# Wide-range Prandtl/Schmidt number power spectrum of optical turbulence and its application to oceanic light propagation

## TL;DR

This paper develops an accurate analytic model for the power spectrum of optical turbulence in oceans, accounting for a wide range of Prandtl and Schmidt numbers, improving predictions of light propagation in turbulent water.

## Contribution

It introduces a new analytic approximation to Hill's fourth model, enabling precise power spectrum calculations across broad Prandtl/Schmidt number ranges for oceanic turbulence.

## Key findings

- Enhanced accuracy in power spectrum modeling for oceanic turbulence.
- Demonstrated improved predictions of underwater light scintillation.
- Applicable to various turbulent fluids with different temperature and salinity conditions.

## Abstract

Light influenced by the turbulent ocean can be fully characterized with the help of the power spectrum of the water's refractive index fluctuations, resulting from the combined effect of two scalars, temperature and salinity concentration advected by the velocity field. The Nikishovs' model [ Fluid Mech. Res. 27, 8298 (2000)] frequently used in the analysis of light evolution through the turbulent ocean channels is the linear combination of the temperature spectrum, the salinity spectrum and their co-spectrum, each being described by an approximate expression developed by Hill [ J. Fluid Mech. 88, 541562 (1978)] in the first of his four suggested models. The fourth of the Hill's models provides much more precise power spectrum than the first one expressed via a non-linear differential equation that does not have a closed-form solution. We develop an accurate analytic approximation to the fourth Hill's model valid for Prandtl/Schmidt numbers in the interval [3, 3000] and use it for the development of a more precise oceanic power spectrum. To illustrate the advantage of our model, we include numerical examples relating to the spherical wave scintillation index evolving in the underwater turbulent channels with different average temperatures, and, hence, different Prandtl numbers for temperature and different Schmidt numbers for salinity. Since our model is valid for a large range of Prandtl number (or/and Schmidt number), it can be readily adjusted to oceanic waters with seasonal or extreme average temperature and/or salinity or any other turbulent fluid with one or several advected quantities.