共查询到20条相似文献,搜索用时 31 毫秒
1.
Adriano Montanaro 《Archive for Rational Mechanics and Analysis》1998,143(4):375-400
We consider equilibria arising in a model for phase transitions which correspond to stable critical points of the constrained
variational problem Here W is a double‐well potential and is a strictly convex domain. For ε small, this is closely related to the problem of partitioning Ω into two subdomains of fixed volume, where the subdomain boundaries correspond to the transitional boundary between phases.
Motivated by this geometry problem, we show that in a strictly convex domain, stable critical points of the original variational
problem have a connected, thin transition layer separating the two phases. This relates to work in [GM] where special geometries
such as cylindrical domains were treated, and is analogous to the results in [CHo] which show that
in a convex domain, stable critical points of the corresponding unconstrained problem are constant. The proof of connectivity employs tools from geometric measure theory including the co‐area formula
and the isoperimetric inequality on manifolds. The thinness of the transition layer follows from a separate calculation establishing
spatial decay of solutions to the pure phases.
(Accepted July 15, 1996) 相似文献
2.
Experiments were performed to study the stability characteristics of an unsteady circular Couette flow generated by an impulsive stop of the outer cylinder; the initial condition was a state of rigid-body rotation. Instability of the unsteady basic state is manifested by Görtler vortices, which themselves become unstable to longer-wavelength disturbances, or Taylor vortices which persist indefinitely. The quantities of primary interest are the onset time of instability, the axial vortex wavelength at onset, and the time-evolution of this wavelength. A one-dimensional photodiode array is used to gather data from the flow, which is seeded with flow-visualization material. At sufficiently high values of the Reynolds number, the influence of the inner cylinder on the onset of instability is negligible, based on comparisons with previous experimental data. 相似文献
3.
It is well known that plane creeping Couette flow of UCM and Oldroy-B fluids are linearly stable. However, for Burges fluid, which includes UCM and Oldroyd-B fluids as special cases, unstable modes are detected in the present work. The wave speed, critical parameters and perturbation mode are studied for neutral waves. Energy analysis shows that the sustaining of perturbation energy in Poiseuille flow and Couette flow is completely different. At low Reynolds number limit, analytical solutions are obtained for simplified perturbation equations. The essential difference between Burgers fluid and Oldroyd-B fluid is revealed to be the fact that neutral mode exists only in the former. 相似文献
4.
J. Langenberg M. Heise G. Pfister J. Abshagen 《Theoretical and Computational Fluid Dynamics》2004,18(2-4):97-103
We present results of an experimental study on the stability of Taylor–Couette flow in case of counter-rotating cylinders and an imposed axial through flow. We are able to confirm results form recent numerical investigations done by Pinter et al. [24] by measuring the absolute and convective stability boundaries of both propagating Taylor vortices (PTV) and spiral vortices (SPI). Thus our work shows that these theoretical concepts from hydrodynamic stability in open flows apply to experimental counter-rotating Taylor–Couette systems with an imposed axial through flow. PACS 47.20.-k, 05.45.-a, 47.15.fe 相似文献
5.
A finite element formulation for global linear stability analysis of a nominally two‐dimensional base flow 下载免费PDF全文
A stabilized finite element method, to carry out the linear stability analysis of a two‐dimensional base flow to three‐dimensional perturbations that are periodic along span, is presented. The resulting equations for the time evolution of the disturbance requires a solution to the generalized eigenvalue problem. The analysis is global in nature and is also applicable to non‐parallel flows. Equal‐order‐interpolation functions for velocity and pressure are utilized. Stabilization terms are added to the Galerkin formulation to admit the use of equal‐order‐interpolation functions and to eliminate node‐to‐node oscillations that might arise in advection‐dominated flows. The proposed formulation is tested on two flow problems. First, the mode transitions in the circular Couette flow are investigated. Two scenarios are considered. In the first one, the outer cylinder is at rest, while the inner one spins. Two linearly unstable modes are identified. The primary mode is real and represents the axisymmetric Taylor vortices. The second mode is complex and consists of spiral vortices. For the counter‐rotating cylinders, the primary transition is via the appearance of spiral vortices. Excellent agreement with results from earlier studies is observed. The formulation is also utilized to investigate the parallel and oblique modes of vortex shedding past a cylinder for the Re = 100 flow. It is found that the flow is associated with a large number of unstable oblique shedding modes. The parallel mode of vortex shedding is a special case of this family of modes and is associated with the largest growth rate. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
6.
