Effect of non-uniformity of source vibration amplitude on the sound field wave number, attenuation coefficient and Reynolds stress for the acoustic streaming

The aim of this paper is to analytically solve the sound field generated by a standing wave induced in a vibrating beam. This case is different from a plane wave which is the traditional way of inducing acoustic streaming. The analytical solution shows that the amplitude non-uniformity can be represented by a non-uniformity coefficient gamma, which characterizes the ratio of the wave number or the attenuation coefficient to their values for the classical plane wave case. The non-uniformity coefficient gamma is also obtained by resolving the acoustic field utilizing full numerical solution. Numerical and analytical results are in a good agreement. The Reynolds stress generated by a beam vibrating at one of its modes is also calculated. The maximum values of the Reynolds stress are achieved at the anti-node coordinates and small negative minimum values of the Reynolds stress are observed at the node coordinates. An interesting four-vortex-per-wavelength structure is predicted for such sound field. (C) 2003 Elsevier Science Ltd.