Linear instabilities in modulated Taylor-Couette flows”

he modulated Taylor-Couette flow takes place in the annular gap between two concentric cylinders, assumed of infinite extent in the
axial direction. Inner and outer cylinders rotate about their common axis with two independent rotation rates that are periodically modulated in time. While there exists a significant literature on the time-periodic Taylor-Couette configuration, many investigations have addressed purely oscillating situations, and the dynamics of the general problem where steady and oscillating flow components cooperate is not yet fully understood.
The radius ratio fixes the geometry and the Womersley number characterizes the modulation frequency. Assuming harmonic modulation of the cylinders’ rotation rates, the flow dynamics is further governed by four Reynolds numbers accounting for the steady and
oscillating velocities of inner and outer cylinders.

Linear instability features such as complex growth rates and Floquetmultipliers are computed with two different methods: generalized eigenvalue problems using Floquet theory and direct numerical simulations of the linearized Navier-Stokes equations. Neutral
stability boundaries in the multi-dimensional parameter space are obtained with continuation methods.
Our study systematically explores the effects of varying all non-dimensional control parameters.
For narrow-gap configurations, low Womersley numbers and increasing oscillation amplitudes initially show destabilizing effects and  eventually lead to the emergence of multiple neutral curves, demarcated by harmonic and subharmonic instability transitions. At higher Womersley numbers, these transitions shift to significantly larger oscillation amplitudes. Wider-gap systems display harmonic-subharmonic bifurcations at even lower values of oscillation
amplitude, indicating enhanced sensitivity of the flow to temporalmodulation and large curvature effects.
Our findings analyse the fine mechanisms of the harmonic-subharmonic bifurcations, provide a comprehensive map of the stability boundaries in modulated Taylor-Couette systems and reveal the critical role of geometry and modulation parameters in shaping the onset of instabilities.

Speaker : Benoît PIER