Stability of Bödewadt flow

Savaş, Ömer

doi:10.1017/s0022112087002532

Cited by 73 publications

(77 citation statements)

References 22 publications

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“…Many studies have been performed to reveal the similarities in the stability characteristics across the entire BEK class (see, for example, the theoretical and experimental studies discussed in papers [9][10][11][12][13][14] for the Bödewadt layer; papers [15,16] for the Ekman layer; and papers [17][18][19][20] for the von Kármán flow). These studies have shown the existence of two main flow instability mechanisms, commonly referred to as the Type I and the Type II modes.…”

Section: Introductionmentioning

confidence: 99%

An energy analysis of convective instabilities of the Bödewadt and Ekman boundary layers over rough surfaces

Alveroğlu

Segalini

Garrett

2017

European Journal of Mechanics - B/Fluids

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An energy balance equation for the three-dimensional Bödewadt and Ekman layers of the so called "BEK family" of rotating boundary-layer flows is derived. A Chebyshev discretisation method is used to solve the equations and investigate the effect of surface roughness on the physical mechanisms of transition. All roughness types lead to a stabilization of the Type I (cross-flow) instability mode for both flows, with the exception of azimuthally-anisotropic roughness (radial grooves) within the Bödewadt layer which is destabilising. In the case of the viscous Type II instability mode, the results predict a destabilisation effect of radially-anisotropic roughness (concentric grooves) on both flows, whereas both azimuthally-anisotropic roughness and isotropic roughness have a stabilisation effect. The results presented here confirm the results of our prior linear stability analyses.

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Section: Introductionmentioning

confidence: 99%

An energy analysis of convective instabilities of the Bödewadt and Ekman boundary layers over rough surfaces

Alveroğlu

Segalini

Garrett

2017

European Journal of Mechanics - B/Fluids

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“…For disk boundary layer problems, this generally means that the finite disk needs to be shrouded by a cylinder. Savaş 20,21 conducted a series of experiments where initially a regime corresponding to quasisteady finite Bödewadt flow exists. The initial state consists of a filled circular cylinder in solid-body rotation of angular rotation rate ⍀.…”

Section: Introductionmentioning

confidence: 99%

“…Lopez and Weidman 22 repeated the experiments of Savaş, 21 reproducing the radially inward traveling circular waves in the disk boundary layer, and also simulated these states using the Navier-Stokes equations. They further showed numerically that if instead of impulsively stopping the entire cylinder, only the end walls are stopped while the cylindrical sheath continues rotating, then the development of the disk boundary layer and its inflectional instability leading to the formation of the circular waves is essentially the same, but without the large disturbances from the sidewall due to the whole flow spinning down.…”

Section: Introductionmentioning

confidence: 99%

Crossflow instability of finite Bödewadt flows: Transients and spiral waves

et al. 2009

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The flow in an enclosed rotating cylinder with a stationary lower end wall is investigated numerically. For fast rotation rates, the flow in the interior is primarily in the azimuthal direction, with an angular momentum distribution very close to that corresponding to solid-body rotation for about the inner-half radius. The differential rotation sets up a large-scale circulation that is primarily present in the boundary layers on the rotating top and sidewalls and the stationary bottom wall, with a very weak effusive component throughout the bulk interior providing a matching between the boundary layer flows on the top and bottom. The top end wall boundary layer has a profile that very closely matches the von Kármán solution for a rotating disk boundary layer; it is stable and very robust to finite disturbances for all rotation rates considered. The boundary layer on the stationary bottom end wall has a profile that agrees with the Bödewadt solution for a stationary disk with an ambient flow in solid-body rotation. This boundary layer is not robust, suffering crossflow instability to multiarmed spiral waves via a supercritical Hopf bifurcation, as well as being susceptible to axisymmetric circular waves that travel radially inward where the boundary layer profile is most inflectional. In the absence of any external forcing, the circular waves are transitory, but low amplitude forcing can sustain them indefinitely, whereas the spiral waves are essentially unaffected by the external forcing.

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“…More recently, and following the pioneer work of Lingwood [9], Serre et al [11] studied theoretically and numerically the transition from convective to absolute instability of these flows. Experimentally, Savas [12,13] followed by Itoh [14,15] were the first to visualize the different waves occurring in a rotor/stator system. The complete transition diagram was then built by Schouveiler, Le Gal & Chauve [16] as function of the ratio h/δ of the cavity and of the Reynolds number Re = ΩR 2 /ν (R being the radius of the disk).…”

Section: Introductionmentioning

confidence: 99%

Transition to turbulence of the Batchelor flow in a rotor/stator device

Cros

Floriani

Gal

et al. 2005

European Journal of Mechanics - B/Fluids

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This experimental study is devoted to the transition to turbulence of the flow confined between a stationary and a rotating disk. Using visualization and video image analysis, we describe the different transitions occurring in the flow as the rotating velocity of the disk is varied. The space-time behavior of the wave patterns is analyzed using the BiOrthogonal Decomposition (BOD) technique. This decomposition of the experimental signals on proper modes permits to project the dynamics of the waves in a reduced embedding phase space. By this means, a torus doubling bifurcation is revealed before its complete destruction during the transition to a weak turbulence. Finally, a more classical 2D-Fourier analysis completes our description of the transition and shows for higher rotation rates, the appearance of a more developed turbulence issued from the former chaotic waves.

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Stability of Bödewadt flow

Cited by 73 publications

References 22 publications

An energy analysis of convective instabilities of the Bödewadt and Ekman boundary layers over rough surfaces

An energy analysis of convective instabilities of the Bödewadt and Ekman boundary layers over rough surfaces

Crossflow instability of finite Bödewadt flows: Transients and spiral waves

Transition to turbulence of the Batchelor flow in a rotor/stator device

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