Computation of small-scale velocity turbulence and its effect on optical scintillations and stimulated thermal Rayleigh scattering

J. A. Viecelli; D. H. Chambers; T. J. Karr

doi:10.1364/AO.31.002085

Applied Optics
Vol. 31,
Issue 12,
pp. 2085-2094
(1992)
•https://doi.org/10.1364/AO.31.002085

Computation of small-scale velocity turbulence and its effect on optical scintillations and stimulated thermal Rayleigh scattering

J. A. Viecelli, D. H. Chambers, and T. J. Karr

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J. A. Viecelli, D. H. Chambers, and T. J. Karr, "Computation of small-scale velocity turbulence and its effect on optical scintillations and stimulated thermal Rayleigh scattering," Appl. Opt. 31, 2085-2094 (1992)

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Abstract

Coherent high-power light beams propagating long distances through turbulent fluids are subject to many kinds of scattering effects; among these are small-scale thermal index instabilities, in which the fluid is heated by the small fraction of light that is absorbed, amplifying the pre-existing index fluctuations and producing small-angle stimulated thermal Rayleigh scattering. Turbulent velocity fluctuations can inhibit the rate of growth of these instabilities by dispersing the thermal perturbations created by the beam. Methods for computing the turbulent diffusion of the heating perturbations, compatible with fast-Fourier-transform beam propagation computations, are presented. Propagation calculations of scintillation coherence times and small-scale velocity turbulence thresholds for stimulated thermal Rayleigh scattering are included.

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Diffusivity (m²/s)	10⁻⁵	10⁻⁵	10⁻⁵	10⁻⁵	10⁻⁵	10⁻⁵	10⁻⁵
$K_{o}^{- 3 / 8} L_{K} (mm)$	1.4	18	0.45	9.0	4.8	0.9	2.3
Root mean square of mesh velocity fluctuations	8.0 cm/s	2.5 mm/s	35. cm/s	6.4 mm/s	1.5 cm/s	14 cm/s	4.1 cm/s
Mean velocity (segments)	0	0	0	0	0	0	0
Path length Z (km)	2	2	2	2	2	2	2
Mesh width W (cm)	44.72	44.72	44.72	44.72	44.72	44.72	44.72
Fresnel number	100	100	100	100	100	100	100
Scintillation t_c (s)	0.56	14	0.16	9.5	2.1	0.12	1.25
Coherence length/W	0.1	0.1	0.1	0.1	0.1	0.1	0.1
Path length divided by saturation length	0.69	0.69	0.69	0.69	0.69	0.69	0.69
Thermal spectrum decay constant(s)	12	58	2.5	34	40	46	16
Mesh	64² × 100	64² × 100	64² × 100	64² × 100	64² × 100	64² × 100	64² × 100
$\frac{Λ_{Nyquist}}{K_{o}^{- 3 / 8} L_{K}}$	10.3	0.77	30.9	1.54	2.9	15.5	6.2

Diffusivity (m²/s)	10⁻⁵	10⁻⁵	10⁻⁵
$K_{o}^{- 3 / 8} L_{K} (mm)$	0.9	0.9	4.5
Root mean square of mesh velocity fluctuations (cm/s)	14	14	1.6
Mean velocity (segments)	0	0	0
Path length Z (km)	2	2	2
Mesh width W (cm)	14.14	14.14	14.14
Fresnel number, W²/λZ	10	10	10
Scintillation t_c (s)	0.29	0.29	2.5
Coherence length/W	$1 / \sqrt{10}$	$1 / \sqrt{10}$	$1 / \sqrt{10}$
Path length divided by saturation length	0.69	0.69	0.69
τ (s)	0.117	0.058	0.5
Mesh	64² × 1000	64² × 1000	64² × 1000
$\frac{Λ_{Nyquist}}{K_{o}^{- 3 / 8} L_{K}}$	4.42	4.42	0.88

α	10⁻⁴m⁻¹
ρ	1.2 kg m⁻³
c	340 ms⁻¹
n_o − 1	3 × 10⁻⁴
γ	1.4
χ	10⁻⁵m²s⁻¹

L (mm)	τ (s)
10	2.6
5.0	1.0
2.5	0.41
1.0	0.12

Diffusivity (m²/s)	10⁻⁵	10⁻⁵	10⁻⁵	10⁻⁵	10⁻⁵	10⁻⁵	10⁻⁵
$K_{o}^{- 3 / 8} L_{K} (mm)$	1.4	18	0.45	9.0	4.8	0.9	2.3
Root mean square of mesh velocity fluctuations	8.0 cm/s	2.5 mm/s	35. cm/s	6.4 mm/s	1.5 cm/s	14 cm/s	4.1 cm/s
Mean velocity (segments)	0	0	0	0	0	0	0
Path length Z (km)	2	2	2	2	2	2	2
Mesh width W (cm)	44.72	44.72	44.72	44.72	44.72	44.72	44.72
Fresnel number	100	100	100	100	100	100	100
Scintillation t_c (s)	0.56	14	0.16	9.5	2.1	0.12	1.25
Coherence length/W	0.1	0.1	0.1	0.1	0.1	0.1	0.1
Path length divided by saturation length	0.69	0.69	0.69	0.69	0.69	0.69	0.69
Thermal spectrum decay constant(s)	12	58	2.5	34	40	46	16
Mesh	64² × 100	64² × 100	64² × 100	64² × 100	64² × 100	64² × 100	64² × 100
$\frac{Λ_{Nyquist}}{K_{o}^{- 3 / 8} L_{K}}$	10.3	0.77	30.9	1.54	2.9	15.5	6.2

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Applied Optics