Analytic expression for Taylor–Couette stability boundary

Esser, Axel T.; Großmann, S.

doi:10.1063/1.868963

Cited by 107 publications

(117 citation statements)

References 17 publications

(73 reference statements)

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“…The rotation number can be used to distinguish between Rayleigh-stable flows (R Ω ≤ −1 or R Ω ≥ (1 − η)/η) and those that are linearly unstable (−1 < R Ω < (1 − η)/η). b) All of our measurements for −1 < R Ω < 0.38 are well above the linear stability curve (blue line) described by Esser & Grossmann (1996) with…”

Section: Resultsmentioning

confidence: 99%

“…2), spanning a wide variety of flow states, including linearly stable cyclonic and anticyclonic flows as well as linearly unstable states. Esser & Grossmann (1996) derived an analytical expression that approximates the boundary for linear stability for all radius ratios and cylinder rotation rate ratios. Their result for the critical Reynolds number Re c may be expressed using the above control parameters, as in Eqs.…”

Section: Resultsmentioning

confidence: 99%

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Angular momentum transport and turbulence in laboratory models of Keplerian flows

Paoletti

Gils

Dubrulle

et al. 2012

A&A

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We present angular momentum transport (torque) measurements in two recent experimental studies of the turbulent flow between independently rotating cylinders. In addition to these studies, we reanalyze prior torque measurements to expand the range of control parameters for the experimental Taylor-Couette flows. We find that the torque may be described as a product of functions that depend only on the Reynolds number, which describes the turbulent driving intensity, and the rotation number, which characterizes the effects of global rotation. For a given Reynolds number, the global angular momentum transport for Keplerian-like flow profiles is approximately 14% of the maximum achievable transport rate. We estimate that this level of transport would produce an accretion rate ofṀ/Ṁ 0 ∼ 10 −3 in astrophysical disks. We argue that this level of transport from hydrodynamics alone could be significant. We also discuss the possible role of finite-size effects in triggering or sustaining turbulence in our laboratory experiments.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Angular momentum transport and turbulence in laboratory models of Keplerian flows

Paoletti

Gils

Dubrulle

et al. 2012

A&A

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“…normal mode analysis with numerical solutions [28]. Interestingly a very good approximate analytical formula in the whole parameter space has recently been derived by Esser and Grossmann [29]. It is:…”

Section: Stability Propertiesmentioning

confidence: 99%

Stability and turbulent transport in Taylor–Couette flow from analysis of experimental data

et al. 2005

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This paper provides a prescription for the turbulent viscosity in rotating shear flows for use e.g. in geophysical and astrophysical contexts. This prescription is the result of the detailed analysis of the experimental data obtained in several studies of the transition to turbulence and turbulent transport in Taylor-Couette flow. We first introduce a new set of control parameters, based on dynamical rather than geometrical considerations, so that the analysis applies more naturally to rotating shear flows in general and not only to Taylor-Couette flow. We then investigate the transition thresholds in the supercritical and the subcritical regime in order to extract their general dependencies on the control parameters. The inspection of the mean profiles provides us with some general hints on the mean to laminar shear ratio. Then the examination of the torque data allows us to propose a decomposition of the torque dependence on the control parameters in two terms, one completely given by measurements in the case where the outer cylinder is at rest, the other one being a universal function provided here from experimental fits. As a result, we obtain a general expression for the turbulent viscosity and compare it to existing prescription in the literature. Finally, throughout all the paper we discuss the influence of additional effects such as stratification or magnetic fields.

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“…Van Gils et. al (2011b) wondered whether the optimal transport in general lies in or at least close to the Voronoi boundary (meaning a line of equal distance) of the Esser-Grossmann stability lines (Esser & Grossmann 1996) in the (Re o , Re i ) phase space as it does for η = 0.714. However, this bisector value does not give the correct optimal transport for η = 0.5 (Merbold et al 2013;Brauckmann & Eckhardt 2013b).…”

Section: Optimal Taylor-couette Flow: Radius Ratio Dependencementioning

confidence: 99%

Optimal Taylor–Couette flow: radius ratio dependence

et al. 2014

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Taylor-Couette flow with independently rotating inner (i) & outer (o) cylinders is explored numerically and experimentally to determine the effects of the radius ratio η on the system response. Numerical simulations reach Reynolds numbers of up to Re i = 9.5 · 10 3 and Re o = 5 · 10 3 , corresponding to Taylor numbers of up to T a = 10 8 for four different radius ratios η = r i /r o between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor-Couette (T 3 C) setup, reach Reynolds numbers of up to Re i = 2 · 10 6 and Re o = 1.5 · 10 6 , corresponding to T a = 5 · 10 12 for η = 0.714−0.909. Effective scaling laws for the torque J ω (T a) are found, which for sufficiently large driving T a are independent of the radius ratio η. As previously reported for η = 0.714, optimum transport at a non-zero Rossby number Ro = r i |ω i − ω o |/[2(r o − r i )ω o ] is found in both experiments and numerics. Ro opt is found to depend on the radius ratio and the driving of the system. At a driving in the range between T a ∼ 3 · 10 8 and T a ∼ 10 10 , Ro opt saturates to an asymptotic η-dependent value. Theoretical predictions for the asymptotic value of Ro opt are compared to the experimental results, and found to differ notably. Furthermore, the local angular velocity profiles from experiments and numerics are compared, and a link between a flat bulk profile and optimum transport for all radius ratios is reported.

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Analytic expression for Taylor–Couette stability boundary

Cited by 107 publications

References 17 publications

Angular momentum transport and turbulence in laboratory models of Keplerian flows

Angular momentum transport and turbulence in laboratory models of Keplerian flows

Stability and turbulent transport in Taylor–Couette flow from analysis of experimental data

Optimal Taylor–Couette flow: radius ratio dependence

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