Revisiting and revising Tatarskii's formulation for the temperature structure parameter ($C_T^2$) in atmospheric flows

TL;DR

This paper revises Tatarskii's classical formulation of the temperature structure parameter ($C_T^2$) in atmospheric flows by introducing a physically-based outer length scale derived from turbulence variance, improving its applicability.

Contribution

The paper presents a new formulation of $C_T^2$ that addresses limitations of Tatarskii's original model using turbulence variance, flux equations, and a novel outer length scale.

Findings

Revised $C_T^2$ formulation improves accuracy in atmospheric turbulence modeling

Introduces a physically-based outer length scale estimable from routine data

Addresses limitations of previous $C_T^2$ models

Abstract

In this paper, we revisit a well-known formulation of temperature structure parameter ($C_T^2$), originally proposed by V.~I.~Tatarskii. We point out its limitations and propose a revised formulation based on turbulence variance and flux budget equations. Our formulation includes a novel physically-based outer length scale which can be estimated from routine meteorological data.