Nonlinear acoustic wave propagation in atmosphere

Abstract

Abstract. In this paper we consider a model problem that simulates an atmospheric acoustic wave propagation situation that is nonlinear. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well-posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.1. Introduction. In this paper we are interested in a two-dimensional model of acoustic wave propagation in the atmosphere. The propagation originates from a point source with a high intensity of sound. It is well known that acoustic wave propagation in the atmosphere is rather a complex phenomenon. It is influenced by atmospheric conditions such as pressure, density, temperature, and wind variations. To analyze the complete problem is a difficult task. However, numerical methods have proven capabilities of handling such problems, but it has not yet been carried out for this class of problems. During the 1960s approximate analytical methods have been attempted for simplified models of the atmosphere. Axisymmetric three-dimensional time-dependent models were

Linear and Nonlinear Acoustic Wave Propagation in the Atmosphere

“…, as well as in [4), is to solve for the next correction and add the correction to the solution of (P) to obtain the solution of the nonlinear problem. In this process, the equations governed by the next order terms contain exactly the same differential operator, except the right hand side contains the solution of problem (P).…”

“…Our model is an improvement over the model proposed in [1]. Our work appearing in [3] and [4] discuss analysis of the problem in two dimensions. Our work appearing in [5] discusses the first computational effort in the three-dimensional situation but only the linear case was discussed.…”

“…In the sequence of work reported in [3] and [4] the nonlinear problem was reduced to a sequence of linear problems using appropriate asymptotic expansions. Then one could show the linearized problems were well-posed.…”