Yao Jin-Ren, Wang Han-Tao, Zhang Hua-Jun, Cai Jian-Dong, Ren Ming-Yuan, Zhang Yu, Korotkova Olga
Opt Express. 2021 Jan 18;29(2):1340-1359. doi: 10.1364/OE.409498.
Light propagation in turbulent media is conventionally studied with the help of the spatio-temporal power spectra of the refractive index fluctuations. In particular, for natural water turbulence several models for the spatial power spectra have been developed based on the classic, Kolmogorov postulates. However, as currently widely accepted, non-Kolmogorov turbulent regime is also common in the stratified flow fields, as suggested by recent developments in atmospheric optics. Until now all the models developed for the non-Kolmogorov optical turbulence were pertinent to atmospheric research and, hence, involved only one advected scalar, e.g., temperature. We generalize the oceanic spatial power spectrum, based on two advected scalars, temperature and salinity concentration, to the non-Kolmogorov turbulence regime, with the help of the so-called "Upper-Bound Limitation" and by adopting the concept of spectral correlation of two advected scalars. The proposed power spectrum can handle general non-Kolmogorov, anisotropic turbulence but reduces to Kolmogorov, isotropic case if the power law exponents of temperature and salinity are set to 11/3 and anisotropy coefficient is set to unity. To show the application of the new spectrum, we derive the expression for the second-order mutual coherence function of a spherical wave and examine its coherence radius (in both scalar and vector forms) to characterize the turbulent disturbance. Our numerical calculations show that the statistics of the spherical wave vary substantially with temperature and salinity non-Kolmogorov power law exponents and temperature-salinity spectral correlation coefficient. The introduced spectrum is envisioned to become of significance for theoretical analysis and experimental measurements of non-classic natural water double-diffusion turbulent regimes.
传统上，湍流介质中的光传播是借助折射率涨落的时空功率谱来研究的。特别是对于天然水体湍流，基于经典的柯尔莫哥洛夫假设已经开发了几种空间功率谱模型。然而，正如目前广泛接受的那样，非柯尔莫哥洛夫湍流状态在分层流场中也很常见，正如大气光学的最新进展所表明的那样。到目前为止，为非柯尔莫哥洛夫光学湍流开发的所有模型都与大气研究相关，因此只涉及一个平流标量，例如温度。我们借助所谓的“上限限制”并采用两个平流标量的谱相关概念，将基于温度和盐度浓度这两个平流标量的海洋空间功率谱推广到非柯尔莫哥洛夫湍流状态。所提出的功率谱可以处理一般的非柯尔莫哥洛夫各向异性湍流，但如果将温度和盐度的幂律指数设为11/3且各向异性系数设为1，则可简化为柯尔莫哥洛夫各向同性情况。为了展示新谱的应用，我们推导了球面波二阶互相关函数的表达式，并研究其相干半径（标量和矢量形式）以表征湍流扰动。我们的数值计算表明，球面波的统计特性随温度和盐度的非柯尔莫哥洛夫幂律指数以及温度 - 盐度谱相关系数有很大变化。所引入的谱预计对于非经典天然水体双扩散湍流状态的理论分析和实验测量具有重要意义。
