Spherical One-Way Wave Equation

Acoustics

Oskar Bschorr¹  Hans-Joachim Raida² 

[1] Aeroakustik Stuttgart, D-81679 Munich, Germany;Independent Researcher, D-42799 Leichlingen, Germany;

关键词: one-way wave equation;    two-way wave equation;    spherical coordinates;    spherical wave propagation;    monopole;    point source;   

DOI  :  10.3390/acoustics3020021

来源: DOAJ

【 摘 要 】

The coordinate-free one-way wave equation is transferred in spherical coordinates. Therefore it is necessary to achieve consistency between $gradient$, $divergence$ and $Laplace$ operators and to establish, beside the conventional radial Nabla operator $\partial \Phi /\partial r$, a new variant $\partial r\Phi /r\partial r$. The two Nabla operator variants differ in the near field term $\Phi /r$ whereas in the far field $r\gg 0$ there is asymptotic approximation. Surprisingly, the more complicated gradient $\partial r\Phi /r\partial r$ results in unexpected simplifications for – and only for – spherical waves with the $1/r$ amplitude decrease. Thus the calculation always remains elementary without the wattless imaginary near fields, and the spherical Bessel functions are obsolete.

【 授权许可】

Unknown