Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchive

Chesnokov, A. A.

Gavrilyuk, S. L.

Liapidevskii, V. Yu

English

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Conference Paper, Published VersionGavrilyuk, S. L.; Liapidevskii, V. Yu; Chesnokov, A. A.Toward a Universal Model of Breaking Waves on ShallowWaterZur Verfügung gestellt in Kooperation mit/Provided in Cooperation with:Kuratorium für Forschung im Küsteningenieurwesen (KFKI)Verfügbar unter/Available at: https://hdl.handle.net/20.500.11970/108581Vorgeschlagene Zitierweise/Suggested citation:Gavrilyuk, S. L.; Liapidevskii, V. Yu; Chesnokov, A. A. (2016): Toward a Universal Model ofBreaking Waves on Shallow Water. In: Yu, Pao-Shan; Lo, Wie-Cheng (Hg.): ICHE 2016.Proceedings of the 12th International Conference on Hydroscience & Engineering,November 6-10, 2016, Tainan, Taiwan. Tainan: NCKU.Standardnutzungsbedingungen/Terms of Use:Die Dokumente in HENRY stehen unter der Creative Commons Lizenz CC BY 4.0, sofern keine abweichendenNutzungsbedingungen getroffen wurden. Damit ist sowohl die kommerzielle Nutzung als auch das Teilen, dieWeiterbearbeitung und Speicherung erlaubt. Das Verwenden und das Bearbeiten stehen unter der Bedingung derNamensnennung. Im Einzelfall kann eine restriktivere Lizenz gelten; dann gelten abweichend von den obigenNutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.Documents in HENRY are made available under the Creative Commons License CC BY 4.0, if no other license isapplicable. Under CC BY 4.0 commercial use and sharing, remixing, transforming, and building upon the materialof the work is permitted. In some cases a different, more restrictive license may apply; if applicable the terms ofthe restrictive license will be binding.Verwertungsrechte: Alle Rechte vorbehalten12th International Conference on Hydroscience & Engineering Hydro-Science & Engineering for Environmental Resilience November 6-10, 2016, Tainan, Taiwan.  Toward a Universal Model of Breaking Waves on Shallow Water S. L. Gavrilyuk1, V. Yu. Liapidevskii2, A. A. Chesnokov3 1. Aix-Marseille University Marseille, France 2. Lavrentyev Institute of Hydrodynamics 3. Novosibirsk State University Novosibirsk, Russia    ABSTRACT  If a wave approaching the coast is long and the variation of the coastal slope is gradual, spilling breakers usually appear. They are characterized by the appearance of a finite turbulent fluid zone riding down the forward slope of the wave (LonguetHiggins \& Turner, 1974, Duncan, 2001). At the toe of this turbulent zone  the wave slope changes sharply, resulting to the flow separation  and the vorticity creation. The breaking waves entrain the air the water by forming whitecaps' where an intensive dissipation occurs. Such a turbulent zone has a strong influence on the wave evolution.   As it was mentioned in Duncan (2011), theoretical models of spilling breakers are rare. Indeed, beyond the multiphase aspects, the modelling depends crucially on a precise description of the flow structure. In the case where the flow potentiality is supposed, one actually uses an interesting approach based on a coupling between the dispersive GreenNaghdi equations describing waves far from the coast, and the hyperbolic Saint-Venant equations near the coast (cf. Tissier {\it et al.} (2012)). The difficulty is to understand when we replace one model by another one. A search of such a `switching criteria' is not a well defined problem even if several empirical criteria were proposed in the literature (wave phase velocity  becomes larger than the flow velocity, or the wave slope attains a critical value, for example).   The main issue of our work is a two-layer modelling, where the upper turbulent layer is considered within the framework of shear shallow water flows (cf. Teshukov, 2007, Richard \& Gavrilyuk, 2012, 2013, Castro \& Lannes, 2014), while the lower layer is potential and can be described by a GreenNaghdi type model. The interaction between layers is taken account through a natural mixing process, where the mixing velocity is proportional to the intensity of large eddies of the upper layer. Experimental data on the structure of the turbulent flow field under breaking waves show that the frontiers between the turbulent region caused by the wave breaking and the potential region are clearly visible (Nadaoka {\it et al.} 1989, Lin \& Rockwell, 1994). This justifies a two-layer scheme for the modelling of the breaking waves. The model generalizes that derived in Liapidevskii \& Chesnokov (2014) where the hydrostatic approximation in both layers was used, and that in Richard \& Gavrilyuk (2015) where such a two-layer approach was used in the limit where the thickness of the upper shear layer was vanishing.   In particular, we show that our model is able to describe the transition from undular to breaking bores when the Froude number varies between $1.3$ and $1.4$. The shoaling and the breaking of solitary waves on mild slopes is also well predicted by the model.     

Toward a Universal Model of Breaking Waves on Shallow Water

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Toward a Universal Model of Breaking Waves on Shallow Water

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