ISSN 1063-7710, Acoustical Physics, 2010, Vol. 56, No. 2, pp. 158–167. © Pleiades Publishing, Ltd., 2010. Published in Russian in Akusticheskiі Zhurnal, 2010, Vol. 56, No. 2, pp. 179–189. 158 1. INTRODUCTION A model of an infinitely thin random phase screen has been widely used as a simplified approach to study various problems of linear and nonlinear wave propa- gation in random inhomogeneous media [1–5]. Con- trary to the continuous inhomogeneous medium the phase screen model incorporates only initial distortion of the phase front of the wave. However, this model includes basic effects of nonlinear propagation and random focusing that lead to distortion of statistical characteristics of the wave field in randomly inhomo- geneous medium. Propagation of high intensity noise through turbulent layers in the atmosphere is an exam- ple of where the phase screen model may be imple- mented. An ideal symmetrical N-wave is often used as an initial waveform of noise wave generated by the supersonic aircraft. Up to date, the statistical properties of nonlinear N-waves behind a random phase screen were studied in detail using nonlinear geometrical acoustics (NGA) approximation [1–3]. The geometry of the problem in case of a one-dimensional screen is illustrated in Fig. 1. Initially plane N-wave propagates along the coordi- nate x perpendicular to the screen located at x = 0 [1]. At each transverse coordinate y the phase screen intro- duces a random time delay that leads to the distortion of the wave front. In NGA approach the spatial fluctu- ations of the time delay define areas of converging and diverging rays, i.e. focusing and defocusing of the wave (Fig. 1). Ray convergence corresponds to focusing, i.e. to the increase of the wave amplitude, and ray diver- gence corresponds to defocusing, i.e. decrease of the wave amplitude. In NGA approximation the statistical properties of acoustic field behind the screen depend on the proba- bility distribution function of ray convergence after passing the screen and the initial wave amplitude that determines nonlinear propagation effects. Analytic solutions have been obtained for probability distribu- tions and mean values of the amplitude and duration of an N-wave after passing through one-dimensional phase screen having either broadband or narrowband Gaussian probability distribution of ray convergence [1]. The problem was farther extended and analytic Statistical Properties of Nonlinear Diffracting N-Wave behind a Random Phase Screen 1 P. V. Yuldashev a , N. A. Bryseva a , M. V. Averiyanov a , Ph. Blanc-Benon b , and V. A. Khokhlova a a Department of Acoustics, Faculty of Physics, Moscow State University, Moscow, 119991 Russia b LMFA, UMR CNRS 5509, Ecole Centrale de Lyon, 69134 Ecully Cedex, France e-mail: {petr,misha,vera}@acs366.phys.msu.ru, Philippe.Blanc-Benon@ec-lyon.fr Received April 14, 2009 Abstract—Propagation of high amplitude N-wave behind a random phase screen is modeled based on the Khokhlov-Zabolotskaya-Kuznetsov equation. One-dimensional random phase screens with Gaussian power spectrum density are considered. The effects of nonlinear propagation, random focusing, and diffraction on the statistical properties of the acoustic field behind the screen, including propagation through caustics and beyond caustics, are analyzed. Statistical distributions and mean values of the acoustic field parameters obtained within the developed diffraction model and using nonlinear geometrical acoustics approach are compared. DOI: 10.1134/S1063771010020065 NONLINEAR ACOUSTICS 1 The article was translated by the authors. y x p 0 x = x r x max = 3x r τ = t – x/c 0 focusing defocusing Fig. 1. Propagation of initially plane N-wave through infi- nitely thin phase screen (dashed line) located at x = 0. Arrows illustrate focusing and defocusing effects behind the screen. The refraction length is denoted as x r , maxi- mum propagation distance in numerical simulations is x max = 3x r .