مرکز منطقه ای اطلاع رساني علوم و فناوري - A new approach to the problem of wave fluctuations in localized smoothly varying turbulence

Abstract :

In the past, smoothly varying turbulence has been studied by changing the structure constant to the function $C_{n}^{2}(\\bar{r}$ ). The purpose of this paper is to show that this approach is insufficient, and that a random process developed by Silverman can be used to describe the wave fluctuations in localized smoothly varying turbulence. The localized turbulence is characterized by a correlation function which is a product of a function of the average coordinate and a function of the difference coordinate. The corresponding spectrum is also given by a product of a function of the difference wavenumber and a function of the average wavenumber. They are related to each other through two Fourier transform pairs. Making use of the preceding representations, the fluctuations of a wave propagating through such a turbulence can be given either by the integrals with respect to the two wavenumbers or by a convolution integral of the structure constant $C_{n}^{2}(\\bar{r}$ ) and a function involving the outer scale of the turbulence $L_{0}$ . It is shown that for a plane wave case, if the distance $L$ is within ( $L_{0}^{2}/\\lambda$ ), then the usual formula given by Tatarski is valid. But if the distance is between $L_{0}^{2}/\\lambda$ and $(bL_{0})/\\lambda$ where $b$ is the total transverse size of the turbulence, the variance of the wave is nearly constant, and if $L \\gg (bL_{0})/\\lambda$ , the variance decays as $L^{-2}$ . Similar conclusions are shown for a spherical wave case. Some examples are shown illustrating the effectiveness of this method.