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Uwe Ehrenstein - One of the best experts on this subject based on the ideXlab platform.
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two dimensional nonlinear plane poiseuille Couette Flow homotopy revisited
Physics of Fluids, 2008Co-Authors: Uwe Ehrenstein, Masato Nagata, F RinconAbstract:A recent paper by Rincon [Phys. Fluids 19, 074105 (2007)] readdressed the question of the existence of two-dimensional steady nonlinear states in plane Couette Flow, coming to the conclusion that it is not possible to obtain the nonlinear plane Couette Flow solutions reported by Cherhabili and Ehrenstein [Eur. J. Mech. B/Fluids 14, 667 (1995)] using their Poiseuille–Couette homotopy. Exploring the multiparameter space by performing several consecutive and distinct continuations, we show that it is possible to find a complex numerical path from plane Poiseuille streamwise periodic waves to two-dimensional nonlinear steady states for the plane Couette Flow limit. The nonlinear Couette Flow states are retrieved using three independent solution procedures and the disturbance Flow structure is shown to be localized in the streamwise periodic box. Numerical evidence is provided that the width of the nonlinear plane Couette Flow disturbance decreases with increasing resolution at fixed boxlength. This singular-t...
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Two-dimensional nonlinear plane Poiseuille–Couette Flow homotopy revisited
Physics of Fluids, 2008Co-Authors: Uwe Ehrenstein, Masato Nagata, F RinconAbstract:A recent paper by Rincon [Phys. Fluids 19, 074105 (2007)] readdressed the question of the existence of two-dimensional steady nonlinear states in plane Couette Flow, coming to the conclusion that it is not possible to obtain the nonlinear plane Couette Flow solutions reported by Cherhabili and Ehrenstein [Eur. J. Mech. B/Fluids 14, 667 (1995)] using their Poiseuille–Couette homotopy. Exploring the multiparameter space by performing several consecutive and distinct continuations, we show that it is possible to find a complex numerical path from plane Poiseuille streamwise periodic waves to two-dimensional nonlinear steady states for the plane Couette Flow limit. The nonlinear Couette Flow states are retrieved using three independent solution procedures and the disturbance Flow structure is shown to be localized in the streamwise periodic box. Numerical evidence is provided that the width of the nonlinear plane Couette Flow disturbance decreases with increasing resolution at fixed boxlength. This singular-t...
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Two-dimensional nonlinear plane Poiseuille-Couette Flow homotopy revisited
Physics of Fluids, 2008Co-Authors: Uwe Ehrenstein, Masato Nagata, F RinconAbstract:A recent paper by Rincon [Phys. Fluids {\bf 19}, 074105 (2007)] readdresses the question of the existence of two-dimensional steady nonlinear states in plane Couette Flow, coming to the conclusion that it is not possible to obtain the nonlinear plane Couette Flow solutions reported by Cherhabili and Ehrenstein [Eur. J. Mech. B/FLUIDS {\bf 14}, 667 (1995)], using their Poiseuille-Couette homotopy. Exploring the multi-parameter space by performing several consecutive and distinct continuations, we show that it is possible to find a complex numerical path from plane Poiseuille streamwise periodic waves to two-dimensional nonlinear steady states for the plane Couette Flow limit. The nonlinear Couette Flow states are retrieved using three independent solution procedures and the disturbance Flow structure is shown to be localized in the streamwise periodic box. Numerical evidence is provided that the width of the nonlinear plane Couette Flow disturbance decreases with increasing resolution at fixed box length. This singular-type behavior of the solution structure for increasing resolution suggests that the pseudospectral solutions do not converge to smooth two-dimensional physical solutions of the continuous nonlinear system, the existence of which remains an open question.
