On multiple stable states in Taylor-Couette flow with realistic end-wall boundary conditions

TL;DR

This study explores how realistic end-wall boundary conditions influence the flow dynamics, stability, and multiple states in Taylor-Couette flow through simulations and theoretical analysis, revealing complex transitions and hysteresis effects.

Contribution

It extends the angular-momentum-flux framework to include axial transport and demonstrates the significant impact of realistic boundary conditions on flow states and transitions.

Findings

Multiple long-lived flow states with different roll numbers at the same Reynolds number.

Hysteresis loops indicating coexistence of different flow configurations.

Sequence of structural transitions from vortex flow to turbulence as Re increases.

Abstract

We investigate Taylor-Couette flow with realistic no-slip boundary conditions at all surfaces through direct numerical simulations (DNS) and theoretical analysis. Imposing physically consistent end-wall conditions at the top and bottom lids significantly alters the flow dynamics compared to that for periodic boundary conditions. We extend the classical angular-momentum-flux framework to account for axial transport, which leads to a significantly improved agreement with the Eckhardt-Grossmann-Lohse model (Eckhardt et al. 2007). A systematic exploration of the parameter space $(Re, n) $ uncovers multiple long-lived states with different roll number $n$ configurations at identical Reynolds numbers $Re$, giving rise to pronounced hysteresis loops occurring under realistic boundary conditions. Our DNS for no-slip axial end caps reveal a sequence of structural transitions: as the inner-cylinder Reynolds number increases, the flow evolves from Taylor vortex flow through chaotic wavy vortex flow and turbulent wavy vortex flow to an axisymmetric turbulent Taylor vortex flow. Using modal energy budgets we identify transition mechanisms and quantify how the accessible phase-space volume and associated roll-specific angular momentum flux depend on control parameters and the specific flow state. Our findings demonstrate the impact of realistic boundary conditions on the dynamics in Taylor-Couette flow, and how they change the stability landscape of multiple states. The coexistence of distinct flow patterns and their stability analysis offers promising insights into transition dynamics between laminar and turbulent regimes in closed sheared flows.