Modeling of finite-amplitude sound beams: second order fields generated by a parametric loudspeaker

2005 ◽  
Vol 52 (4) ◽  
pp. 610-618 ◽  
Author(s):  
Jun Yang ◽  
Kan Sha ◽  
Woon-Seng Gan ◽  
Jing Tian
Keyword(s):  
Finite Amplitude ◽  
Second Order ◽  
Sound Beams

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.

Propagation and interaction of two collinear finite amplitude sound beams

1987 ◽  
Vol 82 (S1) ◽  
pp. S12-S12
Author(s):  
Jacqueline Naze Tjøtta ◽  
Sigve Tjøtta ◽  
Erlend H. Vefring
Keyword(s):  
Finite Amplitude ◽  
Sound Beams

On the reflection of a train of finite-amplitude internal waves from a uniform slope

1987 ◽  
Vol 178 ◽  
pp. 279-302 ◽  
Author(s):  
S. A. Thorpe ◽  
S. A. Thorpe ◽  
A. P. Haines
Keyword(s):  
Internal Waves ◽  
Incident Wave ◽  
Finite Amplitude ◽  
Second Order ◽  
Buoyancy Frequency ◽  
Inviscid Fluid ◽  
Strong Nonlinearity ◽  
Third Order ◽  
Direction Parallel ◽  
Reflected Wave

The reflection of a train of two-dimensional finite-amplitude internal waves propagating at an angle β to the horizontal in an inviscid fluid of constant buoyancy frequency and incident on a uniform slope of inclination α is examined, specifically when β > α. Expressions for the stream function and density perturbation are derived to third order by a standard iterative process. Exact solutions of the equations of motion are chosen for the incident and reflected first-order waves. Whilst these individually generate no harmonics, their interaction does force additional components. In addition to the singularity at α = β when the reflected wave propagates in a direction parallel to the slope, singularities occur for values of α and β at which the incident-wave and reflected-wave components are in resonance; strong nonlinearity is found at adjacent values of α and β. When the waves are travelling in a vertical plane normal to the slope, resonance is possible at second order only for α < 8.4° and β < 30°. At third order the incident wave is itself modified by interaction with reflected components. Third-order resonances are only possible for α < 11.8° and, at a given α, the width of the β-domain in which nonlinearities connected to these resonances is important is much less than at second order. The effect of nonlinearity is to reduce the steepness of the incident wave at which the vertical density gradient in the wave field first becomes zero, and to promote local regions of low static stability remote from the slope. The importance of nonlinearity in the boundary reflection of oceanic internal waves is discussed.In an Appendix some results of an experimental study of internal waves are described. The boundary layer on the slope is found to have a three-dimensional structure.

Analytical method for describing the paraxial region of finite amplitude sound beams

1994 ◽  
Vol 96 (5) ◽  
pp. 3321-3321 ◽  
Author(s):  
Mark F. Hamilton ◽  
Vera A. Khokhlova ◽  
Oleg V. Rudenko
Keyword(s):  
Analytical Method ◽  
Finite Amplitude ◽  
Sound Beams

scholarly journals Propagation of pulsed finite amplitude sound beams in a liquid with strong absorption.

1992 ◽  
Vol 91 (4) ◽  
pp. 2455-2455
Author(s):  
Michalakis A. Averkiou ◽  
Yang‐Sub Lee ◽  
Mark F. Hamilton
Keyword(s):  
Finite Amplitude ◽  
Strong Absorption ◽  
Sound Beams

NONLINEAR ENERGY TRANSFER IN ELASTIC WAVES

Geophysics ◽  
1968 ◽  
Vol 33 (5) ◽  
pp. 734-746 ◽  
Author(s):  
Geoffrey Holstrom
Keyword(s):  
Energy Transfer ◽  
High Frequency ◽  
Finite Amplitude ◽  
Second Order ◽  
Loss Mechanism ◽  
Low Frequencies ◽  
Nonlinear Energy Transfer ◽  
Apparent Loss ◽  
Apparent Attenuation ◽  
The One

If an elastic pulse of finite amplitude propagates through a solid, the energy originally associated with one frequency is partially transferred to other frequencies. This transfer can lead, for lossless compressive pulses, to the formation of a shock wave. Changes of entropy occur in steady shocks only in terms beginning with third order in the compression, and hence a perturbation treatment neglecting heat conduction is valid to second order. The one‐dimensional mass and momentum conversation equations are solved to second order, and the solutions are used to study energy transfer. Generally speaking, transfer occurs from lows to highs, leading to apparent attentuation of frequencies in the seismic range. A drop in energy of low frequencies might occur even if the only apparent loss mechanism is high frequency scattering. Formulas are developed giving the apparent attenuation over propagation distances or oscillation times small enough that perturbation treatment remains valid. It appears that this process could be important as a loss mechanism at low frequencies if initial pulses are sufficiently sharp, or if initial free oscillations have sufficiently large high‐frequency content.

Numerical modeling of finite-amplitude sound beams: Shock formation in the near field of a cw plane piston source

2001 ◽  
Vol 110 (1) ◽  
pp. 95-108 ◽  
Author(s):  
V. A. Khokhlova ◽  
R. Souchon ◽  
J. Tavakkoli ◽  
O. A. Sapozhnikov ◽  
D. Cathignol
Keyword(s):  
Numerical Modeling ◽  
Near Field ◽  
Finite Amplitude ◽  
Shock Formation ◽  
Sound Beams
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