Analysis of ray tube area in geometrical shock dynamics |
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Authors: | Gholam-Ali Zakeri |
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Institution: | Mathematics Department, California State University-Northridge, Northridge, CA 91330-8313, USA |
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Abstract: | We provide a rigorous analysis of structure of a ray tube in geometrical shock dynamics. Our aim is to shed more lights on the cross-sectional area function of a ray tube. We have shown that for a given ray tube and a given initial value of cross-sectional area, then its cross-sectional area can be determined uniquely everywhere. We give a definition of cross-sectional area of a ray tube in precise mathematical terms and from that we derive a set of relations, each describing the cross-sectional area for an arbitrary ray tube in geometrical shock dynamics. We have shown that from our results one can deduce Whitham’s area function relation as a partial differential equation from our general formulations. Some applications are discussed. |
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Keywords: | Lie derivative Pull-back Cross-sectional area function Ray tube Wavefront Geometrical shock dynamics |
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