  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.

Atmospheric and Oceanic Physics;Optics