@phdthesis{Xu2021, author = {Xu, Wenchao}, title = {Experiments on nonlinear waves in homogeneous flows with free upper surface and time-dependent forcing}, doi = {10.26127/BTUOpen-5386}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-53860}, school = {BTU Cottbus - Senftenberg}, year = {2021}, abstract = {The linear-theory assumption is a fundamental approach for the study of waves in fluids. The governing equations are linearized by assuming the perturbations are small so that the consequences of nonlinear terms are negligible. Nevertheless, if a wave approaches a critical level, in which the wave amplitude grows so as to create an instability of the background flow, the assumption of linearity may not hold any longer. In this case, the nonlinear terms are required to be taken into consideration. In this thesis, two experimental setups have been proposed for the study of two scenarios, in which the nonlinear effects become significant and a traditional linear solution is no longer valid. The first experiment focuses on an inertially oscillating rotating fluid. In the thesis, we present experimental results from a system that is simpler than classical precession experiments but still shows very similar wave interactions and a collapse to turbulence. This system consists of a partly filled rotating annulus that rotates about its symmetry axis slightly tilted with respect to the gravity vector. In the experiments, we find a resonant collapse when the forcing frequency corresponds with a resonant frequency of the rotating tank. Two types of instability can be triggered: a parametric triadic instability, in which two free Kelvin modes arise and form a triad with the forced Kelvin mode, and a shear-type instability related to the nonlinearly excited geostrophic flow. The latter instability gives rise to a barotropic mode that interacts with the forced mode and generates secondary modes. We also observed dependency of the mode frequencies on the Ekman number, which can, at least partly, be explained by a Doppler shift due to the mean flow. Finally, we try to connect our data to a low-order dynamical system based on the weakly nonlinear theory that describes the main features of single triad interaction in precession experiments. The second experiment concerns the study of undular bores (or tidal bores), in which the nonlinearity plays an important role. An experiment has been performed in which undular bores are produced in an open circular channel. More specifically, two different cases have been investigated: a single bore case with a rigid boundary setup and a bore colliding case with a periodic lateral boundary setup. Bores are generated by abruptly releasing a barrier that separates fluids with different surface levels. Up to our knowledge, this is the first experimental study of undular bores in a circular channel. For a setup without barriers, this geometry accomplishes in a natural way the periodic lateral boundary conditions, which is very often used in numerical simulations. The experimental results have been compared with the nonlinear numeric simulations and achieved an excellent agreement.}, subject = {Nonlinear waves; Flow instability; Rotating geophysical flows; Inertial waves; Weak turbulence; Tidal bore; Nichtlinearit{\"a}t; Rotierende Str{\"o}mung; Instabilit{\"a}t; Tr{\"a}gheitswellen; Gezeitenwellen; Flutwelle; Tr{\"a}gheitswelle; Instabile Str{\"o}mung; Rotationsstr{\"o}mung}, language = {en} }