Refine
Document Type
- Doctoral thesis (1)
Has Fulltext
- yes (1)
Is part of the Bibliography
- no (1)
Year of publication
- 2021 (1)
Language
- English (1)
Keywords
- Nonlinear dynamics (1) (remove)
Institute
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.