Abstract
We will not analyze new phenomena in this chapter, nor will we develop new analytical techniques. Rather, our objective is to create the foundation for study of a variety of phenomena that do not fit the planar wave model. One possible difference is that the wavefront, which is the locus of points at which the acoustic disturbance was generated at a common time, is not planar.
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Any velocity field can be represented in terms of a scalar potential function \(\phi \) and a solenoidal vector field \(\bar{\chi }\) according to \(\bar{v}=\nabla \phi +\nabla \times \bar{\chi }\). The circulation is \(\nabla \times \bar{v}\equiv \nabla \times \left( \nabla \times \bar{\chi }\right) \). The implication of neglecting viscosity is that it is not possible to induce circulation. Hence, the velocity potential may be used to represent the velocity field of any inviscid fluid, even in an analysis that includes nonlinear effects.
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Ginsberg, J.H. (2018). Principles and Equations for Multidimensional Phenomena. In: Acoustics-A Textbook for Engineers and Physicists. Springer, Cham. https://doi.org/10.1007/978-3-319-56844-7_4
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DOI: https://doi.org/10.1007/978-3-319-56844-7_4
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