European Journal of Mechanics / B Fluids 79 (2020) 67–73 Contents lists available at ScienceDirect European Journal of Mechanics / B Fluids journal homepage: www.elsevier.com/locate/ejmflu Undular bores in a large circular channel ✩ Ion Dan Borcia a,∗ , Rodica Borcia b , Wenchao Xu c , Michael Bestehorn b , Sebastian Richter b , Uwe Harlander c a Department of Computational Physics, Brandenburg University of Technology (BTU) Cottbus–Senftenberg, Erich–Weinert–Strasse 1, 03046 Cottbus, Germany b Department of Statistical Physics and Nonlinear Dynamics, Brandenburg University of Technology (BTU) Cottbus–Senftenberg, Erich–Weinert–Strasse 1, 03046 Cottbus, Germany c Department of Aerodynamics and Fluid Mechanics, Brandenburg University of Technology (BTU) Cottbus–Senftenberg, Siemens–Halske–Ring 14, 03046 Cottbus, Germany article info Article history: Received 31 January 2019 Received in revised form 9 July 2019 Accepted 3 September 2019 Available online 5 September 2019 Keywords: Undular bores Bore collision Periodical boundary conditions abstract 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. © 2019 Elsevier Masson SAS. All rights reserved. 1. Introduction Tidal bores are natural phenomena observed in at least 450 river estuaries all around the world from Europe (Baie du Mont Saint Michel — France) to America (Colorado River — Mexico) and Asia (Qiantang River — China) ([1] and references therein). Tidal bores manifest as series of waves propagating upstream in the estuarine zone of a river. They are formed during the flood tide, favorable conditions to observe them are in spring or in autumn. The wave height of a tidal bore can be of some tenth of centimeters but under some specific condition can reach 5 to 9 m. One of the most important tidal bore is Pororoca, at the entrance of the Amazon. The phenomenon that occurs between February and March causes waves up to 4 m high and travel more than 800 km inland upstream on the Amazon and adjacent rivers. As can be expected, bores with large amplitudes cause damages and also loss of human lives (like in 12 − 13 November 1970 on the southern coastal region of East Bengal and East Pakistan [2]). Tidal bores are usually smaller and less dangerous than Tsunamis, but they can have unpredictable development near the river bank. ✩ This document is the results of the research project funded by the German Research Foundation (DFG). ∗ Corresponding author. E-mail addresses: IonDan.Borcia@b-tu.de (I.D. Borcia), Rodica.Borcia@b-tu.de (R. Borcia), Wenchao.Xu@b-tu.de (W. Xu), Bestehorn@b-tu.de (M. Bestehorn), Sebastian.Richter@b-tu.de (S. Richter), Uwe.Harlander@b-tu.de (U. Harlander). Moreover, they occur twice a day and have a strong impact on sediment transfer and fishery in the river estuary. Undular bores occur in a long open channel when a constant mass flux is fed into the channel, while the water ahead of the bore is initially at rest (in this case we have a tidal bore). It manifests itself as a propagation of the change in water level [3–6]. The traveling train of the waves has a slow time depen- dence, a property that bores share with solitary waves [6]. Sozer and Greenberg, using a fully nonlinear dispersive free-surface flow method, are the first in modeling undular bores produced by sources or sinks [7]. Positive bores are induced by switching on sources and negative bores by switching on sinks. Another way to produce undular bores in the laboratory is to start from two level regions separated by an abrupt change in height (ideally step function). In practice, this can be realized by the sudden removal of a barrier, a method also used in Scott Russell’s experiments for the generation of solitary waves [8]. If the length of the two zones with different levels is large enough comparing to the bore wavelength, the structure of the generated bores will be similar with those produced by a constant pumping (the case of tidal bores). The difference is the following: in place of only one bore (positive for pumping or negative for sucking as showed in Fig. 1(a) [6]) one obtains a pair of bores, one positive and one negative, propagating in different directions, originated from the middle of the height difference (as one can see in Fig. 1(b)–1(f)). To better understand the bore structure, a simple model is presented in Fig. 2. If we assume that at the onset of the bore formation the surface is still flat outside the abrupt bore https://doi.org/10.1016/j.euromechflu.2019.09.003 0997-7546/© 2019 Elsevier Masson SAS. All rights reserved.