Abstract

For almost four decades, Hill’s “Model 4” [J. Fluid Mech. 88, 541 (1978) [CrossRef]  ] has played a central role in research and technology of optical turbulence. Based on Batchelor’s generalized Obukhov–Corrsin theory of scalar turbulence, Hill’s model predicts the dimensionless function h(κl0,Pr) that appears in Tatarskii’s well-known equation for the 3D refractive-index spectrum in the case of homogeneous and isotropic turbulence, Φn(κ)=0.033Cn2κ11/3h(κl0,Pr). Here we investigate Hill’s model by comparing numerical solutions of Hill’s differential equation with scalar spectra estimated from direct numerical simulation (DNS) output data. Our DNS solves the Navier–Stokes equation for the 3D velocity field and the transport equation for the scalar field on a numerical grid containing 40963 grid points. Two independent DNS runs are analyzed: one with the Prandtl number Pr=0.7 and a second run with Pr=1.0. We find very good agreement between h(κl0,Pr) estimated from the DNS output data and h(κl0,Pr) predicted by the Hill model. We find that the height of the Hill bump is 1.79Pr1/3, implying that there is no bump if Pr<0.17. Both the DNS and the Hill model predict that the viscous-diffusive “tail” of h(κl0,Pr) is exponential, not Gaussian.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Temperature variance dissipation equation and its relevance for optical turbulence modeling

Andreas Muschinski
J. Opt. Soc. Am. A 32(11) 2195-2200 (2015)

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

Jin-Ren Yao, Hua-Jun Zhang, Ruo-Nan Wang, Jian-Dong Cai, Yu Zhang, and Olga Korotkova
Opt. Express 27(20) 27807-27819 (2019)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (9)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (25)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription