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Instability of diverging and converging flows in an annulus  [PDF]
Konstantin Ilin,Andrey Morgulis
Physics , 2012,
Abstract: The stability of two-dimensional diverging and converging flows in an annulus between two permeable cylinders is examined. The basic flow is irrotational and has both the radial and azimuthal components. It is shown that for a wide range of the parameters of the problem, the basic flow is unstable to small two-dimensional perturbations. The instability is inviscid and oscillatory and persists if the viscosity of the fluid is taken into consideration.
Bistable flows in precessing spheroids  [PDF]
D Cébron
Physics , 2015, DOI: 10.1088/0169-5983/47/2/025504
Abstract: Precession driven flows are found in any rotating container filled with liquid, when the rotation axis itself rotates about a secondary axis that is fixed in an inertial frame of reference. Because of its relevance for planetary fluid layers, many works consider spheroidal containers, where the uniform vorticity component of the bulk flow is reliably given by the well-known equations obtained by Busse in 1968. So far however, no analytical result on the solutions is available. Moreover, the cases where multiple flows can coexist have not been investigated in details since their discovery by Noir et al. (2003). In this work, we aim at deriving analytical results on the solutions, aiming in particular at, first estimating the ranges of parameters where multiple solutions exist, and second studying quantitatively their stability. Using the models recently proposed by Noir \& C{\'e}bron (2013), which are more generic in the inviscid limit than the equations of Busse, we analytically describe these solutions, their conditions of existence, and their stability in a systematic manner. We then successfully compare these analytical results with the theory of Busse (1968). Dynamical model equations are finally proposed to investigate the stability of the solutions, which allows to describe the bifurcation of the unstable flow solution. We also report for the first time the possibility that time-dependent multiple flows can coexist in precessing triaxial ellipsoids. Numerical integrations of the algebraic and differential equations have been efficiently performed with the dedicated script FLIPPER (supplementary material).
Thermal convection in a cylindrical annulus heated laterally  [PDF]
S. Hoyas,H. Herrero,A. M. Mancho
Physics , 2001, DOI: 10.1088/0305-4470/35/18/306
Abstract: In this paper we study thermoconvective instabilities appearing in a fluid within a cylindrical annulus heated laterally. As soon as a horizontal temperature gradient is applied a convective state appears. As the temperature gradient reaches a critical value a stationary or oscillatory bifurcation may take place. The problem is modelled with a novel method which extends the one described in (numerico). The Navier Stokes equations are solved in the primitive variable formulation, with appropriate boundary conditions for pressure. This is a low order formulation which in cylindrical coordinates introduces lower order singularities. The problem is discretized with a Chebyshev collocation method easily implemented and its convergence has been checked. The results obtained are not only in very good agreement with those obtained in experiments, but also provide a deeper insight into important physical parameters developing the instability, which has not been reported before.
On the necessary conditions for bursts of convection within the rapidly rotating cylindrical annulus  [PDF]
Robert J. Teed,Chris A. Jones,Rainer Hollerbach
Physics , 2013, DOI: 10.1063/1.4711398
Abstract: Zonal flows are often found in rotating convective systems. Not only are these jet-flows driven by the convection, they can also have a profound effect on the nature of the convection. In this work the cylindrical annulus geometry is exploited in order to perform nonlinear simulations seeking to produce strong zonal flows and multiple jets. The parameter regime is extended to Prandtl numbers that are not unity. Multiple jets are found to be spaced according to a Rhines scaling based on the zonal flow speed, not the convective velocity speed. Under certain conditions the nonlinear convection appears in quasi-periodic bursts. A mean field stability analysis is performed around a basic state containing both the zonal flow and the mean temperature gradient found from the nonlinear simulations. The convective growth rates are found to fluctuate with both of these mean quantities suggesting that both are necessary in order for the bursting phenomenon to occur.
Subcritical transition to turbulence of a precessing flow in a cylindrical vessel  [PDF]
Johann Herault,Thomas Gundrum,Andre Giesecke,Frank Stefani
Physics , 2015,
Abstract: The transition to turbulence in a precessing cylindrical vessel is experimentally investigated. Our measurements are performed for a { nearly-resonant} configuration with an initially laminar flow dominated by an inertial mode with azimuthal wave number $m=1$ superimposed on a solid body rotation. By increasing the precession ratio, we observe a transition from the laminar to a non-linear regime, which then breakdowns to turbulence for larger precession ratio. Our measurements show that the transition to turbulence is subcritical, with a discontinuity of the wall-pressure and the power consumption at the threshold $\epsilon_{LT}$. The turbulence is self-sustained below this threshold, describing a bifurcation diagram with a hysteresis. In this range of the control parameters, the turbulent flows can suddenly collapse after a finite duration, leading to a definitive relaminarization of the flow. The average lifetime $\langle \tau \rangle$ of the turbulence increases rapidly when $\epsilon$ tends to $\epsilon_{LT}$.
