the Taylor number is further increased to cross another critical value so that a structural bifurcation occurs. This structural bifurcation corresponds to the boundary-layer and interior separations of the flow structure in the physical space.