On nonstationary thermodynamics, relativistic acceleration waves in ideal fluids

2005 ◽  
pp. 185-201
Author(s):  
Aldo Bressan
Keyword(s):  
Ideal Fluids ◽  
Acceleration Waves

scholarly journals Hamiltonian Aspects of Three-Layer Stratified Fluids

2021 ◽  
Vol 31 (4) ◽  
Author(s):  
R. Camassa ◽  
G. Falqui ◽  
G. Ortenzi ◽  
M. Pedroni ◽  
T. T. Vu Ho
Keyword(s):  
Hamiltonian Structure ◽  
Linear Equations ◽  
Hamiltonian Formalism ◽  
Reduction Process ◽  
Ideal Fluids ◽  
Upper Lid ◽  
Stratification Structure ◽  
Special Solutions ◽  
Dispersionless Limit ◽  
Unbounded Fluid

AbstractThe theory of three-layer density-stratified ideal fluids is examined with a view toward its generalization to the n-layer case. The focus is on structural properties, especially for the case of a rigid upper lid constraint. We show that the long-wave dispersionless limit is a system of quasi-linear equations that do not admit Riemann invariants. We equip the layer-averaged one-dimensional model with a natural Hamiltonian structure, obtained with a suitable reduction process from the continuous density stratification structure of the full two-dimensional equations proposed by Benjamin. For a laterally unbounded fluid between horizontal rigid boundaries, the paradox about the non-conservation of horizontal total momentum is revisited, and it is shown that the pressure imbalances causing it can be intensified by three-layer setups with respect to their two-layer counterparts. The generator of the x-translational symmetry in the n-layer setup is also identified by the appropriate Hamiltonian formalism. The Boussinesq limit and a family of special solutions recently introduced by de Melo Viríssimo and Milewski are also discussed.

scholarly journals Euler equations for incompressible ideal fluids

2007 ◽  
Vol 62 (3) ◽  
pp. 409-451 ◽  
Author(s):  
Claude Bardos ◽  
Edriss Titi
Keyword(s):  
Euler Equations ◽  
Ideal Fluids

Shocks in Thermoelastic Rods

1999 ◽  
Author(s):  
Oliver M. O’Reilly ◽  
Peter C. Varadi
Keyword(s):  
Phase Transformations ◽  
Internal Constraints ◽  
Acceleration Waves ◽  
Axially Moving

Abstract A theory of a thermoelastic rod is presented in this paper. The theory is based on the work of Green and Naghdi, supplemented by singular supplies of momenta, energy and entropies at a discontinuity. In addition, several aspects of the theory in the presence of internal constraints are presented. The theory is suited to the study of numerous applications, including studies of phase transformations, propagation of shock and acceleration waves and axially moving rods.

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