Experiments on transitions of baroclinic waves in a differentially heated rotating annulus
Th. von Larcher,C. Egbers
Nonlinear Processes in Geophysics (NPG) , 2005,
Abstract: Experiments of baroclinic waves in a rotating, baroclinic annulus of fluid are presented for two gap widths. The apparatus is a differentially heated cylindrical gap, rotated around its vertical axis of symmetry, cooled from within, with a free surface, and filled with de-ionised water as working fluid. The surface flow was observed with visualisation technique while thermographic measurements gave a detailed understanding of the temperature distribution and its time-dependent behaviour. We focus in particular on transitions between different flow regimes. Using a wide gap, the first transition from axisymmetric flow to the regular wave regime was characterised by complex flows. The transition to irregular flows was smooth, where a coexistence of the large-scale jet-stream and small-scale vortices was observed. Furthermore, temperature measurements showed a repetitive separation of cold vortices from the inner wall. Experiments using a narrow gap showed no complex flows but strong hysteresis in the steady wave regime, with up to five different azimuthal wave modes as potential steady and stable solutions.
Low-order models of 2D fluid flow in annulus  [PDF]
N. V. Petrovskaya,M. Yu. Zhukov
Physics , 2009,
Abstract: The two-dimensional flow of viscous incompressible fluid in the domain between two concentric circles is investigated numerically. To solve the problem, the low-order Galerkin models are used. When the inner circle rotates fast enough, two axially asymmetric flow regimes are observed. Both regimes are the stationary flows precessing in azimuthal direction. First flow represents the region of concentrated vorticity. Another flow is the jet-like structure similar to one discovered earlier in Vladimirov's experiments.
The Influence of Horizontal Boundaries on Ekman Circulation and Angular Momentum Transport in a Cylindrical Annulus  [PDF]
Aleksandr V. Obabko,Fausto Cattaneo,Paul F. Fischer
Physics , 2008, DOI: 10.1088/0031-8949/2008/T132/014029
Abstract: We present numerical simulations of circular Couette flow in axisymmetric and fully three-dimensional geometry of a cylindrical annulus inspired by Princeton MRI liquid gallium experiment. The incompressible Navier-Stokes equations are solved with the spectral element code Nek5000 incorporating realistic horizontal boundary conditions of differentially rotating rings. We investigate the effect of changing rotation rates (Reynolds number) and of the horizontal boundary conditions on flow structure, Ekman circulation and associated transport of angular momentum through the onset of unsteadiness and three-dimensionality. A mechanism for the explanation of the dependence of the Ekman flows and circulation on horizontal boundary conditions is proposed.
Pulsatile Viscous Flows in Elliptical Vessels and Annuli: Solution to the Inverse Problem, with Application to Blood and Cerebrospinal Fluid Flow  [PDF]
Luigi C. Berselli,Francesca Guerra,Barbara Mazzolai,Edoardo Sinibaldi
Mathematics , 2012,
Abstract: We consider the fully-developed flow of an incompressible Newtonian fluid in a cylindrical vessel with elliptical cross-section (both an ellipse and the annulus between two confocal ellipses). In particular, we address an inverse problem, namely to compute the velocity field associated with a given, time-periodic flow rate. This is motivated by the fact that flow rate is the main physical quantity which can be actually measured in many practical situations. We propose a novel numerical strategy, which is nonetheless grounded on several analytical relations. The proposed method leads to the solution of some simple ordinary differential systems. It holds promise to be more amenable to implementation than previous approaches, which are substantially based on the challenging computation of Mathieu functions. Some numerical results are reported, based on measured data for human blood flow in the internal carotid artery, and cerebrospinal fluid (CSF) flow in the upper cervical region of the human spine. As expected, computational efficiency is the main asset of our solution: a speed-up factor over 10^3 was obtained, compared to more elaborate numerical approaches. The main goal of the present study is to provide an improved source of initial/boundary data for more ambitious numerical approaches, as well as a benchmark solution for pulsatile flows in elliptical sections with given flow rate. The proposed method can be effectively applied to bio-fluid dynamics investigations (possibly addressing key aspects of relevant diseases), to biomedical applications (including targeted drug delivery and energy harvesting for implantable devices), up to longer-term medical microrobotics applications.
Precessing AGN Jets, Bubbles and Cooling Flows  [PDF]
D. Falceta-Goncalves,A. Caproni,Z. Abraham,E. M. de Gouveia Dal Pino,D. M. Teixeira
Physics , 2011,
Abstract: Several galaxy clusters are known to present multiple and misaligned pairs of cavities seen in X-rays, as well as twisted kiloparsec-scale jets at radio wavelengths. It suggests that the AGN precessing jets play a role in the formation of the misaligned bubbles. Also, X-ray spectra reveal that typically these systems are also able to supress cooling flows, predicted theoretically. The absence of cooling flows in galaxy clusters has been a mistery for many years since numerical simulations and analytical studies suggest that AGN jets are highly energetic, but are unable to redistribute it at all directions. We performed 3D hydrodynamical simulations of the interaction between a precessing AGN jet and the warm intracluster medium plasma, which dynamics is coupled to a NFW dark matter gravitational potential. Radiative cooling has been taken into account and the cooling flow problem was studied. We found that precession is responsible for multiple pairs of bubbles, as observed. The misaligned bubbles rise up to scales of tens of kiloparsecs, where the thermal energy released by the jets are redistributed. After $\sim 150$ Myrs, the temperature of the gas within the cavities is kept of order of $\sim 10^7$ K, while the denser plasma of the intracluster medium at the central regions reaches $T \sim 10^5$ K. The existence of multiple bubbles, at diferent directions, result in an integrated temperature along the line of sight much larger than the simulations of non-precessing jets. This result is in agreement with the observations. The simulations reveal that the cooling flows cessed $\sim 50 - 70$ Myr after the AGN jets are started.
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