Simple waves for two-dimensional compressible pseudo-steady Euler system

2010 ◽  
Vol 31 (7) ◽  
pp. 827-838 ◽  
Author(s):  
Geng Lai ◽  
Wan-cheng Sheng
Keyword(s):  
Euler System ◽  
Two Dimensional ◽  
Simple Waves

Incompressible limit for the two-dimensional isentropic Euler system with critical initial data

2014 ◽  
Vol 144 (6) ◽  
pp. 1127-1154 ◽  
Author(s):  
Taoufik Hmidi ◽  
Samira Sulaiman
Keyword(s):  
Mach Number ◽  
Initial Data ◽  
Euler System ◽  
Incompressible Limit ◽  
Two Dimensional ◽  
Low Mach Number ◽  
Low Mach Number Limit ◽  
Critical Besov Space ◽  
Convergence Results ◽  
Incompressible Euler

We study the low-Mach-number limit for the two-dimensional isentropic Euler system with ill-prepared initial data belonging to the critical Besov space . By combining Strichartz estimates with the special structure of the vorticity, we prove that the lifespan of the solutions goes to infinity as the Mach number goes to zero. We also prove strong convergence results of the incompressible parts to the solution of the incompressible Euler system.

Instability of Shielded Surface Temperature Vortices

2011 ◽  
Vol 68 (5) ◽  
pp. 964-971 ◽  
Author(s):  
Benjamin J. Harvey ◽  
Maarten H. P. Ambaum ◽  
Xavier J. Carton
Keyword(s):  
Surface Temperature ◽  
Smooth Surface ◽  
Numerical Study ◽  
Normal Modes ◽  
Euler System ◽  
The Other ◽  
Two Dimensional ◽  
Dynamics Model ◽  
Contour Dynamics ◽  
The Stability

Abstract The stability characteristics of the surface quasigeostrophic shielded Rankine vortex are found using a linearized contour dynamics model. Both the normal modes and nonmodal evolution of the system are analyzed and the results are compared with two previous studies. One is a numerical study of the instability of smooth surface quasigeostrophic vortices with which qualitative similarities are found and the other is a corresponding study for the two-dimensional Euler system with which several notable differences are highlighted.

scholarly journals On two-dimensional Riemann problem for pressure-gradient equations of the Euler system

1998 ◽  
Vol 4 (4) ◽  
pp. 609-634 ◽  
Author(s):  
Peng Zhang ◽  
◽  
Jiequan Li ◽  
Tong Zhang ◽  
◽  
...  
Keyword(s):  
Pressure Gradient ◽  
Riemann Problem ◽  
Euler System ◽  
Two Dimensional ◽  
Pressure Gradient Equations

Supersonic Flow Past a Wedge with a Flame at its Apex

1968 ◽  
Vol 19 (1) ◽  
pp. 80-90 ◽  
Author(s):  
R. Foster ◽  
J. F. Clarke
Keyword(s):  
Supersonic Flow ◽  
Flame Front ◽  
Flow Patterns ◽  
Chemical Energy ◽  
Two Dimensional ◽  
Pressure Flow ◽  
Simple Waves ◽  
Flow Past ◽  
Flow Deflection ◽  
Plane Flame

SummaryThe wholly supersonic flow past a two-dimensional wedge is analysed on the assumption that release of chemical energy into the stream can be accomplished across a thin discontinuous plane flame front attached to the apex. Forces experienced by the wedge are calculated and representative flow patterns exhibited. Some typical interactions between the flame and shocks or centred simple waves are discussed, with emphasis on the use of pressure-flow-deflection diagrams to obtain results.

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