Abstract
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.
Highlights
The stable temperature stratification and the stable salinity stratification in marine environment may be disturbed by the velocity field, which results in the inhomogeneous spatio-temporal distribution of temperature and salinity, and leads to the spatio-temporal fluctuations of refractive-index
The Oceanic Turbulence Optical Power Spectrum (OTOPS) being the Fourier transform of the spatial covariance function of the refractive index provides an essential tool for characterizing the spatial statistics of any order for stationary light fields propagating through the natural waters
The paper is organized as follows: using a non-Kolmogorov structure function, we derive the non-Kolmogorov temperature and salinity spectra based on the Hill’s model 4 (H4)-based model (Section 2.1); using the Upper-Bound limitation, we develop a temperature-salinity co-spectrum (Section 2.2); on combining the results for the temperature spectrum, the salinity spectrum and the co-spectrum, we introduce a non-Kolmogorov OTOPS (NK-OTOPS) model (Section 3); we apply the NK-OTOPS model for the analysis of the spherical wave propagation (Section 4); and we summarize the obtained results (Section 5)
Summary
The stable temperature stratification and the stable salinity stratification in marine environment may be disturbed by the velocity field, which results in the inhomogeneous spatio-temporal distribution of temperature and salinity, and leads to the spatio-temporal fluctuations of refractive-index. On considering the results of these oceanic turbulence measurements and the practical need for light propagation predictions made in various oceanic turbulence regimes, we set the aim for this paper to develop an OTOPS that extends the model suggested in [21, 22] to non-Kolmogorov regime This requires (I) developing the non-Kolmogorov temperature/salinity spectrum which is applicable for the marine environment with the wide-ranged Prandtl/Schmidt numbers, and (II) deriving the temperature-salinity co-spectrum which can not be directly obtained by analogy with a single-scalar spectrum, since the power law exponents of the two advected scalars can be generally different. (14), (17) and (18) constitute the main results of this section They give the non-Kolmogorov spectrum of oceanic temperature/salinity turbulence, and the proposed spectrum agrees well with the widely accepted asymptotic structure function. We consider ci as a direct parameter, and set its range in Appendix I
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