Instabilities of the sidewall boundary layer in a rapidly rotating split cylinder

Gutiérrez-Castillo, Paloma; Lopez, Juan M.

doi:10.1016/j.euromechflu.2015.02.006

Cited by 8 publications

(15 citation statements)

References 11 publications

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“…Later, van Heijst [27] studied the finite case of the split cylinder with a differential rotation using a boundary layer analysis in the limit of very fast rotation velocity (inviscous problem) and very small differential rotation. Gutierrez-Castillo and Lopez [28] reproduced this analysis numerically in two dimensions (axisymmetric flows) and extended it for large but finite rotation velocities (nonlinear viscous problem) and larger differential rotations studying the stability of the main flow. Later this numerical analysis was extended in three dimensions [23] finding nonaxisymmetric instabilities.…”

Section: Introductionmentioning

confidence: 89%

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Experimental lateral wall boundary layer behavior of a differentially rotating split-cylinder flow

Rodriguez-Garcia

Burguete

2019

Phys. Rev. E

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The cylindrical wall boundary layer of a closed cylinder split in two halves at the equator is studied experimentally. When these two parts rotate in exact corotation the internal flow is essentially in solid-body rotation at the angular velocity of both halves. When a slight difference between the rotation frequencies is established a secondary flow is created due to the differential rotation between both sides and restricted to the boundary layer. This behavior of the boundary layer is compared with theoretical and numerical results finding the "sandwich" structure of a Stewartson boundary layer. Time-dependent waves are observed near the cylindrical wall. Their behavior for different values of the control parameters are presented. Finally, a global recirculation mode is also found due to a symmetry-breaking induced between sides that appears because of a slight misalignment of the experimental setup, whose characteristics are compatible with the behavior of a precessing cylinder.

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Section: Introductionmentioning

confidence: 89%

“…[24]. For a large enough differential rotation, instabilities can appear on the confluence of both boundary layers (end wall: Ekman type; lateral wall: Stewartson type) and propagate through the cylindrical wall creating periodic or quasiperiodic states [28].…”

Section: Introductionmentioning

confidence: 99%

Experimental lateral wall boundary layer behavior of a differentially rotating split-cylinder flow

Rodriguez-Garcia

Burguete

2019

Phys. Rev. E

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“…However with an axisymmetric forcing mechanism, azimuthal waves m = 0 are quickly damped. Recently, Gutierrez-Castillo & Lopez (2015) have carried out three dimensional simulations involving the sidewall instability of a rapidly rotating cylinder split at midheight and an extensive characterization of axisymmetric different states is done for a wide range of γ and Rossby number. It appears that the basic state loses stability through diverse ways involving sidewall boundary layer breathing causing inertial waves to propagate in the core of the flow.…”

Section: Inertial Waves and Rotating Turbulencementioning

confidence: 99%

Large scale dynamics in a turbulent compressible rotor/stator cavity flow at high Reynolds number

Lachize¹,

Verhille²,

Gal³

2016

Fluid Dyn. Res.

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This paper reports an experimental investigation of a turbulent flow confined within a rotor/stator cavity of aspect ratio close to unity at high Reynolds number. The experiments have been driven by changing both the rotation rate of the disk and the thermodynamical properties of the working fluid. This fluid is sulfur hexafluoride (SF 6 ) whose physical properties are adjusted by imposing the operating temperature and the absolute pressure in the pressurized vessel, especially near the critical point of SF 6 reached for T c = 45.58 • C, P c = 37.55 bar. This original setup allows to obtain Reynolds numbers as high as 2 10 7 together with compressibility effects as the Mach number can reach 0.5. Pressure measurements reveal that the resulting fully turbulent flow shows both a direct and an inverse cascade as observed in rotating turbulence and in accordance with Kraichnan conjecture for 2D-turbulence. The spectra are however dominated by low-frequency peaks, which are subharmonics of the rotating disk frequency, involving large scale structures at small azimuthal wavenumbers. These modes appear for a Reynolds number around 10 5 and experience a transition at a critical Reynolds number Re c ≈ 10 6 . Moreover they show an unexpected non linear behavior that we understand with the help of a low dimensional amplitude equations.

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“…The axisymmetric simulations of [12] showed that the discontinuity at the split plays no significant dynamic role, other than to provide the differential rotation that drives a large scale meridional flow, as in [23], and that it is the nonlinear sidewall layer instability that leads to unsteady flows that are able to drive inertial waves into the interior. They considered larger ω 0 flows over an extensive range of δω, observed a period doubling sequence of bifurcations which resulted in quasiperiodic flows that drove inertial waves along cones with different cone angles associated with the various frequencies, resulting in a complicated internal flow criss-crossed by an intricate network of conical shear layers.…”

Section: Steady Differential Rotationmentioning

confidence: 99%

“…Figure 1(b) shows an example of such a flow, which has many of the features observed in the experimental flow of [13]. In order to address the question concerning the role of the discontinuous boundary condition at the junction where the faster rotating endwall meets the slower rotating sidewall, [12] considered the differentially rotating split cylinder, where the cylinder is split into two halves at mid-height, and one half rotates faster than the other. The governing equations in the laboratory frame are (1) with b = 0, and the boundary conditions are:…”

Section: Steady Differential Rotationmentioning

confidence: 99%

Inertial waves in rapidly rotating flows: a dynamical systems perspective

Lopez¹,

Marqués²

2016

Phys. Scr.

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Abstract.An overview of recent developments in a wide variety of enclosed rapidly rotating flows is presented. Highlighted is the interplay between inertial waves, which have been predicted from linear inviscid considerations, and the viscous boundary layer dynamics which result from instabilities as the nonlinearities in the systems are increased. Further, even in the absence of boundary layer instabilities, nonlinearity in the system often leads to complicated interior flows due to subcritical instabilities, Eckhaus bands and heteroclinic dynamics. The ensuing spatio-temporally complex dynamics are analysed in terms of equivariant dynamical systems, providing a general perspective for the wide range of dynamics involved.

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Instabilities of the sidewall boundary layer in a rapidly rotating split cylinder

Cited by 8 publications

References 11 publications

Experimental lateral wall boundary layer behavior of a differentially rotating split-cylinder flow

Experimental lateral wall boundary layer behavior of a differentially rotating split-cylinder flow

Large scale dynamics in a turbulent compressible rotor/stator cavity flow at high Reynolds number

Inertial waves in rapidly rotating flows: a dynamical systems perspective

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