On the velocity of turbidity currents over moderate slopes

V. Yu Liapidevskii (1, 2) , Denys Dutykh (3, 4)

1 NSU - Novosibirsk State University
2 LIH - Lavrentyev Institute of Hydrodynamics
3 LAMA - Laboratoire de Mathématiques
4 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques

In 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. 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. As a second goal of our study, we would like also to underline the finite depth effect of the still water above the mixing layer on the wave front velocity. This investigation can be performed in the framework of a two-layer shallow water model taking into account the mass and momentum exchanges among different layers. 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.

Mots clés: turbidity currents; self-similar solutions; density flows; moderate slopes; head velocity

Domaines: Mécanique des fluides [physics.class-ph]; Dynamique des Fluides [physics.flu-dyn]; Formation de Structures et Solitons [nlin.PS]; Physique Numérique [physics.comp-ph]; Physique Classique [physics.class-ph]; Equations aux dérivées partielles [math.AP]; Systèmes dynamiques [math.DS]; Analyse classique [math.CA]; Physique Atmosphérique et Océanique [physics.ao-ph]

V. Yu Liapidevskii, Denys Dutykh. On the velocity of turbidity currents over moderate slopes. 2018. ⟨hal-01719313v1⟩