Refine
Document Type
- Doctoral thesis (3)
Has Fulltext
- yes (3)
Is part of the Bibliography
- no (3)
Language
- English (3)
Keywords
- Musterbildung (3) (remove)
Stratified vortices can be found from small to large scales in geophysical and astrophysical flows. On the one hand, tornadoes and hurricanes can lead to devastation and even a large
number of casualties. On the other hand, vortices can distribute heat and momentum in the atmosphere which is important for a habitable environment on Earth. In the astrophysical context, accretion disks (from which solar systems are formed) can be seen as stratified vortices. In such systems, understanding the mechanisms that can result in an outward transport of angular momentum is a central problem. For a planet or star to be formed in a disk, angular momentum has to be carried away from its center to allow matter aggregation by gravity; otherwise, its rotation speed would be far too large, avoiding this matter aggregation (and the consequent star formation) to happen. In such gas systems, turbulence is the most likely mechanism to achieve such a large angular momentum transport. However, it was shown that the flow profile of accretion disks is stable with respect to purely shear instabilities, and the question arises about how the turbulence can be generated. Among other candidates, the strato-rotational instability (SRI) has attracted attention in recent years. The SRI is a purely hydrodynamic instability that can be modeled by a classical Taylor-Couette (TC) system with stable density stratification due to axial salinity or temperature gradients.
In this thesis, a combined experimental and high-performance computing study of new specific behaviors of the strato-Rotational Instability (SRI) is performed. The density stratification causes a change in the marginal instability transition when compared to classical non-stratified TC systems, making the flow unstable in regions where – without stratification – it would be stable. This characteristic makes the SRI a relevant phenomenon in planetary and astrophysical applications, particularly in accretion disk theory.
Despite many advances in the understanding of strato-rotational flows, the confrontation of experimental data with non-linear numerical simulations remains relevant, since it involves
linear aspects and non-linear interactions of SRI modes which still need to be better understood. These comparisons also reveal new non-linear phenomena and patterns not yet observed in the SRI, that can contribute to our understanding of geophysical flows.
We investigate the dynamics of a Newtonian liquid layer bounded on one side by a horizontal and planar substrate and on the other side by its free and deformable surface. The system is subjected to a time-periodic gravitation field in lateral or normal direction. Based on a nonlinear coordinate transformation, which maps the time-dependent surface onto a constant domain and thus eliminates the need for tracking the interface, a finite-difference method on staggered grids is presented, allowing direct numerical simulations of the full incompressible Navier-Stokes equations in two and three dimensions. Taking into account the continuity equation, a sparse linear system for the pressure is obtained from the discretized Navier-Stokes equations whose solution satisfies the conservation of momentum and mass, so that pressure corrections can be avoided. In the case of a harmonic force perpendicular to the substrate, we find in high frequency ranges the classical square patterns oscillating subharmonically with half of the driver’s frequency. For a slow excitation, hexagonal Faraday waves emerge oscillating at the forcing frequency. Vertical two-frequency excitations lead to more complex patterns — surface waves having the shape of a square superlattice are found. In the case of a lateral excitation, the formation of coarsening droplets is observed. We show that ratchet-like forces generate a nonvanishing averaged flow rate inducing a preferred direction of motion of the drops. These results correspond well with those of a simplified model based on the lubrication approximation. Our investigations also include systems in Rayleigh-Taylor configuration, where the liquid is located on the underside of the substrate. By considering rigid walls instead of periodic boundaries, wave amplification due to resonance can be studied. The corresponding numerical results are in good agreement with experimentally obtained data.
This work deals with static and dynamic properties of thin one- and two-layer liquid films. Regarding one-layer films, we study large scale surface deformations of a liquid film unstable due to the Marangoni effect caused by external heating on a smooth and solid substrate. To prevent rupture, a repelling disjoining pressure is included which accounts for the stabilization of a thin precursor film and so prevents the occurrence of completely dry regions. Linear stability analysis, nonlinear stationary solutions, as well as three-dimensional time dependent numerical solutions for horizontal and inclined substrates reveal a rich scenario of possible structures for several realistic liquid parameters. We also propose two methods to control the structuring of unstable thin films of soft matter. The first one is a non-contact method, where an external disturbance can be used to move a single drop, front or hole in a certain direction. The principle is illustrated by incorporating a sonic disturbance in a thin film equation to study the evolution of ultrathin films unstable due to their wetting properties. The second one is based on inhomogeneous templating of the substrate. Here we study the influence of periodic modulation on coarsening in the long time limit. Finally, the fully nonlinear evolution of a 3D system is presented by numerical integration. Further on, we consider a thin film consisting of two layers of immiscible liquids on a solid horizontal (heated) substrate. Both, the free liquid-liquid and the liquid-gas interface of such a bilayer liquid film may be unstable due to effective molecular interactions relevant for ultrathin layers below 100 nm thickness, or due to temperature-gradient caused Marangoni flows in the heated case. Using a long wave approximation we derive coupled evolution equations for the interface profiles for the general non-isothermal situation allowing for slip at the substrate. Linear and nonlinear analyses of the short- and long-time film evolution are performed for isothermal ultrathin layers taking into account destabilizing long-range and stabilizing short-range molecular interactions. It is shown that the initial instability can be of a varicose, zigzag or mixed type. However, in the nonlinear stage of the evolution the mode type and therefore the pattern morphology can change via switching between two different branches of stationary solutions or via coarsening along a single branch.