Experimental investigation of finite amplitude distortion-based, second harmonic pulse echo ultrasonic imaging

1998 ◽  
Vol 45 (1) ◽  
pp. 158-162 ◽  
Author(s):  
T. Christopher
Keyword(s):  
Experimental Investigation ◽  
Second Harmonic ◽  
Ultrasonic Imaging ◽  
Finite Amplitude ◽  
Amplitude Distortion ◽  
Pulse Echo

On resonant over-reflexion of internal gravity waves from a Helmholtz velocity profile

1979 ◽  
Vol 90 (1) ◽  
pp. 161-178 ◽  
Author(s):  
R. H. J. Grimshaw
Keyword(s):  
Velocity Profile ◽  
Gravity Waves ◽  
Second Harmonic ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Weakly Nonlinear ◽  
Velocity Discontinuity ◽  
Interface Displacement ◽  
Boussinesq Fluid

A Helmholtz velocity profile with velocity discontinuity 2U is embedded in an infinite continuously stratified Boussinesq fluid with constant Brunt—Väisälä frequency N. Linear theory shows that this system can support resonant over-reflexion, i.e. the existence of neutral modes consisting of outgoing internal gravity waves, whenever the horizontal wavenumber is less than N/2½U. This paper examines the weakly nonlinear theory of these modes. An equation governing the evolution of the amplitude of the interface displacement is derived. The time scale for this evolution is α−2, where α is a measure of the magnitude of the interface displacement, which is excited by an incident wave of magnitude O(α3). It is shown that the mode which is symmetrical with respect to the interface (and has a horizontal phase speed equal to the mean of the basic velocity discontinuity) remains neutral, with a finite amplitude wave on the interface. However, the other modes, which are not symmetrical with respect to the interface, become unstable owing to the self-interaction of the primary mode with its second harmonic. The interface displacement develops a singularity in a finite time.

Ultrasonic Imaging Using the Instantaneous Frequency of Pulse-Echo Signals

1985 ◽  
pp. 487-496 ◽  
Author(s):  
D. A. Seggie ◽  
G. M. Doherty ◽  
S. Leeman ◽  
L. A. Ferrari
Keyword(s):  
Instantaneous Frequency ◽  
Ultrasonic Imaging ◽  
Pulse Echo
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