scholarly journals Effects of boundary conditions on the propagation and interaction of finite amplitude sound beams

1989 ◽  
Vol 86 (S1) ◽  
pp. S106-S106
Author(s):  
Jacqueline Naze Tjøtta ◽  
James A. TenCate ◽  
Sigve Tjøtta
Keyword(s):  
Boundary Conditions ◽  
Finite Amplitude ◽  
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 numerical stability analysis of double-diffusive convection in confined enclosures

2001 ◽  
Vol 433 ◽  
pp. 209-250 ◽  
Author(s):  
M. MAMOU ◽  
P. VASSEUR ◽  
M. HASNAOUI
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Travelling Waves ◽  
Neumann Boundary ◽  
Finite Amplitude ◽  
Parallel Flow ◽  
Neumann Boundary Conditions ◽  
Thermosolutal Convection ◽  
Quiescent State

The onset of thermosolutal convection and finite-amplitude flows, due to vertical gradients of heat and solute, in a horizontal rectangular enclosure are investigated analytically and numerically. Dirichlet or Neumann boundary conditions for temperature and solute concentration are applied to the two horizontal walls of the enclosure, while the two vertical ones are assumed impermeable and insulated. The cases of stress-free and non-slip horizontal boundaries are considered. The governing equations are solved numerically using a finite element method. To study the linear stability of the quiescent state and of the fully developed flows, a reliable numerical technique is implemented on the basis of Galerkin and finite element methods. The thresholds for finite-amplitude, oscillatory and monotonic convection instabilities are determined explicitly in terms of the governing parameters. In the diffusive mode (solute is stabilizing) it is demonstrated that overstability and subcritical convection may set in at a Rayleigh number well below the threshold of monotonic instability, when the thermal to solutal diffusivity ratio is greater than unity. In an infinite layer with rigid boundaries, the wavelength at the onset of overstability was found to be a function of the governing parameters. Analytical solutions, for finite-amplitude convection, are derived on the basis of a weak nonlinear perturbation theory for general cases and on the basis of the parallel flow approximation for a shallow enclosure subject to Neumann boundary conditions. The stability of the parallel flow solution is studied and the threshold for Hopf bifurcation is determined. For a relatively large aspect ratio enclosure, the numerical solution indicates horizontally travelling waves developing near the threshold of the oscillatory convection. Multiple confined steady and unsteady states are found to coexist. Finally, note that all the numerical solutions presented in this paper were found to be stable.

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

scholarly journals Nonlinear Thermal Convection in a Layer with Imposed Energy Flux

1974 ◽  
Vol 27 (4) ◽  
pp. 481 ◽  
Author(s):  
R Van der Borght
Keyword(s):  
Boundary Conditions ◽  
Energy Flux ◽  
Thermal Convection ◽  
Average Energy ◽  
Finite Amplitude ◽  
Solar Granulation ◽  
Convective Motions ◽  
Rayleigh Numbers

Results are reported of an investigation into the effect of the chosen boundary conditions on the steady finite-amplitude convective motions in a layer in which the average energy flux is imposed. The boundary conditions are chosen with a view to the application of the results to solar granulation and supergranulation. It is shown that, at high Rayleigh numbers, solutions do in fact exist for which there is no modulation in the energy flux and little fluctuation in the temperature across the boundaries.

Nonlinear Finite-Amplitude Dynamics

2013 ◽  
Author(s):  
Gary A. Glatzmaier
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Linear Model ◽  
Finite Amplitude ◽  
Numerical Code ◽  
Spectral Space ◽  
Simple Geometry ◽  
Nonlinear Simulations ◽  
The Galerkin Method

This chapter modifies the numerical code by adding the nonlinear terms to produce finite-amplitude simulations. The nonlinear terms are calculated using a Galerkin method in spectral space. After explaining the modifications to the linear model, the chapter shows how to add the nonlinear terms to the code. It also discusses the Galerkin method, the strategy of computing the contribution to the nonlinear terms for each mode due to the binary interactions of many other modes. The Galerkin method works fine as far as calculating the nonlinear terms is concerned because of the simple geometry and convenient boundary conditions. The chapter concludes by showing how to construct a nonlinear code and performing nonlinear simulations.

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