TY - JOUR A1 - Guimaraes, Ana H. F. A1 - Albers, Nicole A1 - Spahn, Frank A1 - Seiss, Martin A1 - Vieira-Neto, Ernesto A1 - Brilliantov, Nikolai V. T1 - Aggregates in the strength and gravity regime Particles sizes in Saturn's rings JF - Icarus : international journal of solar system studies N2 - Particles in Saturn's main rings range in size from dust to kilometer-sized objects. Their size distribution is thought to be a result of competing accretion and fragmentation processes. While growth is naturally limited in tidal environments, frequent collisions among these objects may contribute to both accretion and fragmentation. As ring particles are primarily made of water ice attractive surface forces like adhesion could significantly influence these processes, finally determining the resulting size distribution. Here, we derive analytic expressions for the specific self-energy Q and related specific break-up energy Q(star) of aggregates. These expressions can be used for any aggregate type composed of monomeric constituents. We compare these expressions to numerical experiments where we create aggregates of various types including: regular packings like the face-centered cubic (fcc), Ballistic Particle Cluster Aggregates (BPCA), and modified BPCAs including e.g. different constituent size distributions. We show that accounting for attractive surface forces such as adhesion a simple approach is able to: (a) generally account for the size dependence of the specific break-up energy for fragmentation to occur reported in the literature, namely the division into "strength" and "gravity" regimes and (b) estimate the maximum aggregate size in a collisional ensemble to be on the order of a few tens of meters, consistent with the maximum particle size observed in Saturn's rings of about 10 m. KW - Collisional physics KW - Accretion KW - Planetary rings KW - Saturn, Rings Y1 - 2012 U6 - https://doi.org/10.1016/j.icarus.2012.06.005 SN - 0019-1035 SN - 1090-2643 VL - 220 IS - 2 SP - 660 EP - 678 PB - Elsevier CY - San Diego ER - TY - THES A1 - Szklarski, Jacek T. T1 - Helical magnetorotational instability in MHD Taylor-Couette flow T1 - Helikale Magnetorotationsinstabilität in MHD Taylor-Couette Strömung N2 - Magnetorotational instability (MRI) is one of the most important and most common instabilities in astrophysics. Today it is widely accepted that it serves as a major source of turbulent viscosity in accretion disks, the most energy efficient objects in the universe. The importance of the MRI for astrophysics has been realized only in recent fifteen years. However, originally it was discovered much earlier, in 1959, in a very different context. Theoretical flow of a conducting liquid confined between differentially rotating cylinders in the presence of an external magnetic field was analyzed. The central conclusion is that the additional magnetic field parallel to the axis of rotation can destabilize otherwise stable flow. Theory of non-magnetized fluid motion between rotating cylinders has much longer history, though. It has been studied already in 1888 and today such setup is usually referred as a Taylor-Couette flow. To prove experimentally the existence of MRI in a magnetized Taylor-Couette flow is a demanding task and different MHD groups around the world try to achieve it. The main problem lies in the fact that laboratory liquid metals which are used in such experiments are characterized by small magnetic Prandtl number. Consequently rotation rates of the cylinders must be extremely large and vast amount of technical problems emerge. One of the most important difficulties is an influence of plates enclosing the cylinders in any experiment. For fast rotation the plates tend to dominate the whole flow and the MRI can not be observed. In this thesis we discuss a special helical configuration of the applied magnetic field which allows the critical rotation rates to be much smaller. If only the axial magnetic field is present, the cylinders must rotate with angular velocities corresponding to Reynolds numbers of order Re ≈ 10^6. With the helical field this number is dramatically reduced to Re ≈ 10^3. The azimuthal component of the magnetic field can be easily generated by letting an electric current through the axis of rotation, In a Taylor-Couette flow the (primary) instability manifests itself as Taylor vortices. The specific geometry of the helical magnetic field leads to a traveling wave solution and the vortices are drifting in a direction determined by rotation and the magnetic field. In an idealized study for infinitely long cylinders this is not a problem. However, if the cylinders have finite length and are bounded vertically by the plates the situation is different. In this dissertation it is shown, with use of numerical methods, that the traveling wave solution also exists for MHD Taylor-Couette flow at finite aspect ratio H/D, H being height of the cylinders, D width of the gap between them. The nonlinear simulations provide amplitudes of fluid velocity which are helpful in designing an experiment. Although the plates disturb the flow, parameters like the drift velocity indicate that the helical MRI operates in this case. The idea of the helical MRI was implemented in a very recent experiment PROMISE. The results provided, for the first time, an evidence that the (helical) MRI indeed exists. Nevertheless, the influence of the vertical endplates was evident and the experiment can be, in principle, improved. Exemplary methods of reduction of the end-effect are here proposed. Near the vertical boundaries develops an Ekman-Hartmann layer. Study of this layer for the MHD Taylor-Couette system as well as its impact on the global flow properties is presented. It is shown that the plates, especially if they are conducting, can disturb the flow far more then previously thought also for relatively slow rotation rates. N2 - Die magnetische Scherinstabilitaet (engl. MRI) ist eine sehr häufig in der Astrophysik anzutreffende Instabilität. Es wird heute weithin angenommen, dass sie die Ursache für die turbulente Viskosität in Akkretionsscheiben ist, den Objekten mit der höchsten Energieeffizienz im Kosmos. Die Bedeutung der MRI ist erst in den letzten fünfzehn Jahren klargeworden. Entdeckt wurde sie jedoch schon viel früher, im Jahre 1959 in einem völlig anderen physikalischen Kontext. Die Strömung in einer leitfähigen Flüssigkeit zwischen differentiell rotierenden Zylindern unter dem Einfluss eines externen Magnetfeldes wurde theoretisch untersucht. Die Schlussfolgerung war, dass das zugesetzte Magnetfeld eine sonst stabile Strömung destabilisieren kann. Die Geschichte der Theorie von Strömungen zwischen Zylindern reicht bis ins Jahr 1888 zurück. Heute wird ein solcher Aufbau üblicherweise als Taylor-Couette-Strömung bezeichnet. Ein System rotierender Zylinder, zwischen denen sich flüssiges Metall befindet, war Gegenstand des kürzlich durchgeführten Experiments PROMISE. Die Ergebnisse belegen zum ersten Mal experimentell die Existenz der MRI. Um die notwendigen Drehzahlen gering zu halten, wurde ein spezielles, helikales Magnetfeld angelegt. Gegenstand dieser Dissertation ist die theoretische Behandlung der magnetohydrodynamischen Taylor-Couette-Strömung, ähnlich der des Experiments PROMISE. Insbesondere der Einfluss der vertikalen Ränder (Deckel) wird untersucht. Es wird gezeigt, dass die MRI auch in Zylindern mit endlicher Höhe und mit begrenzenden Deckeln einsetzt. In der Nähe der vertikalen Ränder bildet sich eine Ekman-Hartmann-Schicht. Die Untersuchung dieser Schicht im Zusammenhang mit dem MHD-Taylor-Couette-System sowie ihr Einfluss auf die globalen Strömungseigenschaften werden vorgestellt. Es wird gezeigt, dass die Deckel - insbesondere wenn sie elektrisch leitend sind - die Strömung stärker beeinflussen können als bisher angenommen, selbst bei den geringen Drehzahlen. Es werden Methoden zur Verringerung dieser unerwünschten Effekte vorgeschlagen. KW - MHD KW - Simulationen KW - Taylor-Couette KW - Akkretion KW - MHD KW - Simulations KW - Taylor-Couette KW - Accretion Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-16002 ER -