It is known that the Van der Waals‐Cahn‐Hilliard (W‐C‐H) dynamics can be approximated by a Quasi‐static Stefan problem with
surface tension. It turns out that the Stefan problem has a manifold of equilibria equal in dimension to that of the domain
Ω: any sphere of fixed radius with interface contained in the domain is an equilibrium (indistinguishable from the point of
view of the perimeter functional). We resolve this degeneracy by showing that at the W‐C‐H level this manifold is replaced
by a quasi‐invariant stable manifold, on which the typical solution preserves its “bubble” like shape until it reaches the
boundary. Moreover, we show that the “bubble” moves superslowly. We also obtain an equation that determines those special
spheres that correspond to equilibria at the W‐C‐H level. Our work establishes the
phenomenon of superslow motion in higher space dimensions in the class of single interface solutions.
(Accepted February 12, 1996) 相似文献
7.
Perturbed plane Couette flow containing a thin spanwise-oriented ribbon undergoes a subcritical bifurcation at Re≈230 to a steady three-dimensional state containing streamwise vortices. This bifurcation is followed by several others giving
rise to a fascinating series of stable and unstable steady states of different symmetries and wavelengths. First, the backwards-bifurcating
branch reverses direction and becomes stable near Re≈200. Then the spanwise reflection symmetry is broken, leading to two asymmetric branches which are themselves destabilized
at Re≈420. Above this Reynolds number, time evolution leads first to a metastable state whose spanwise wavelength is halved and
then to complicated time-dependent behavior. These features are in agreement with experiments.
Received 15 December 2001 and accepted 29 March 2002 Published online: 2 October 2002
Communicated by H.J.S. Fernando 相似文献
8.
Charles M. Elliott Reiner Schätzle Barbara E. E. Stoth 《Archive for Rational Mechanics and Analysis》1998,145(2):99-127
In a Type‐II superconductor the magnetic field penetrates the superconducting body through the formation of vortices. In
an extreme Type‐II superconductor these vortices reduce to line singularities. Because the number of vortices is large it
seems feasible to model their evolution by an averaged problem, known as the mean-field model of superconductivity. We assume
that the evolution law of an individual vortex, which underlies the averaging process, involves the current of the generated
magnetic field as well as the curvature vector. In the present paper we study a two‐dimensional reduction, assuming all vortices
to be perpendicular to a given direction. Since both the magnetic field H and the averaged vorticity ω are curl‐free, we may represent them via a scalar magnetic potential q and a scalar stream function ψ, respectively. We study existence, uniqueness and asymptotic behaviour of solutions (ψ, q) of the resulting degenerate elliptic‐parabolic system (with curvature taken into account or not) by means of viscosity and
weak solutions. In addition we relate (ψ, q) to solutions (ω, H) of the mean‐field equations without curvature. Finally we construct special solutions of the corresponding stationary equations
with two or more superconducting phases.
(Accepted August 8, 1997) 相似文献
9.
Olivier Czarny Eric Serre Patrick Bontoux Richard M. Lueptow 《Theoretical and Computational Fluid Dynamics》2002,16(1):5-15
Differentially rotating cylinders result in a rich variety of vortical flows for cylindrical Couette flow. In this study we
investigate the case of a short, finite-length cavity with counter-rotating cylinders via direct numerical simulation using
a three-dimensional spectral method. We consider aspect ratios ranging from 5 to 6. Two complex flow regimes, wavy vortices
and interpenetrating spirals, occur with similar appearance to those found experimentally for much larger aspect ratios. For
wavy vortices the wave speed is similar to that found for counter-rotating systems and systems in which the outer cylinder
is stationary. For the interpenetrating spiral structure, the vortices are largely confined to the unstable region near the
inner cylinder. The endwalls appear to damp and stabilize the flow as the aspect ratio is reduced to the point that in some
cases the vortical flow is suppressed. At higher inner cylinder speeds, the interpenetrating spirals acquire a waviness and
the vortices, while generally near the inner cylinder, can extend all of the way to the outer cylinder.
Received 5 November 2001 and accepted 29 March 2002 Published online 2 October 2002
Communicated by H.J.S. Fernando 相似文献
10.
Axisymmetrically stable turbulent Taylor vortices between two concentric cylinders are studied with respect to the transition from vortex to wall driven turbulent production. The outer cylinder is stationary and the inner cylinder rotates. A low Reynolds number turbulence model using the k‐ω formulation, facilitates an analysis of the velocity gradients in the Taylor–Couette flow. For a fixed inner radius, three radius ratios 0.734, 0.941 and 0.985 are employed to identify the Reynolds number range at which this transition occurs. At relatively low Reynolds numbers, turbulent production is shown to be dominated by the outflowing boundary of the Taylor vortex. As the Reynolds number increases, shear driven turbulence (due to the rotating cylinder) becomes the dominating factor. For relatively small gaps turbulent flow is shown to occur at Taylor numbers lower than previously reported. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
11.
