Journal of Engineering Mathematics

, Volume 69, Issue 2–3, pp 243–259 | Cite as

The uniform asymptotic form of the internal gravity-wave field generated by a source moving above a smoothly varying bottom



The uniform asymptotic form of the internal gravity-wave field generated by a source moving above a smoothly varying bottom is constructed. The problem of reconstructing non-harmonic internal gravity-wave packets generated by a source moving in a stratified ocean is considered. The solution is proposed in terms of wave modes, propagating independently at the adiabatic approximation, and described as a non-integral-degree series of a small parameter characterizing the stratified medium. A specific form of the wave packets, which can be parameterized in terms of model functions (Airy functions), depends on the local behavior of the dispersion curves of the individual wave mode. A modified space–time ray method was proposed, which belongs to the class of geometrical-optics methods. The key point of the proposed technique is the possibility to derive the asymptotic representation of the solution in terms of a non-integral-degree series of the some small parameter.


Caustic surface Eikonal equation Rays and wave fronts Stratified medium WKB approximation 


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Institute for Problems in MechanicsRussian Academy of SciencesMoscowRussia

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