The Boussinesq approximation in rapidly rotating flows

Lopez, José M.; Marqués, Francisco; Avila, Marc

doi:10.1017/jfm.2013.558

Cited by 57 publications

(64 citation statements)

References 32 publications

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“…Fully nonlinear simulations were performed using the Boussinesq-approximation [16], which was added with the heat equation to the finite-difference-Fourier-Galerkin (hybrid MPI-OpenMP) code of Shi et al [17]. A time-step dt ¼ 2 Â 10 À5 viscous time units was used in all computations.…”

Section: Methodsmentioning

confidence: 99%

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Conductive and convective heat transfer in fluid flows between differentially heated and rotating cylinders

Lopez

Marqués

Avila

2015

International Journal of Heat and Mass Transfer

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The flow of fluid confined between a heated rotating cylinder and a cooled stationary cylinder is a canonical experiment for the study of heat transfer in engineering. The theoretical treatment of this system is greatly simplified if the cylinders are assumed to be of infinite length or periodic in the axial direction. In these cases heat transfer in the laminar regime occurs only through conduction as in a solid. We here investigate numerically heat transfer and the onset of turbulence in such flows by using both periodic and no-slip boundary conditions in the axial direction. The influence of the geometric parameters is comprehensively studied by varying the radius ratio (0.1 <= eta <= 0.99) and the length-to-gap aspect ratio (5 <= Gamma <= 80). Similarly, a wide range of Prandtl, Rayleigh, and Reynolds numbers is explored (0.01 <= sigma <= 100, Ra <= 30,000, and Re <= 1000, respectively). We obtain a simple criterion, Ra which determines whether the infinite-cylinder assumption can be employed. The coefficient a is well approximated by a cubic fit over the whole n-range. Noteworthy the criterion is independent of the Prandtl number and appears robust with respect to Reynolds number even beyond the laminar regime. (C) 2015 Elsevier Ltd. All rights reserved.Postprint (published version

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Section: Methodsmentioning

confidence: 99%

“…We consider the Boussinesq approximation including centrifugal buoyancy in an inertial reference frame as described in [16]. The dimensionless governing equations are…”

Section: Governing Equationsmentioning

confidence: 99%

Conductive and convective heat transfer in fluid flows between differentially heated and rotating cylinders

Lopez

Marqués

Avila

2015

International Journal of Heat and Mass Transfer

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“…In strongly rotating flows, 'centrifugal buoyancy' can be taken into account by including the nonlinear term (∆ρ/ρ 0 )ρ(u · ∇)u in the convective derivative (Lopez et al 2013). This term is O(∆ρ/ρ 0 ) with our choice of reference scales, whereas the usual buoyancy term related to gravity is O(Ri g ).…”

Section: Governing Equationsmentioning

confidence: 99%

Using stratification to mitigate end effects in quasi-Keplerian Taylor–Couette flow

et al. 2016

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Efforts to model accretion disks in the laboratory using Taylor–Couette flow apparatus are plagued with problems due to the substantial impact the end plates have on the flow. We explore the possibility of mitigating the influence of these end plates by imposing stable stratification in their vicinity. Numerical computations and experiments confirm the effectiveness of this strategy for restoring the axially homogeneous quasi-Keplerian solution in the unstratified equatorial part of the flow for sufficiently strong stratification and moderate layer thickness. If the rotation ratio is too large, however (e.g. ${\it\Omega}_{o}/{\it\Omega}_{i}=(r_{i}/r_{o})^{3/2}$, where ${\it\Omega}_{o}/{\it\Omega}_{i}$ is the angular velocity at the outer/inner boundary and $r_{i}/r_{o}$ is the inner/outer radius), the presence of stratification can make the quasi-Keplerian flow susceptible to the stratorotational instability. Otherwise (e.g. for ${\it\Omega}_{o}/{\it\Omega}_{i}=(r_{i}/r_{o})^{1/2}$), our control strategy is successful in reinstating a linearly stable quasi-Keplerian flow away from the end plates. Experiments probing the nonlinear stability of this flow show only decay of initial finite-amplitude disturbances at a Reynolds number $Re=O(10^{4})$. This observation is consistent with most recent computational (Ostilla-Mónico, et al.J. Fluid Mech., vol. 748, 2014, R3) and experimental results (Edlund & Ji, Phys. Rev. E, vol. 89, 2014, 021004) at high $Re$, and reinforces the growing consensus that turbulence in cold accretion disks must rely on additional physics beyond that of incompressible hydrodynamics.

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“…The fluid is assumed to satisfy the Boussinesq approximation (see Lopez, Marques & Avila 2013), with constant properties except for the density when applied to the centrifugal and gravitational accelerations where ρ = ρ 0 (1 − α(T − T 0 )), where α is the coefficient of thermal expansion and T 0 is a reference temperature T 0 = (T b + T a )/2. The reference scales are the velocity U * = gα T/2Ω and the time t * = (2Ω) −1 , and the non-dimensional normalized temperature is 2( Randriamampianina et al 2006;Randriamampianina & Crespo del Arco 2014).…”

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confidence: 99%

Inertia–gravity waves in a liquid-filled, differentially heated, rotating annulus

Randriamampianina

Arco²

2015

J. Fluid Mech.

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International audienceDirect numerical simulations based on high-resolution pseudospectral methods are carried out for detailed investigation into the instabilities arising in a differentially heated, rotating annulus, the baroclinic cavity. Following previous works using air (Randriamampianina et al., J. Fluid Mech., vol. 561, 2006, pp. 359–389), a liquid defined by Prandtl number Pr=16 is considered in order to better understand, via the Prandtl number, the effects of fluid properties on the onset of gravity waves. The computations are particularly aimed at identifying and characterizing the spontaneously emitted small-scale fluctuations occurring simultaneously with the baroclinic waves. These features have been observed as soon as the baroclinic instability sets in. A three-term decomposition is introduced to isolate the fluctuation field from the large-scale baroclinic waves and the time-averaged mean flow. Even though these fluctuations are found to propagate as packets, they remain attached to the background baroclinic waves, locally triggering spatio-temporal chaos, a behaviour not observed with the air-filled cavity. The properties of these features are analysed and discussed in the context of linear theory. Based on the Richardson number criterion, the characteristics of the generation mechanism are consistent with a localized instability of the shear zonal flow, invoking resonant over-reflection

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The Boussinesq approximation in rapidly rotating flows

Cited by 57 publications

References 32 publications

Conductive and convective heat transfer in fluid flows between differentially heated and rotating cylinders

Conductive and convective heat transfer in fluid flows between differentially heated and rotating cylinders

Using stratification to mitigate end effects in quasi-Keplerian Taylor–Couette flow

Inertia–gravity waves in a liquid-filled, differentially heated, rotating annulus

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