W. M. Yang 《International Journal of Computational Fluid Dynamics》2013,27(9):643-648
This study investigates the instability analysis of modulated Taylor vortices flow by utilising a numerical method. Based on the consideration that the outer cylinder is fixed and the inner cylinder rotates at a non-zero averaged speed under varying modulated amplitudes and frequencies, the flow is converted from one-dimension Couette flow to Taylor vortices. When the modulated amplitude is greater than 1 and the rotation speed of the inner cylinder exceeds the threshold value for one-dimensional flow, the flow will be more stable at intermediate and high frequencies. When the modulated amplitude is sufficiently large and the inner cylinder rotates at medium frequency, subharmonic flow arises. 相似文献
12.
We perform a detailed numerical study of transient Taylor vortices arising from the instability of cylindrical Couette flow
with the exterior cylinder at rest for radius ratio η = 0.5 and variable aspect ratio Γ. The result of Abshagen et al. (J Fluid Mech 476:335–343, 2003) that onset transients apparently evolve on a much smaller
time–scale than decay transients is recovered. It is shown to be an artefact of time scale estimations based on the Stuart–Landau
amplitude equation which assumes frozen space dependence while full space–time dependence embedded in the Ginzburg–Landau
formalism needs to be taken into account to understand transients already at moderate aspect ratio. Sub-critical pattern induction
is shown to explain the apparently anomalous behaviour of the system at onset while decay follows the Stuart–Landau prediction
more closely. The dependence of time scales on boundary effects is studied for a wide range of aspect ratios, including non-integer
ones, showing general agreement with the Ginzburg–Landau picture able to account for solutions modulated by Ekman pumping
at the disks bounding the cylinders.
相似文献
13.
We study two‐dimensional Riemann problems with piecewise constant data. We identify a class of two‐dimensional systems, including
many standard equations of compressible flow, which are simplified by a transformation to similarity variables. For equations
in this class, a two‐dimensional Riemann problem with sectorially constant data becomes a boundary‐value problem in the finite
plane. For data leading to shock interactions, this problem separates into two parts: a quasi‐one‐dimensional problem in supersonic
regions, and an equation of mixed type in subsonic regions.
We prove a theorem on local existence of solutions of quasi‐one‐dimensional Riemann problems. For 2 × 2 systems, we generalize
a theorem of Courant & Friedrichs, that any hyperbolic state adjacent to a constant state must be a simple wave.
In the subsonic regions, where the governing equation is of mixed hyperbolic‐elliptic type, we show that the elliptic part
is degenerate at the boundary, with a nonlinear variant of a degeneracy first described by Keldysh.
(Accepted December 4, 1997) 相似文献
14.
We consider the Ginzburg‐Landau system with an applied magnetic field and analyze the behavior of solutions when the domain
is a cylinder (of radius ) and the applied field is parallel to the axis. It is shown that there is an upper critical value such that if the modulus of the applied field is greater than , the normal (nonsuperconducting) state (in which the order parameter is identically zero) is stable and if the modulus of
the applied field is slightly below , the normal state is unstable. In addition, it is shown that there is a positive lower critical value such that the normal state is unstable if the modulus of the applied field is less than and stable if the modulus is slightly above . In the case of type‐II materials for whic
h the Ginzburg‐Landau constant κ is large, it is shown that there is a discrete set of radii ℬ(κ) such that if and is sufficiently large, then for each applied field of modulus slightly less than (or slightly more than ) there is precisely one small superconducting solution (up to a gauge transformation) which is stable. Moreover for this
solution, the complex‐valued order parameter ψ is zero only on the axis of the cylinder, and its winding number is proportional
to the product of κ2 and the cross‐sectional area of the cylinder. In addition, the solution exhibits “surface superconductivity” as predicted
by the physicists de Gennes and St. James.
(Accepted July 15, 1996) 相似文献
15.
The stability of Couette flow of a viscous incompressible fluid between two concentric rotating cylinders in the presence
of a radial temperature gradient due to a constant heat flux at the outer cylinder is studied. The critical values of `a' (the wave number) and Ta (the Taylor number) are listed in a table and some critical Taylor numbers are shown graphically.
It is shown that as the heat flux is increased the flow becomes more unstable for all values of μ calculated, where μ is the
ratio of the angular velocity of the outer cylinder to that of the inner cylinder.
Received on 04 March 1997 相似文献
16.
In this work we examine first the flow field of a confined jet produced by a turbulent flow in a long cylindrical pipe issuing
in an abrupt angle diffuser. Second, we examine the dispersion of inertial micro-particles entrained by the turbulent flow.