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Finite-amplitude equilibrium states in plane Couette Flow
Journal of Fluid Mechanics, 1997Co-Authors: A. Cherhabili, Uwe EhrensteinAbstract:A numerical bifurcation study in plane Couette Flow is performed by computing successive finite-amplitude equilibrium states, solutions of the Navier–Stokes equations. Plane Couette Flow being linearly stable for all Reynolds numbers, first two-dimensional equilibrium states are computed by extending nonlinear travelling waves in plane Poiseuille Flow through the Poiseuille–Couette Flow family to the plane Couette Flow limit. The resulting nonlinear states are stationary with a spatially localized structure; they are subject to two-dimensional and three-dimensional secondary disturbances. Three-dimensional disturbances dominate the dynamics and three-dimensional stationary equilibrium states bifurcating at criticality on the two-dimensional equilibrium surface are computed. These nonlinear states, periodic in the spanwise direction and spatially localized in the streamwise direction, are computed for Reynolds numbers (based on half the velocity difference between the walls and channel half-width) close to 1000. While a possible relationship between the computed solutions and experimentally observed coherent structures in turbulent plane Couette Flow has to be assessed, the present findings reinforce the idea that subcritical transition may be related to the existence of finite-amplitude states which are (unstable) fixed points in a dynamical systems formulation of the Navier–Stokes system.
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Existence and Stability of Finite-Amplitude States in Plane Couette Flow
Advances in Turbulence VI, 1996Co-Authors: A. Cherhabili, Uwe EhrensteinAbstract:To elucidate the transition mechanism in plane Couette Flow we compute finite-amplitude equilibrium solutions by extending numerically 2D nonlinear waves in plane Poiseuille Flow to the plane Couette Flow limit. The 2D nonlinear states in plane Couette Flow take the form of spatially localized (solitarylike) stationary waves, they represent a new basic state for a secondary stability analysis. Secondary stability characteristics are computed as well as secondary bifurcation branches leading to 3D nonlinear states spatially localized in the streamwise direction and periodic in the spanwise direction.
F Rincon - One of the best experts on this subject based on the ideXlab platform.
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two dimensional nonlinear plane poiseuille Couette Flow homotopy revisited
Physics of Fluids, 2008Co-Authors: Uwe Ehrenstein, Masato Nagata, F RinconAbstract:A recent paper by Rincon [Phys. Fluids 19, 074105 (2007)] readdressed the question of the existence of two-dimensional steady nonlinear states in plane Couette Flow, coming to the conclusion that it is not possible to obtain the nonlinear plane Couette Flow solutions reported by Cherhabili and Ehrenstein [Eur. J. Mech. B/Fluids 14, 667 (1995)] using their Poiseuille–Couette homotopy. Exploring the multiparameter space by performing several consecutive and distinct continuations, we show that it is possible to find a complex numerical path from plane Poiseuille streamwise periodic waves to two-dimensional nonlinear steady states for the plane Couette Flow limit. The nonlinear Couette Flow states are retrieved using three independent solution procedures and the disturbance Flow structure is shown to be localized in the streamwise periodic box. Numerical evidence is provided that the width of the nonlinear plane Couette Flow disturbance decreases with increasing resolution at fixed boxlength. This singular-t...
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Two-dimensional nonlinear plane Poiseuille–Couette Flow homotopy revisited
Physics of Fluids, 2008Co-Authors: Uwe Ehrenstein, Masato Nagata, F RinconAbstract:A recent paper by Rincon [Phys. Fluids 19, 074105 (2007)] readdressed the question of the existence of two-dimensional steady nonlinear states in plane Couette Flow, coming to the conclusion that it is not possible to obtain the nonlinear plane Couette Flow solutions reported by Cherhabili and Ehrenstein [Eur. J. Mech. B/Fluids 14, 667 (1995)] using their Poiseuille–Couette homotopy. Exploring the multiparameter space by performing several consecutive and distinct continuations, we show that it is possible to find a complex numerical path from plane Poiseuille streamwise periodic waves to two-dimensional nonlinear steady states for the plane Couette Flow limit. The nonlinear Couette Flow states are retrieved using three independent solution procedures and the disturbance Flow structure is shown to be localized in the streamwise periodic box. Numerical evidence is provided that the width of the nonlinear plane Couette Flow disturbance decreases with increasing resolution at fixed boxlength. This singular-t...
