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Migration of the Gas Globe from Underwater Explosions: The Effects of Drag and Radiative Energy Loss,

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In this article the problem of the motion of the bubble from an underwater explosion is considered. Previous derivations of the equations of motion are summarized. It is shown how a Lagrangian method can be utilized to obtain the equations of motion, and how generalized dissipative forces can be formally incorporated. The generalized dissipative force for energy loss by radiation of sound is obtained from first principles, and found to be approximately proportional to the cube of the rate of change of the bubble radius with respect to time. The algorithm by which the equations of motion were solved numerically is briefly discussed, and some results of the computations presented. It is found that the approximate formula for energy loss by radiation of sound by a bubble in the absence of vertical motion derived by Herring gives results similar to those obtained using the more exact formulation developed in this work. It is also found that the rate of energy loss is affected slightly by processes analogous to radiation reaction in electromagnetic theory. Results are also presented for the cases for which energy is lost by drag as well as by radiation of sound, and for the case for which the effects of free and rigid surfaces on the bubble motion, but not energy loss, are considered. Author

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