AN ENERGY-CONSISTENT DEPTH-AVERAGED EULER SYSTEM: DERIVATION AND PROPERTIES

作者：Bristeau Marie Odile^*; Mangeney Anne; Sainte Marie Jacques; Seguin Nicolas

来源：Discrete and Continuous Dynamical Systems-Series B, 2015, 20(4): 961-988.

DOI：10.3934/dcdsb.2015.20.961

• Navier-Stokes equations
• Saint-Venant equations
• free surface flows
• non-hydrostatic model
• dispersive terms
• analytical solutions

In this paper, we present an original derivation process of a non-hydrostatic shallow water-type model which aims at approximating the incompressible Euler and Navier-Stokes systems with free surface. The closure relations are obtained by a minimal energy constraint instead of an asymptotic expansion. The model slightly differs from the well-known Green-Naghdi model and is confronted with stationary and analytical solutions of the Euler system corresponding to rotational flows. At the end of the paper, we give time-dependent analytical solutions for the Euler system that are also analytical solutions for the proposed model but that are not solutions of the Green-Naghdi model. We also give and compare analytical solutions of the two non-hydrostatic shallow water models.

• 出版日期2015-6