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Two-dimensional nonlinear plane Poiseuille-Couette Flow homotopy revisited
Physics of Fluids, 2008Co-Authors: Uwe Ehrenstein, Masato Nagata, F RinconAbstract:A recent paper by Rincon [Phys. Fluids {\bf 19}, 074105 (2007)] readdresses the question of the existence of two-dimensional steady nonlinear states in plane Couette Flow, coming to the conclusion that it is not possible to obtain the nonlinear plane Couette Flow solutions reported by Cherhabili and Ehrenstein [Eur. J. Mech. B/FLUIDS {\bf 14}, 667 (1995)], using their Poiseuille-Couette homotopy. Exploring the multi-parameter space by performing several consecutive and distinct continuations, we show that it is possible to find a complex numerical path from plane Poiseuille streamwise periodic waves to two-dimensional nonlinear steady states for the plane Couette Flow limit. The nonlinear Couette Flow states are retrieved using three independent solution procedures and the disturbance Flow structure is shown to be localized in the streamwise periodic box. Numerical evidence is provided that the width of the nonlinear plane Couette Flow disturbance decreases with increasing resolution at fixed box length. This singular-type behavior of the solution structure for increasing resolution suggests that the pseudospectral solutions do not converge to smooth two-dimensional physical solutions of the continuous nonlinear system, the existence of which remains an open question.
Andrew Ooi - One of the best experts on this subject based on the ideXlab platform.
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Superfluid spherical Couette Flow
Journal of Physics: Conference Series, 2009Co-Authors: C. Peralta, Andrew Melatos, M. Giacobello, Andrew OoiAbstract:We solve numerically for the first time the two-fluid, Hall--Vinen--Bekarevich--Khalatnikov (HVBK) equations for a He-II-like superfluid contained in a differentially rotating, spherical shell, generalizing previous simulations of viscous spherical Couette Flow (SCF) and superfluid Taylor--Couette Flow. In axisymmetric superfluid SCF, the number of meridional circulation cells multiplies as $\Rey$ increases, and their shapes become more complex, especially in the superfluid component, with multiple secondary cells arising for $\Rey > 10^3$. The torque exerted by the normal component is approximately three times greater in a superfluid with anisotropic Hall--Vinen (HV) mutual friction than in a classical viscous fluid or a superfluid with isotropic Gorter-Mellink (GM) mutual friction. HV mutual friction also tends to "pinch" meridional circulation cells more than GM mutual friction. The boundary condition on the superfluid component, whether no slip or perfect slip, does not affect the large-scale structure of the Flow appreciably, but it does alter the cores of the circulation cells, especially at lower $\Rey$. As $\Rey$ increases, and after initial transients die away, the mutual friction force dominates the vortex tension, and the streamlines of the superfluid and normal fluid components increasingly resemble each other. In nonaxisymmetric superfluid SCF, three-dimensional vortex structures are classified according to topological invariants.
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superfluid spherical Couette Flow
25TH INTERNATIONAL CONFERENCE ON LOW TEMPERATURE PHYSICS (LT25) PART 3, 2009Co-Authors: C. Peralta, Andrew Melatos, M. Giacobello, Andrew OoiAbstract:We solve numerically the two-fluid, Hall-Vinen-Bekarevich-Khalatnikov equations for a He-II-like superfluid contained in a differentially rotating, spherical shell, generalizing previous simulations of viscous spherical Couette Flow (SCF) and superfluid Taylor-Couette Flow. The system tends towards a stationary but unsteady state, where the torque oscillates persistently, with amplitude and period determined by dimensionless gap width δ and rotational shear ΔΩ. In axisymmetric superfluid SCF, the number of meridional circulation cells multiplies as the Reynolds number Re increases. In nonaxisymmetric superfluid SCF, three-dimensional vortex structures are classified according to topological invariants. We find that the mutual friction is patchy; that is, it takes different forms in different parts of the vessel, a surprising new result.
