Three-dimensional instabilities in a discretely heated annular flow: Onset of spatio-temporal complexity via defect dynamics

Marqués

2021

J. Fluid Mech.

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A series of experiments on stratified Taylor–Couette flow in short aspect ratio wide-gap annuli found an intriguing and not-well-understood dynamics: nonlinear coherent structures appearing and disappearing periodically, along with density layering reminiscent of staircase profiles. A detailed numerical study is presented of the nonlinear dynamics near onset of instability in this setting, which explains most of the characteristics found in the experiments. The simulations show that centrifugal instability of the boundary layer on the inner rotating cylinder produces jets of angular momentum forming Taylor cells that are compressed axially due to the strong stratification. These cells are not axisymmetric from the onset, but are in fact two sets of Taylor cells displaced axially that meet in localized azimuthal defect regions where the cells are patched together; the whole structure is a rotating wave with azimuthal wavenumber $m=1$ . The presence of endwalls in this short aspect ratio annulus is critical for the understanding of the dynamics. Their impact cannot be accounted for in idealized axially periodic models. Another key ingredient is the role played by the symmetries of the system. Although the axial reflection symmetry is weakly broken by centrifugal buoyancy effects, following instability there are various branches of solutions corresponding to the different ways the system's symmetries may be broken.

Section: Governing Equationsmentioning

confidence: 99%

Stratified Taylor–Couette flow: nonlinear dynamics

Marqués

2021

J. Fluid Mech.

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“…This seems to be a fairly general phenomenon when wave beams are the result of an instability rather than due to an extraneously imposed periodic forcing, and has also been found to occur in librating spheres (Sauret, Cébron & Le Bars 2013). Analogous frequency selections leading to approximately retracing wave beams have been more extensively studied in stratified flows (Sutherland & Linden 1998;Taylor & Sarkar 2007;Munroe & Sutherland 2014;Lopez & Marques 2014b), which are well known to have analogous wave properties to rotating flows, with buoyancy providing the restoring force instead of Coriolis (Veronis 1970).…”

Section: Discussionmentioning

confidence: 94%

Three-dimensional instabilities and inertial waves in a rapidly rotating split-cylinder flow

Gutiérrez-Castillo

2016

J. Fluid Mech.

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The nonlinear dynamics of the flow in a differentially rotating split cylinder is investigated numerically. The differential rotation, with the top half of the cylinder rotating faster than the bottom half, establishes a basic state consisting of a bulk flow that is essentially in solid-body rotation at the mean rotation rate of the cylinder and boundary layers where the bulk flow adjusts to the differential rotation of the cylinder halves, which drives a strong meridional flow. There are Ekman-like layers on the top and bottom end walls, and a Stewartson-like side wall layer with a strong downward axial flow component. The complicated bottom corner region, where the downward flow in the side wall layer decelerates and negotiates the corner, is the epicentre of a variety of instabilities associated with the local shear and curvature of the flow, both of which are very non-uniform. Families of both high and low azimuthal wavenumber rotating waves bifurcate from the basic state in Eckhaus bands, but the most prominent states found near onset are quasiperiodic states corresponding to mixed modes of the high and low azimuthal wavenumber rotating waves. The frequencies associated with most of these unsteady three-dimensional states are such that spiral inertial wave beams are emitted from the bottom corner region into the bulk, along cones at angles that are well predicted by the inertial wave dispersion relation, driving the bulk flow away from solid-body rotation.

“…The spectral solver used here has been extensively tested in enclosed annular domains [34,35] and it is based on a previous scheme used in a wide variety of flows in enclosed cylinders [36][37][38][39][40]. We have checked the spectral convergence of the code using the infinity norm of the spectral coefficients of the computed solutions, defined as ||a l || ∞ = max n,m |a l,n,m | for the radial direction, and analogously for the axial and azimuthal directions.…”

Section: B Numerical Formulation and Methodologymentioning

confidence: 99%

Dynamics of axially localized states in Taylor-Couette flows

Marqués

2015

Phys. Rev. E

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We present numerical simulations of the flow confined in a wide gap Taylor-Couette system, with a rotating inner cylinder and variable length-to-gap aspect ratio. A complex experimental bifurcation scenario differing from the classical Ruelle-Takens route to chaos has been experimentally reported in this geometry. The wavy vortex flow becomes quasiperiodic due to an axisymmetric very low frequency mode. This mode plays a key role in the dynamics of the system, leading to the occurrence of chaos via a period-doubling scenario. Further increasing the rotation of the inner cylinder results in the appearance of a new flow pattern which is characterized by large amplitude oscillations localized in some of the vortex pairs. The purpose of this paper is to study numerically the dynamics of these axially localized states, paying special attention to the transition to chaos. Frequency analysis from time series simultaneously recorded at several points has been applied in order to identify the flow transitions taking place. It has been found that the very low frequency mode is essential to explain the behavior associated with the different transitions towards chaos including localized states.