Specifically, we examine how the particle dispersion field evolves in the multiscale flow generated by the interactions between
the large-scale structures, which are geometry dependent, with the smaller turbulent scales issued by the pipe which are advected
downstream. We use Large-Eddy-Simulation (LES) for the flow field and Lagrangian tracking for particle dispersion. The complex
shape of the domain is modelled using the immersed-boundaries method. Fully developed turbulence inlet conditions are derived
from an independent LES of a spatially periodic cylindrical pipe flow. The flow field is analyzed in terms of local velocity
signals to determine spatial coherence and decay rate of the coherent K–H vortices and to make quantitative comparisons with
experimental data on free jets. Particle dispersion is analyzed in terms of statistical quantities and also with reference
to the dynamics of the coherent structures. Results show that the particle dynamics is initially dominated by the Kelvin–Helmholtz
(K–H) rolls which form at the expansion and only eventually by the advected smaller turbulence scales. 相似文献
17.
Arjang Alidai Arnoud J. Greidanus René Delfos Jerry Westerweel 《Flow, Turbulence and Combustion》2016,96(3):609-619
The transition from the laminar to the turbulent regime in linearly stable shear flows, for example, pipe and plane Couette flows, occurs abruptly with no precursor. The evolution of turbulent spots has been studied to better understand the dynamics of this transition and the onset of turbulence. These studies have mostly focused on pipe flows for which a finite lifetime of spots was proven. The same conclusion was drawn in the only available study performed in a Taylor Couette setup. Here, the spot lifetime is measured in a different size TC setup. It is shown that the lifetime is indeed finite and also very sensitive to boundary conditions, but not much to perturbation mechanisms. A scaling approach is provided which suggests in addition to the Reynolds number, the aspect and radius ratios are influential parameters on the lifetime. It is found that the spot size varies during its lifetime and increases with the Reynolds number that confirms the rise in turbulence proliferation by approaching the transitional point. 相似文献
18.
E. Carlen R. Esposito J. L. Lebowitz R. Marra A. Rokhlenko 《Archive for Rational Mechanics and Analysis》1998,142(3):193-218
We study, globally in time, the velocity distribution f(v,t) of a spatially homogeneous system that models a system of electrons in a weakly ionized plasma, subjected to a constant
external electric field E. The density f satisfies a Boltzmann-type kinetic equation containing a fully nonlinear electron‐electron collision term as well as linear
terms representing collisions with reservoir particles having a specified Maxwellian distribution. We show that when the constant
in front of the nonlinear collision kernel, thought of as a scaling parameter, is sufficiently strong, then the L
1 distance between f and a certain time-dependent Maxwellian stays small uniformly in t. Moreover, the mean and variance of this time‐dependent Maxwellian satisfy a coupled set of nonlinear ordinary differential
equations that constitute the “hydrodynamical” equations for this kinetic system. This remains
true even when these ordinary differential equations have non‐unique equilibria, thus proving the existence of multiple stable
stationary solutions for the full kinetic model. Our approach relies on scale‐independent estimates for the kinetic equation,
and entropy production estimates. The novel aspects of this approach may be useful in other problems concerning the relation
between the kinetic and hydrodynamic scales globally in time.
(Accepted September 3, 1996) 相似文献
19.
The time evolution of finite amplitude axisymmetric perturbations (Taylor cells) to the purely azimuthal, viscoelastic, cylindrical Couette flow was numerically simulated. Two time integration numerical methods were developed, both based on a pseudospectral spatial approximation of the variables, efficiently implemented using fast Poisson solvers and optimal filtering routines. The first method, applicable for finite Re numbers, is based on a time-splitting integration with the divergence-free condition enforced through an influence matrix technique. The second one, is based on a semi-implicit time integration of the constitutive equation with both the continuity and the momentum equations enforced as constraints. Stability results for an upper convected Maxwell fluid were obtained for the supercritical bifurcations, either steady or time-periodic, developed after the onset of instabilities in the primary flow. At small elasticity values, ? ≡ De/Re, the time integration of finite amplitude disturbances confirms the stability of the single branch of steady Taylor cells. At intermediate ? values the rotating wave family of time-periodic solutions developed at the onset of instability is stable, whereas the standing wave is found to be unstable. At high ? values, and in particular for the limit of creeping flow (? = ∞), the present study shows that the rotating wave family is unstable and the standing (radial) wave is stable, in agreement with previous finite-element investigations. It is thus shown that spectral techniques provide a robust and computationally efficient method for the simulation of complex, non-linear, time-dependent viscoelastic flows. 相似文献
20.
H. A. Snyder 《International Journal of Non》1970,5(4):659-685