Toward a Universal Model of Breaking Waves on Shallow Water

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

On the velocity of turbidity currents over moderate slopes

50 pages, 7 figures, 4 tables, 77 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/International audienceIn the present article we consider the problem of underwater avalanches propagating over moderate slopes. The main goal of our work is to investigate the avalanche front velocity selection mechanism when it propagates downwards. In particular, we show that the front velocity does not depend univocally on the mass of sediments. This phenomenon is investigated and explained in our study. Moreover, we derive from the first principles a depth-averaged model. Then, we assume that sediments are uniformly distributed along the slope. In this case, they can be entrained into the flow head and a self-sustained regime can be established. One of the main findings of our study is that the avalanche front velocity is not unique due to a hysteresis phenomenon. We attempt to explain this phenomenon using dynamical systems considerations

Spilling breakers in shallow water: appilications to Favre waves and to the shoaling and breaking of solitary waves

International audienceA two-layer long-wave approximation of the homogeneous Euler equations for a free-surface flow evolving over mild slopes is derived. The upper layer is turbulent and is described by depth-averaged equations for the layer thickness, average fluid velocity and fluid turbulent energy. The lower layer is almost potential and can be described by Serre-Su-Gardner-Green-Naghdi equations (a second-order shallow water approximation with respect to the parameter H / L, where H is a characteristic water depth and L is a characteristic wavelength). A simple model for vertical turbulent mixing is proposed governing the interaction between these layers. Stationary supercritical solutions to this model are first constructed, containing, in particular, a local turbulent subcritical zone at the forward slope of the wave. The non-stationary model was then numerically solved and compared with experimental data for the following two problems. The first one is the study of surface waves resulting from the interaction of a uniform free-surface flow with an immobile wall (the water hammer problem with a free surface). These waves are sometimes called `Favre waves' in homage to Henry Favre and his contribution to the study of this phenomenon. When the Froude number is between 1 and approximately 1.3, an undular bore appears. The characteristics of the leading wave in an undular bore are in good agreement with experimental data by Favre (Ondes de Translation dans les Canaux Decouverts, 1935, Dunod) and Treske (J. Hydraul Res., vol. 32 (3), 1994, pp. 355-370). When the Froude number is between 1.3 and 1.4, the transition from an undular bore to a breaking (monotone) bore occurs. The shoaling and breaking of a solitary wave propagating in a long channel (300 m) of mild slope (1/60) was then studied. Good agreement with experimental data by Hsiao et al. (Coast. Engng, vol. 55, 2008, pp. 975-988) for the wave profile evolution was found

Mathematical modeling of mixing and dispersion effects in the shallow waters of the coastal zone

SRef-ID: 1607-7962/gra/EGU2007-A-0169