Simple Demonstration of the Presence of Second Harmonic in Progressive Ultrasonic Waves of Finite Amplitude

1958 ◽  
Vol 30 (6) ◽  
pp. 582-583 ◽  
Author(s):  
K. L. Zankel ◽  
E. A. Hiedemann
Keyword(s):  
Second Harmonic ◽  
Finite Amplitude ◽  
Ultrasonic Waves ◽  
Simple Demonstration

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.

A more general model equation of nonlinear Rayleigh waves and their quasilinear solutions

2016 ◽  
Vol 30 (08) ◽  
pp. 1650096 ◽  
Author(s):  
Shuzeng Zhang ◽  
Xiongbing Li ◽  
Hyunjo Jeong
Keyword(s):  
Rayleigh Waves ◽  
General Equation ◽  
Wave Motion ◽  
Numerical Solutions ◽  
Second Harmonic ◽  
Approximate Equation ◽  
Finite Amplitude ◽  
Sound Beam ◽  
Quasilinear Theory ◽  
Sound Beams

A more general two-dimensional wave motion equation with consideration of attenuation and nonlinearity is proposed to describe propagating nonlinear Rayleigh waves of finite amplitude. Based on the quasilinear theory, the numerical solutions for the sound beams of fundamental and second harmonic waves are constructed with Green’s function method. Compared with solutions from the parabolic approximate equation, results from the general equation have more accuracy in both the near distance of the propagation direction and the far distance of the transverse direction, as quasiplane waves are used and non-paraxial Green’s functions are obtained. It is more effective to obtain the nonlinear Rayleigh sound beam distributions accurately with the proposed general equation and solutions. Brief consideration is given to the measurement of nonlinear parameter using nonlinear Rayleigh waves.

Dispersion of Finite Amplitude Ultrasonic Waves in InSb

1971 ◽  
Vol 42 (3) ◽  
pp. 1089-1091 ◽  
Author(s):  
J. G. Miller ◽  
D. I. Bolef
Keyword(s):  
Finite Amplitude ◽  
Ultrasonic Waves

Formation and recurrence of ion wave solitons

1975 ◽  
Vol 13 (2) ◽  
pp. 217-230 ◽  
Author(s):  
S. Watanabe
Keyword(s):  
Exact Solution ◽  
Numerical Analysis ◽  
Nonlinear Wave ◽  
Vries Equation ◽  
Dispersive Medium ◽  
Second Harmonic ◽  
Sine Wave ◽  
Finite Amplitude ◽  
Initial State ◽  
Coupled Mode

The interaction between an ion wave and its second harmonic is discussed theoretically, on the basis of coupled-mode equations derived from the Korteweg–de Vries equation. Using an exact solution of the coupled-mode equations, we give a numerical analysis of the properties of the solutions; and we show that superposition of two waves can describe the formation of two solitons, the interaction between them, and the recurrence of an initial state. Our theory can explain completely recent experimental results on ion wave solitons excited by a continuous sine wave.The propagation of a nonlinear wave in a dispersive medium has been extensively studied in the last decade. In a plasma, a finite-amplitude ion wave can form solitons in the course of its evolution, if wave damping is neglected.

FINITE‐AMPLITUDE ULTRASONIC WAVES IN ALUMINUM

1963 ◽  
Vol 3 (5) ◽  
pp. 77-78 ◽  
Author(s):  
M. A. Breazeale ◽  
D. O. Thompson
Keyword(s):  
Finite Amplitude ◽  
Ultrasonic Waves
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