TY - GEN A1 - Borcia, Ion-Dan A1 - Borcia, Rodica A1 - Xu, Wenchao A1 - Bestehorn, Michael A1 - Richter, Sebastian A1 - Harlander, Uwe T1 - Undular bores in a large circular channel T2 - European Journal of Mechanics - B/Fluids N2 - An experimental device previously developed for studying rotating baroclinic flows has been used to investigate undular bores formation, propagation and collision. 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, very often used in numerical simulations. An excellent agreement between the experiment and simulation has been achieved. The spatio-temporal structure of bores is well reproduced for the first few reflections or collisions. KW - Undular bores KW - Bore collision KW - Periodical boundary conditions Y1 - 2020 UR - https://www.sciencedirect.com/science/article/pii/S0997754619300706?via%3Dihub U6 - https://doi.org/10.1016/j.euromechflu.2019.09.003 SN - 0997-7546 VL - 79 SP - 67 EP - 73 ER - TY - GEN A1 - Bestehorn, Michael T1 - Rayleigh–Taylor and Kelvin–Helmholtz instability studied in the frame of a dimension-reduced model T2 - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences N2 - Introducing an extension of a recently derived dimension-reduced model for an infinitely deep inviscid and irrotational layer, a two-layer system is examined in the present paper. A second thin viscous layer is added on top of the original one-layer system. The set-up is a combination of a long-wave approximation (upper layer) and a deep-water approximation (lower layer). Linear stability analysis shows the emergency of Rayleigh–Taylor and Kelvin–Helmholtz instabilities. Finally, numerical solutions of the model reveal spatial and temporal pattern formation in the weakly nonlinear regime of both instabilities. This article is part of the theme issue ‘Stokes at 200 (Part 1)’. KW - hydrodynamic waves KW - two-layer system KW - reduced models KW - numerical solutions Y1 - 2020 UR - https://royalsocietypublishing.org/doi/epdf/10.1098/rsta.2019.0508 U6 - https://doi.org/10.1098/rsta.2019.0508 SN - 1471-2962 SN - 1364-503X VL - 378 SP - 1 EP - 10 ER - TY - GEN A1 - Tyvand, Peder A. A1 - Bestehorn, Michael T1 - Nonlinear wave resonance from bottom vibrations in uniform open-channel flow T2 - European Journal of Mechanics. B, Fluids N2 - It is known from linear theory that bottom oscillations in uniform open-channel flow can produce resonant surface waves with zero group velocity and diverging amplitude (Tyvand and Torheim 2012). This resonance exists for Froude numbers smaller than one, at a critical frequency dependent on the Froude number. This resonance phenomenon is studied numerically in the time domain, with fully nonlinear free-surface conditions. An oscillatory 2D bottom source is started, and the local elevation at resonance grows until it may reach a saturation amplitude. Four waves exist at subcritical Froude numbers, where resonance represents the third and the fourth wave merging. In the zero-frequency limit, the dispersive second and fourth wave merge into a steady wave with finite group velocity and amplitude, and no other periodic waves exist. In the time-dependent nonlinear analysis at zero frequency, a transient undular bore may emerge as the dominating phenomenon. KW - Froude number KW - Open-channel flow KW - Oscillating source KW - Resonance KW - Undular bore KW - Water waves Y1 - 2020 UR - https://www.sciencedirect.com/science/article/pii/S0997754618307544 U6 - https://doi.org/10.1016/j.euromechflu.2019.07.004 SN - 1873-7390 SN - 0997-7546 VL - 79 SP - 74 EP - 86 ER -