Method of Stationary Phase for Double Integrals

2017 ◽  
pp. 136-162
Author(s):  
Jakob J Stamnes
Keyword(s):  
Stationary Phase ◽  
Method Of Stationary Phase ◽  
Double Integrals

Line-source diffraction by a slit in a moving fluid

2009 ◽  
Vol 87 (11) ◽  
pp. 1139-1149 ◽  
Author(s):  
M. Ayub ◽  
A. Naeem ◽  
R. Nawaz
Keyword(s):  
Mach Number ◽  
Analytical Solution ◽  
Acoustic Wave ◽  
Stationary Phase ◽  
Line Source ◽  
Velocity Potential ◽  
Integral Transform ◽  
Method Of Stationary Phase ◽  
Modified Method ◽  
Moving Fluid

The diffraction of a cylindrical acoustic wave from a slit in a moving fluid using Myers condition (J. Sound Vib. 71, 429 (1980)) is investigated, and an improved form of the analytical solution for the diffracted field is presented. The problem is solved analytically using an integral transform, Wiener–Hopf technique, and the modified method of stationary phase. The mathematical results are well supported by graphical discussion showing how the absorbing parameter and Mach number affect the amplitude of the velocity potential.

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