Weakly nonlinear ray theory in inhomogeneous moving media filled with polytropic gases

The weakly nonlinear ray theory (WNLRT) has been developed for the study of propagation of wavefronts in homogeneous and quiescent media. The main advantage of this theory is that the study of 2D wavefront propagation can be carried over in a ray coordinate system, which is 1D (in the space variable). This makes the theory (along with the shock ray theory, SRT) more efficient than solving the full Euler system in 2D and is well suited for certain applications. However, the WNLRT and the SRT are developed only in a homogeneous and quiescent medium whereas it is important to update these theories to inhomogeneous and moving media. In this article, we derive the WNLRT system in an inhomogeneous and moving medium filled with polytropic gases. The governing system of this theory involves three balance laws in the ray coordinate system, which is strictly hyperbolic under the condition that the wavefront speed is greater than the ambient sound speed. In order to validate the developed theory, we solve the derived system numerically and show that the effect of medium anisotropy has been captured in terms of the geometry of a propagating wavefront. We also compare our numerical results with linear ray theory to highlight the success in capturing the nonlinear geometric effect of the propagating wavefront. (C) 2019 Elsevier B.V. All rights reserved.