arXiv subjects

M. Lücke

Publications and source records attributed to M. Lücke.

12 recordsLinked to original sources

arXiv2009

End-wall effects on the transition between Taylor vortices and spiral vortices

We present numerical simulations as well as experimental results concerning transitions between Taylor vortices and spiral vortices in the Taylor-Couette system with rigid, non-rotating end-walls in axial direction. As in the axial periodic case, these transitions are performed by wavy structures appearing via a secondary bifurcation out of Taylor vortices and spirals, respectively. But in the presence of rigid lids, pure spiral solutions do not occur but are substituted by primary bifurcating, stable wavy spiral structures (wSPI). Similarly to the periodic system, we found a transition from Taylor vortices to wSPI mediated by so called wavy Taylor vortices (wTVF) and, on the other hand, a transition from wSPI to TVF triggered by a propagating defect. We furthermore observed and investigated the primary bifurcation of wSPI out of basic Ekman flow.

nlin.PS↗

arXiv2008

Bifurcation of standing waves into a pair of oppositely traveling waves with oscillating amplitudes caused by a three-mode interaction

A novel flow state consisting of two oppositely travelling waves (TWs) with oscillating amplitudes has been found in the counterrotating Taylor-Couette system by full numerical simulations. This structure bifurcates out of axially standing waves that are nonlinear superpositions of left and right handed spiral vortex waves with equal time-independent amplitudes. Beyond a critical driving the two spiral TW modes start to oscillate in counterphase due to a Hopf bifurcation. The trigger for this bifurcation is provided by a nonlinearly excited mode of different symmetry than the spiral TWs. A three-mode coupled amplitude equation model is presented that captures this bifurcation scenario. The mode-coupling between two symmetry degenerate critical modes and a nonlinearly excited one that is contained in the model can be expected to occur in other structure forming systems as well.

nlin.PS↗

arXiv2008

Wave-number dependence of the transitions between traveling and standing vortex waves and their mixed states in the Taylor-Couette system

Previous numerical investigations of the stability and bifurcation properties of different nonlinear combination structures of spiral vortices in a counterrotating Taylor-Couette system that were done for fixed axial wavelengths are supplemented by exploring the dependence of the vortex phenomena waves on their wavelength. This yields information about the experimental and numerical accessability of the various bifurcation scenarios. Also backwards bifurcating standing waves with oscillating amplitudes of the constituent traveling waves are found.

nlin.PS↗

arXiv2007

Controlling the stability transfer between oppositely traveling waves and standing waves by inversion-symmetry-breaking perturbations

The effect of an externally applied flow on symmetry degenerated waves propagating into opposite directions and standing waves that exchange stability with the traveling waves via mixed states is analyzed. Wave structures that consist of spiral vortices in the counter rotating Taylor-Couette system are investigated by full numerical simulations and explained quantitatively by amplitude equations containing quintic coupling terms. The latter are appropriate to describe the influence of inversion symmetry breaking perturbations on many oscillatory instabilities with O(2) symmetry.

physics.flu-dyn↗

arXiv2006

Periodically forced ferrofluid pendulum: effect of polydispersity

We investigate a torsional pendulum containing a ferrofluid that is forced periodically to undergo small-amplitude oscillations. A homogeneous magnetic field is applied perpendicular to the pendulum axis. We give an analytical formula for the ferrofluid-induced ``selfenergy'' in the pendulum's dynamic response function for monodisperse as well as for polydisperse ferrofluids.

physics.flu-dyn↗

arXiv2006

Competition between Traveling Fluid Waves of Left and Right Spiral Vortices and Their Different Amplitude Combinations

Stability, bifurcation properties, and the spatiotemporal behavior of different nonlinear combination structures of spiral vortices in the counter rotating Taylor-Couette system are investigated by full numerical simulations and by coupled amplitude equation approximations. Stable cross-spiral structures with continuously varying content of left and right spiral modes are found. They provide a stability transferring connection between the initially stable, axially counter propagating wave states of pure spirals and the axially standing waves of so-called ribbons that become stable slightly further away from onset of vortex flow.

physics.flu-dyn↗

arXiv2005

Spiral vortices traveling between two rotating defects in the Taylor-Couette system

Numerical calculations of vortex flows in Taylor-Couette systems with counter rotating cylinders are presented. The full, time dependent Navier-Stokes equations are solved with a combination of a finite difference and a Galerkin method. Annular gaps of radius ratio $η=0.5$ and of several heights are simulated. They are closed by nonrotating lids that produce localized Ekman vortices in their vicinity and that prevent axial phase propagation of spiral vortices. Existence and spatio temporal properties of rotating defects, of modulated Ekman vortices, and of the spiral vortex structures in the bulk are elucidated in quantitative detail.

physics.flu-dyn↗

arXiv2005

Spiral Vortices and Taylor Vortices in the Annulus between Rotating Cylinders and the Effect of an Axial Flow

We present numerical simulations of vortices that appear via primary bifurcations out of the unstructured circular Couette flow in the Taylor-Couette system with counter-rotating as well as with co-rotating cylinders. The full, time dependent Navier-Stokes equations are solved with a combination of a finite difference and a Galerkin method for a fixed axial periodicity length of the vortex patterns and for a finite system of aspect ratio 12 with rigid nonrotating ends in a setup with radius ratio eta=0.5. Differences in structure, dynamics, symmetry properties, bifurcation and stability behavior between spiral vortices with azimuthal wave numbers M=+-1 and M=0 Taylor vortices are elucidated and compared in quantitative detail. Simulations in axially periodic systems and in finite systems with stationary rigid ends are compared with experimental spiral data. In a second part of the paper we determine how the above listed properties of the M=-1,0,1 vortex structures are changed by an externally imposed axial through-flow with Reynolds numbers in the range -40 <= Re <= 40. Among others we investigate when left handed or right handed spirals or toroidally closed vortices are preferred.

physics.flu-dyn↗

arXiv2005

Magnetization of rotating ferrofluids: predictions of different theoretical models

We consider a ferrofluid cylinder, that is rotating with constant rotation frequency Ωe_z as a rigid body. A homogeneous magnetic field H_0 e_x is applied perpendicular to the cylinder axis e_z. This causes a nonequilibrium situation. Therein the magnetization M and the internal magnetic field H are constant in time and homogeneous within the ferrofluid. According to the Maxwell equations they are related to each other via H = H_0 - M/2. However, H and M are not parallel to each other and their directions differ from that of the applied field H_0. We have analyzed several different theoretical models that provide equations for the magnetization in such a situation. The magnetization M is determined for each model as a function of Ωand H_0 in a wide range of frequencies and fields. Comparisons are made of the different model results and the differences in particular of the predictions for the perpendicular components H_y =-M_y/2 of the fields are analyzed.

physics.flu-dyn↗

arXiv2003

Spiral and Taylor vortex fronts and pulses in axial through-flow

The influence of an axial through-flow on the spatiotemporal growth behavior of different vortex structures in the Taylor-Couette system with radius ratio eta=0.5 is determined. The Navier Stokes equations (NSE) linearized around the basic Couette-Poiseuille flow are solved numerically with a shooting method in a wide range of through-flow strengths Re and different rates of co- and counterrotating cylinders for toroidally closed vortices with azimuthal wave number m=0 and for spiral vortex flow with m=+1 and m=-1. For each of these three different vortex varieties we have investigated (i) axially extended vortex structures, (ii) axially localized vortex pulses, and (iii) vortex fronts. The complex dispersion relations of the linearized NSE for vortex modes with the three different m are evaluated for real axial wave numbers for (i) and over the plane of complex axial wave numbers for (ii,iii). We have also determined the Ginzburg-Landau amplitude equation (GLE) approximation in order to analyze its predictions for the vortex stuctures (ii,iii). Critical bifurcation thresholds for extended vortex structures are evaluated. The boundaries between absolute and convective instability of the basic state for vortex pulses are determined with a saddle-point analysis of the dispersion relations. Finally, the linearly selected front behavior of growing vortex structures is investigated. For the two front intensity profiles (increasing in positive or negative axial direction) we have determined front velocities, axial growth rates, and the wave numbers and frequencies of the unfolding vortex patterns with azimuthal wave numbers m=0, +1, -1, respectively.

physics.flu-dyn↗

arXiv2000

Magnetization of ferrofluids with dipolar interactions - a Born--Mayer expansion

For ferrofluids that are described by a system of hard spheres interacting via dipolar forces we evaluate the magnetization as a function of the internal magnetic field with a Born--Mayer technique and an expansion in the dipolar coupling strength. Two different approximations are presented for the magnetization considering different contributions to a series expansion in terms of the volume fraction of the particles and the dipolar coupling strength.

cond-mat.soft↗

arXiv1999

Stability boundaries of roll and square convection in binary fluid mixtures with positive separation ratio

Rayleigh-Bénard convection in horizontal layers of binary fluid mixtures heated from below with realistic horizontal boundary conditions is studied theoretically using multi-mode Galerkin expansions. For positive separation ratios the main difference between the mixtures and pure fluids lies in the existence of stable three dimensional patterns near onset in a wide range of the parameter space. We evaluated the stationary solutions of roll, crossroll, and square convection and we determined the location of the stability boundaries for many parameter combinations thereby obtaining the Busse balloon for roll and square patterns.

patt-sol↗