Radiation from vortex filament motion near a half plane

1972 ◽  
Vol 51 (2) ◽  
pp. 357-362 ◽  
Author(s):  
D. G. Crighton
Keyword(s):  
Mach Number ◽  
Singular Perturbation ◽  
Half Plane ◽  
Perturbation Methods ◽  
Sound Field ◽  
Vortical Flow ◽  
Two Dimensional ◽  
Low Mach Number ◽  
Radiated Energy ◽  
Singular Perturbation Methods

The two-dimensional low Mach number sound field from the passage of a line vortex around the edge of a rigid half plane is calculated by singular perturbation methods. Simple exact expressions are given for the space-time variation of the acoustic field, and for the total radiated energy and its frequency spectrum. These expressions show in particular that the effect of the half plane is to increase the energy radiated by a nearby vortical flow by M−3, where M is a characteristic Mach number.

Inverse cascades in two‐dimensional compressible turbulence. I. Incompressible forcing at low Mach number

1990 ◽  
Vol 2 (8) ◽  
pp. 1481-1486 ◽  
Author(s):  
J. P. Dahlburg ◽  
R. B. Dahlburg ◽  
J. H. Gardner ◽  
J. M. Picone
Keyword(s):  
Mach Number ◽  
Compressible Turbulence ◽  
Two Dimensional ◽  
Low Mach Number

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.

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