Acoustic propagation in strong surface ocean ducts. Scattering from elastic shells that excite the lowest-order symmetric Lamb mode and amplitude-modulated signals

Abstract

The concept of group velocity is routinely used in terms of a mathematical construct but frequently confused with the actual physical process of energy transport. The origin comes either from using the stationary phase method in constructing the time domain from the frequency domain, from calculating sound signals at differing frequencies and identifying the arrivals with an envelop function, or by using wave-packet theory (usually in quantum mechanics) with something like Gaussian pulses centered about some carrier frequency. In many cases this definition of the derivative of angular frequency with respect to wave number is adequate and does characterize the arrival times of energy packets. There are cases for which such a definition is meaningless and occurs when the stationary phase method to first order breaks down. Usually when this happens the related pulse signal is amplitude modulated. Two examples are demonstrated. One has to do with wave propagation in which there is strong ducting at the ocean surface. The other occurs when scattering from an elastic shell, the first symmetric Lamb mode, is excited. In each case the results are atypical, surprising, and delightful. [Work sponsored by the Office of Naval Research and the Naval Research Laboratory.]