1998/04/01 by Sergey L. Gavrilyuk, S.L. Gavrilyuk, Henri Gouin +3 · 3 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #math-ph #math.MP #physics.flu-dyn
paper · pdf · doi:10.1023/a:1004354528016
published as Meccanica 33, 2 (1998) 161-175 · 14 pages
openalex publication_date 1998/04/01 · arxiv created 2008/02/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
One derives the governing equations and the Rankine - Hugoniot conditions for a mixture of two miscible fluids using an extended form of Hamilton's principle of least action. The Lagrangian is constructed as the difference between the kinetic energy and a potential depending on the relative velocity of components. To obtain the governing equations and the jump conditions one uses two reference frames related with the Lagrangian coordinates of each component. Under some hypotheses on flow properties one proves the hyperbolicity of the governing system for small relative velocity of phases.