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Superfluid spherical Couette Flow
Journal of Fluid Mechanics, 2008Co-Authors: C. Peralta, Andrew Melatos, M. Giacobello, Andrew OoiAbstract:We solve numerically the two-fluid, Hall-Vinen-Bekarevich-Khalatnikov equations for a He-II-like superfluid contained in a differentially rotating, spherical shell, generalizing previous simulations of viscous spherical Couette Flow (SCF) and superfluid Taylor-Couette Flow. The system tends towards a stationary but unsteady state, where the torque oscillates persistently, with amplitude and period determined by dimensionless gap widthand rotational shear �. In axisymmetric superfluid SCF, the number of meridional circulation cells multiplies as the Reynolds number Re increases. In nonaxisymmetric superfluid SCF, three-dimensional vortex structures are classified according to topological invariants. We find that the mutual friction is "patchy"; that is, it takes different forms in different parts of the vessel, a surprising new result. < 380) (3). In this paper, we employ a numerical solver recently developed to solve the two-fluid Hall- Vinen-Bekarevich-Khalatnikov (HVBK) equations for a rotating superfluid (4) to study the unsteady behaviour of SCF in viscous (Navier-Stokes) fluids and superfluids, in two and three dimensions. We study the effect of the normal fluid/superfluid dynamics on the time-dependence of the macroscopic hydrodynamics. Differential rotation drives a meridional counterFlow which can excite microscopic turbulence in the superfluid. We study the coupling between the macroscopic Flow and microscopic superfluid turbulence, which has an important effect on the form and strength of the mutual friction between the normal and superfluid components and hence on the torque on the container.
Gerd Pfister - One of the best experts on this subject based on the ideXlab platform.
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Axisymmetric propagating vortices in centrifugally stable Taylor–Couette Flow
Journal of Fluid Mechanics, 2013Co-Authors: Ch. Hoffmann, J. Abshagen, M. Heise, Sebastian Altmeyer, Gerd PfisterAbstract:We present numerical as well as experimental results of axisymmetric, axially propagating vortices appearing in counter-rotating Taylor–Couette Flow below the centrifugal instability threshold of circular Couette Flow without additional externally imposed forces. These propagating vortices are periodically generated by the shear Flow near the Ekman cells that are induced by the non-rotating end walls. These axisymmetric vortices propagate into the bulk towards mid-height, where they get annihilated by rotating, non-propagating defects. These propagating structures appear via a supercritical Hopf bifurcation from axisymmetric, steady vortices, which have been discovered recently in centrifugally stable counter-rotating Taylor–Couette Flow (Abshagen et al. , Phys. Fluids , vol. 22, 2010, 021702). In the nonlinear regime of the Hopf bifurcation, contributions of non-axisymmetric modes also appear.
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Localized modulation of rotating waves in Taylor-Couette Flow
Physical Review E, 2012Co-Authors: J. Abshagen, J. Von Stamm, M. Heise, Ch. Will, Gerd PfisterAbstract:We report the results of an experimental study on the multiplicity of states in Taylor-Couette Flow as a result of axial localization of azimuthally rotating waves. Localized states have been found to appear hysteretically from time-dependent Taylor-Couette Flow at Reynolds numbers significantly above the onset of wavy Taylor vortices. These localized states have the shape of a modulated rotating wave and differ significantly from global modulated wavy Taylor vortex states in their spatial characteristics. Axial localization of rotating waves is accompanied with a significant increase in size of the underlying pair of Taylor vortices. Our work reveals that localization provides a mechanism for the appearance of multiple time-dependent states in Taylor-Couette Flow.
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Localized spirals in Taylor-Couette Flow.
Physical Review E, 2008Co-Authors: M. Heise, J. Abshagen, Gerd Pfister, D. Küter, K. Hochstrate, Ch. HoffmannAbstract:We present a type of spiral vortex state that appears from a supercritical Hopf bifurcation below the linear instability of circular Couette Flow in a Taylor-Couette system with rigid end plates. These spirals have been found experimentally as well as numerically as "pure" states but also coexist with "classical" spirals (or axially standing waves for smaller systems) which typically appear from linear instability in counterrotating Taylor-Couette Flow. These spiral states have an axial distribution of the strongly localized amplitude in the vicinity of the rigid end plates that confine the system in the axial direction. Furthermore, they show significantly different oscillation frequencies compared to the critical spiral frequencies. Despite the localization of the amplitude near the ends, the states appear as global states with spirals that propagate either toward the middle from each end of the system or vice versa. In contrast to classical spirals, these states exhibit a spatial or a spatiotemporal reflection symmetry.
