  We study the flow dynamics inside a high-speed rotating cylinder after
introducing strong symmetry-breaking disturbance factors at cylinder wall
motion. We propose and formulate a mathematically robust stochastic model for
the rotational motion of cylinder wall alongside the stochastic representation
of incompressible Navier-Stokes equations. We employ a comprehensive stochastic
computational fluid dynamics framework combining spectral/$hp$ element method
and probabilistic collocation method to obtain high-fidelity realizations of
our mathematical model in order to quantify the propagation of parametric
uncertainty for dynamics-representative quantities of interests. We observe
that the modeled symmetry-breaking disturbances cause a flow instability
arising from the wall. Utilizing global sensitivity analysis approaches, we
identify the dominant source of uncertainty in our proposed model. We next
perform a qualitative and quantitative statistical analysis on the fluctuating
fields characterizing the fingerprints and measures of intense and rapidly
evolving non-Gaussian behavior through space and time. We claim that such
non-Gaussian statistics essentially emerge and evolve due to an intensified
presence of coherent vortical motions initially triggered by the flow
instability due to symmetry-breaking rotation of the cylinder. We show that
this mechanism causes memory effects in the flow dynamics in a way that
noticeable anomaly in the time-scaling of enstrophy record is observed in the
long run apart from the onset of instability. Our findings suggest an effective
strategy to exploit controlled flow instabilities in order to enhance the
turbulent mixing in engineering applications.
