@misc{BorciaRichterBorciaetal., author = {Borcia, Ion-Dan and Richter, Sebastian and Borcia, Rodica and Sch{\"o}n, Franz-Theo and Harlander, Uwe and Bestehorn, Michael}, title = {Wave propagation in a circular channel: sloshing and resonance}, series = {The European Physical Journal Special Topics}, volume = {Vol. 232}, journal = {The European Physical Journal Special Topics}, number = {4}, issn = {1951-6401}, doi = {10.1140/epjs/s11734-023-00790-z}, pages = {461 -- 468}, abstract = {Surface wave resonance of a liquid (water) layer confined in a circular channel is studied both experimentally and numerically. For the experiment, eight unevenly distributed ultrasonic distance sensors measure the local height of the wave surface. The resonance curves show maxima only for odd multiples of the fundamental resonance frequency . We explained this behavior using a simple intuitive "ping-pong" like model. Collision of wave fronts can be observed for higher frequencies. Also, the wave reflection on the walls can be treated as wave collision with itself. The non-linearity seems to be weak in our study so the delay in the wave propagation before and after the collision is small. Time-space plots show localized propagating waves with high amplitudes for frequencies near resonance. Between the peaks low amplitude and harmonic patterns are observed. However, for higher frequencies, the frequency band for localized waves becomes wider. In the Fourier space-time plane, this can be observed as a point for the harmonic patterns or a superposition of two lines: one line parallel to wave-vector k axis corresponding to the excitation frequency and a second line with inclination given by wave propagation velocity . For planned future work, this result will help us to reconstruct the whole water surface elevation using time-series from only a few measurement points}, language = {en} } @misc{SchoenBestehorn, author = {Sch{\"o}n, Franz-Theo and Bestehorn, Michael}, title = {Instabilities and pattern formation in viscoelastic fluids}, series = {The European Physical Journal Special Topics}, volume = {Vol. 232}, journal = {The European Physical Journal Special Topics}, number = {4}, issn = {1951-6401}, doi = {10.1140/epjs/s11734-023-00792-x}, pages = {375 -- 383}, language = {en} } @phdthesis{Schoen, author = {Sch{\"o}n, Franz-Theo}, title = {Transport and waves in parametrically excited fluid layers}, publisher = {Brandenburgische Technische Universit{\"a}t}, address = {Cottbus ; Senftenberg}, doi = {10.26127/BTUOpen-6995}, pages = {xvi, 133}, abstract = {The transport and waves in parametrically excited fluid layers play a significant role in an understanding of non-linear surface wave phenomena and tidal resonances. In this thesis, we study resonant waves occurring in a circular channel with various obstacles under external oscillatory excitation. Typically, such sloshing experiments are conducted in rectangular, straight channels. The external excitation is implemented using a rotating table on which the entire experiment, including measurement equipment, is mounted. The excitation is either sinusoidal or ratched motion. The obstacles include a fully blocking barrier and a symmetric or asymmetric hill. The channel circumference is 4.76 m, with water depths ranging from 2 cm to 6 cm. Wave displacements within the channel are measured using 17 ultrasonic sensors equidistantly distributed along half of the channel. Particle Image Velocimetry (PIV) is employed to measure the flow. We also consider a simplified numerical model capable of reproducing the experimental results. This model is based on a long-wave approximation and vertical integration using a profile function (K{\´a}rm{\´a}n-Pohlhausen approach). Additionally, we use a wave attractor model to quantitatively explain the development of resonances. These resonances are distributed in bands of the excitation frequency around the linear eigenfrequency. The experimental wave attractor and numerical results are consistent with each other. The waves observed within these resonant frequency bands appear as undular bores or solitary waves. In the fully blocking case, bands of constructive and destructive interference are observed, while in the presence of hills, all eigenfrequencies exhibit resonances of varying intensity. These non-linear wave phenomena are characterized by strong transport properties, which can be studied here due to the fact that the circular channel is not fully blocked. The ratched excitation generated asymmetric wave fields, which also induced asymmetric transport in the channel, leading to the emergence of a mean flow in the channel. A similar mean channel flow is observed for the asymmetric hill; however, wave-induced transport played a lesser role in this case. This is attributed to a large separation vortex on the steep side of the hill, which created a valve effect that rectified part of the oscillatory flow. These results are of interest not only for engineering applications but also for the understanding of tidal flows over seabed topography.}, language = {en} } @misc{SchoenHarlanderBorciaetal., author = {Sch{\"o}n, Franz-Theo and Harlander, Uwe and Borcia, Ion Dan and Borcia, Rodica and Bestehorn, Michael}, title = {Mean fluid transport in an oscillating circular channel with asymmetric forcing}, series = {Water waves : an interdisciplinary journal}, volume = {2025}, journal = {Water waves : an interdisciplinary journal}, publisher = {Birkh{\"a}user, part of Springer Nature}, address = {Basel}, issn = {2523-3688}, doi = {10.1007/s42286-025-00121-w}, pages = {1 -- 21}, abstract = {We investigate surface waves in an oscillating circular channel with local topography. The focus is on spatially or temporally breaking this dynamic system's symmetry. Asymmetrical wave dynamics and a mean flux excitation are detected to varying degrees, depending on the two input parameters, fluid depth and the tank's oscillation frequency. The fluid resonates around multiples of the fundamental eigenfrequency of the channel. The development of solitary wave-trains (undular bores) is observed in these resonance bands. A particle image velocimetry system measures the velocity field in the vertical plane of the free surface flow. Moreover, we are using 17 evenly distributed ultrasonic sensors to measure the surface displacement. This makes it possible to find out how strongly the mean flux depends on the resonance frequencies and to study the influence of the surface waves on the symmetry breaking. A numerical long-wave model helps to isolate the various factors influencing the mean flux.}, language = {en} }