摘要:

This paper describes the propagation of acoustical disturbances in materials where the sound speedc(x,t)varies in space and time. It is shown that there are forms ofc(x,t)for which the general solution to the one dimensional wave equation can be found in closed form. Thec(x,t)are characterized by the condition that the expansion schemes used in the theory of geometrical acoustics should terminate after a finite number of terms to yieldexactsolutions to the wave equation.

ISSN:0022-2526    

DOI:10.1002/sapm19877611

年代:1987

数据来源: WILEY

摘要:

A numerical method is developed to solve a class of nonlinear, nonlocal eigenvalue problems defined in an infinite strip, and is applied to compute solitary planetary waves in a sheared zonal current on the beta‐plane. This method, an iterative procedure derived from the natural variational structure of these problems, is implemented in the physical case when the ambient parallel flow has a linear or a quadratic velocity profile. The results of the numerical experiments establish rigorous limits on the range of validity of the formal asymptotic theory of weakly nonlinear long waves, and also reveal some new phenomena involving strongly nonlinear waves. The iterative procedure is analyzed in a general setting, and is shown to be globally convergent without restriction on the wave amplitud

ISSN:0022-2526    

DOI:10.1002/sapm198776137

年代:1987

数据来源: WILEY

摘要:

The instability properties of weakly nonlinear wave packets show a strong directional dependence. The presence of shear is found to enhance the importance of three dimensional effects.

ISSN:0022-2526    

DOI:10.1002/sapm198776169

年代:1987

数据来源: WILEY