Abstract
It is concluded that a two-variable expansion is sufficient for representing sound propagation through a continuous weakly inhomogeneous medium and that the Debye approximation is a proper two-variable expansion. Its application to the stochastic Helmholtz equation yields, to order ασκ(Rt)12/λg2k02, the eikonal equation and the transport equation; α is the rms refractive index variation, σκ is the Prandtl number, Rt is the turbulent Reynolds number, λg is the Taylor microscale, and k0 is the wavenumber. The resultant acoustic frequency limitations for the Stone and Mintzer experiment and for the turbulent upper ocean are developed and compared. The solution of the eikonal and transport equations in a continuous fluid renders a Lagrangian pressure relation. Finally, the Debye and Born approximations are compared for one-dimensional sound propagation.
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