The inertial range “outer scale” and optical turbulence

Abstract

The crucial parameter used to calculate turbulence effects upon light waves propagating through the atmosphere is known as the structure constant, c 2 n . As Tatarski has shown, this parameter depends upon the "outer scale" of the inertial sub-range of the turbulence. Recently there have been successful predictions of astronomical "seeing" conditions at Mauna Kea Astronomical Observatory which have increased interest in this subject and in the use of the so-called "Dewan Optical Turbulence Model". In the case of the Air Force, there has been a longstanding need for such optical turbulence prediction, especially in the stratosphere. In the past researchers have used a relation due to Tatarski, (which plays a prominent role in this model) in order to deduce values of the "outer scale" from c 2 n measurements. When doing this, they have been surprised to find values very much smaller than expected. The goal of the paper is to explain this unexpected result. As we will show, this result can be explained by two factors: (a) the average turbulent layer thicknesses are smaller than originally believed, and, more importantly, (b) only a minor fraction of the stratosphere is turbulent. In order to arrive at this conclusion, we used the high-resolution (10 m) wind profiles that were originally used to formulate the previously mentioned optical turbulence model.

Comparison of Kolmogorov’s and coherent turbulence

“…In an extended consideration, a coherent structure is a soliton solution of the hydrodynamic equations [6]; it includes both large-scale and small-scale turbulence. As shown in our early optical measurements [7][8][9][10], optical manifestations of actions of extended regions are often observed in the atmosphere, where one coherent structure dominates. So, a question arises about the possible influence of only coherent turbulence on the jitter of optical images.…”

“…The Ferrel and Hadley cells are the largest among them (up to 5000 km in radius) [7][8][9][10]. They can be considered as modifications of Benard cells in a thin spherical layer (at the Earth scale).…”

Features of optical image jitter in a random medium with a finite outer scale

“…In this matter, we will first proceed from the fact that the temperature decreases linearly with altitude z in the atmosphere [9][10][11][12]:…”

“…There are many works where optical parameters are calculated using turbulence spectra of type (1), which considers the finiteness of outer scale of turbulence [5,8,9,11,12,[24][25][26][27][28]. The use of one or another model from Eq.…”

“…The model (A) was not studied in this paper because of its limited applicability. The models (D) and (E) are obtained by generalizing results of measurements performed in the U.S., France, and Chile [6,11,28,33]. The vertical profiles corresponding to these models are shown in Fig.…”