Effect of turbulence on propagation of a coherent beam in the boundary layer and mixing layer

Abstract

A semi-empirical model is developed to study distortions of the phase function of a coherent beam, which are induced by turbulent fluctuations of flow parameters. Large eddy simulations of the boundary-layer and mixing-layer flows and also of related aero-optical effects are performed. Results of numerical calculations are compared with results of physical experiments and with data obtained by solving the Reynolds-averaged Navier-Stokes equations.Introduction. Free shear flows are characterized by the presence of coherent structures, which are vortex configurations (vorticity blobs localized in space) developing and interacting with each other in the case of smallscale turbulence. The size of the coherent structures is commensurable with the width of the mixing layer, and they exist for a rather long time.Formation, interaction, and disintegration of coherent structures play an important role in propagation of a coherent beam through a liquid or gas flow.The transition of a coherent beam through a randomly inhomogeneous medium (e.g., a turbulent boundary layer or a mixing layer) is accompanied by the emergence of optical aberrations. Both the wave amplitude and phase experience fluctuations, which gives rise to noise caused by the change in the optical beam structure (expansion, fluctuations of the propagation direction, or splitting). Distortions of the amplitude characteristics of the beam are negligibly smaller than phase fluctuations [1, 2]. The wavelength is usually assumed to be much smaller than the minimum scale of turbulent vortices, and the approximation of geometric optics is used [3].Propagation of optical radiation in various media has been studied in many publications (see, e.g., [2,4]). The majority of results, however, were obtained for propagation of optical radiation in the atmosphere [1], where the greatest optical distortions are induced by vortex structures of the maximum scale (except for the boundary layer on the ground, where optical distortions are determined by vortices of the minimum scale). The influence of atmospheric effects is caused by comparatively low frequencies, and these effects can be easily identified with the use of modern experimental techniques; the effect of turbulent mixing on propagation of optical radiation is caused by high frequencies. As the spectrum of scales and frequencies of the turbulent flow changes within several orders of magnitude, direct measurements and numerical calculations are rather difficult [2,5].The influence of fluctuations of the refractive index on propagation of optical radiation depends on the ratio D/L (D is the beam diameter and L is the spatial period of changes in the refractive index). At D L, the gradient of the refractive index remains unchanged over the beam cross section, and the entire beam is deflected. At D ∼ L, the turbulence acts as a lens that reforms the wave. At D L, the turbulence makes different elements in the optical beam cross section deflect in different directions (i.e., beam scattering occurs).In contrast to flows for...

Aero-optical effects in free and wall-bounded turbulent compressible flows

“…Using the vortex model [8] and assuming that the beam passes through the vortex center, integrating from −∞ to +∞ gives the following relation The subscript 0 refers to parameters at the stagnation point. An uniform chain of vortices located on one line and moving with a constant velocity is considered.…”

“…The aero-optical interactions along the propagation path in turbulent compressible separated shear layers through experiments on direct imaging of the refractive index field are examined in [7]. To study the nature of optical aberrations, vortex models of the flow in the boundary layer and free mixing layer are considered, which are based on the exact solution of the plane Lamb vortex problem [8].…”