C. Peralta - One of the best experts on this subject based on the ideXlab platform.
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Superfluid spherical Couette Flow
Journal of Physics: Conference Series, 2009Co-Authors: C. Peralta, Andrew Melatos, M. Giacobello, Andrew OoiAbstract:We solve numerically for the first time the two-fluid, Hall--Vinen--Bekarevich--Khalatnikov (HVBK) equations for a He-II-like superfluid contained in a differentially rotating, spherical shell, generalizing previous simulations of viscous spherical Couette Flow (SCF) and superfluid Taylor--Couette Flow. In axisymmetric superfluid SCF, the number of meridional circulation cells multiplies as $\Rey$ increases, and their shapes become more complex, especially in the superfluid component, with multiple secondary cells arising for $\Rey > 10^3$. The torque exerted by the normal component is approximately three times greater in a superfluid with anisotropic Hall--Vinen (HV) mutual friction than in a classical viscous fluid or a superfluid with isotropic Gorter-Mellink (GM) mutual friction. HV mutual friction also tends to "pinch" meridional circulation cells more than GM mutual friction. The boundary condition on the superfluid component, whether no slip or perfect slip, does not affect the large-scale structure of the Flow appreciably, but it does alter the cores of the circulation cells, especially at lower $\Rey$. As $\Rey$ increases, and after initial transients die away, the mutual friction force dominates the vortex tension, and the streamlines of the superfluid and normal fluid components increasingly resemble each other. In nonaxisymmetric superfluid SCF, three-dimensional vortex structures are classified according to topological invariants.
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superfluid spherical Couette Flow
25TH INTERNATIONAL CONFERENCE ON LOW TEMPERATURE PHYSICS (LT25) PART 3, 2009Co-Authors: C. Peralta, Andrew Melatos, M. Giacobello, Andrew OoiAbstract:We solve numerically the two-fluid, Hall-Vinen-Bekarevich-Khalatnikov equations for a He-II-like superfluid contained in a differentially rotating, spherical shell, generalizing previous simulations of viscous spherical Couette Flow (SCF) and superfluid Taylor-Couette Flow. The system tends towards a stationary but unsteady state, where the torque oscillates persistently, with amplitude and period determined by dimensionless gap width δ and rotational shear ΔΩ. In axisymmetric superfluid SCF, the number of meridional circulation cells multiplies as the Reynolds number Re increases. In nonaxisymmetric superfluid SCF, three-dimensional vortex structures are classified according to topological invariants. We find that the mutual friction is patchy; that is, it takes different forms in different parts of the vessel, a surprising new result.
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Superfluid spherical Couette Flow
Journal of Fluid Mechanics, 2008Co-Authors: C. Peralta, Andrew Melatos, M. Giacobello, Andrew OoiAbstract:We solve numerically the two-fluid, Hall-Vinen-Bekarevich-Khalatnikov equations for a He-II-like superfluid contained in a differentially rotating, spherical shell, generalizing previous simulations of viscous spherical Couette Flow (SCF) and superfluid Taylor-Couette Flow. The system tends towards a stationary but unsteady state, where the torque oscillates persistently, with amplitude and period determined by dimensionless gap widthand rotational shear �. In axisymmetric superfluid SCF, the number of meridional circulation cells multiplies as the Reynolds number Re increases. In nonaxisymmetric superfluid SCF, three-dimensional vortex structures are classified according to topological invariants. We find that the mutual friction is "patchy"; that is, it takes different forms in different parts of the vessel, a surprising new result. < 380) (3). In this paper, we employ a numerical solver recently developed to solve the two-fluid Hall- Vinen-Bekarevich-Khalatnikov (HVBK) equations for a rotating superfluid (4) to study the unsteady behaviour of SCF in viscous (Navier-Stokes) fluids and superfluids, in two and three dimensions. We study the effect of the normal fluid/superfluid dynamics on the time-dependence of the macroscopic hydrodynamics. Differential rotation drives a meridional counterFlow which can excite microscopic turbulence in the superfluid. We study the coupling between the macroscopic Flow and microscopic superfluid turbulence, which has an important effect on the form and strength of the mutual friction between the normal and superfluid components and hence on the torque on the container.
