# Transition between inverse and direct energy cascades in multiscale optical turbulence

## Abstract

Transition between inverse and direct energy cascades in multiscale optical turbulence. Multiscale turbulence naturally develops and plays an important role in many fluid, gas, and plasma phenomena. Statistical models of multiscale turbulence usually employ Kolmogorov hypotheses of spectral locality of interactions (meaning that interactions primarily occur between pulsations of comparable scales) and scale-invariance of turbulent pulsations. However, optical turbulence described by the nonlinear Schrodinger equation exhibits breaking of both the Kolmogorov locality and scale-invariance. A weaker form of spectral locality that holds for multi-scale optical turbulence enables a derivation of simplified evolution equations that reduce the problem to a single scale modeling. We present the derivation of these equations for Kerr media with random inhomogeneities. Then, we find the analytical solution that exhibits a transition between inverse and direct energy cascades in optical turbulence.

- Authors:

- Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences

- Publication Date:

- Research Org.:
- Princeton Univ., NJ (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA). Stewardship Science Academic Alliances Program

- OSTI Identifier:
- 1424396

- Alternate Identifier(s):
- OSTI ID: 1423918; OSTI ID: 1424389

- Grant/Contract Number:
- NA0002948

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review E

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 3; Journal ID: ISSN 2470-0045

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 79 ASTRONOMY AND ASTROPHYSICS; Turbulence; Richardson-Kolmogorov-Obukhov cascades; Bose-Einstein condensation; Optical turbulence; Weak turbulence; Nonlinear Schrodinger equation, Laser-plasma interactions; Powerful lasers; High-energy-density plasmas; Photonic crystals; Random lasers; Stochastic processes; Turbulence theory; Optical Turbulence; Weak Turbulence; Propagation of powerful laser pulses in Kerr media with random inhomogeneities; Nonlinear Schrodinger equation

### Citation Formats

```
Malkin, V. M., and Fisch, N. J. Transition between inverse and direct energy cascades in multiscale optical turbulence. United States: N. p., 2018.
Web. doi:10.1103/PhysRevE.97.032202.
```

```
Malkin, V. M., & Fisch, N. J. Transition between inverse and direct energy cascades in multiscale optical turbulence. United States. doi:10.1103/PhysRevE.97.032202.
```

```
Malkin, V. M., and Fisch, N. J. Tue .
"Transition between inverse and direct energy cascades in multiscale optical turbulence". United States. doi:10.1103/PhysRevE.97.032202. https://www.osti.gov/servlets/purl/1424396.
```

```
@article{osti_1424396,
```

title = {Transition between inverse and direct energy cascades in multiscale optical turbulence},

author = {Malkin, V. M. and Fisch, N. J.},

abstractNote = {Transition between inverse and direct energy cascades in multiscale optical turbulence. Multiscale turbulence naturally develops and plays an important role in many fluid, gas, and plasma phenomena. Statistical models of multiscale turbulence usually employ Kolmogorov hypotheses of spectral locality of interactions (meaning that interactions primarily occur between pulsations of comparable scales) and scale-invariance of turbulent pulsations. However, optical turbulence described by the nonlinear Schrodinger equation exhibits breaking of both the Kolmogorov locality and scale-invariance. A weaker form of spectral locality that holds for multi-scale optical turbulence enables a derivation of simplified evolution equations that reduce the problem to a single scale modeling. We present the derivation of these equations for Kerr media with random inhomogeneities. Then, we find the analytical solution that exhibits a transition between inverse and direct energy cascades in optical turbulence.},

doi = {10.1103/PhysRevE.97.032202},

journal = {Physical Review E},

number = 3,

volume = 97,

place = {United States},

year = {2018},

month = {3}

}

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#### Figures / Tables:

Works referenced in this record:

##
Self-focusing of short intense pulses in plasmas

journal, January 1987

- Sun, Guo-Zheng; Ott, Edward; Lee, Y. C.
- Physics of Fluids, Vol. 30, Issue 2

##
Transport and Anderson localization in disordered two-dimensional photonic lattices

journal, March 2007

- Schwartz, Tal; Bartal, Guy; Fishman, Shmuel
- Nature, Vol. 446, Issue 7131

##
Two-Dimensional Turbulence

journal, January 2012

- Boffetta, Guido; Ecke, Robert E.
- Annual Review of Fluid Mechanics, Vol. 44, Issue 1

##
Random Phasing of High-Power Lasers for Uniform Target Acceleration and Plasma-Instability Suppression

journal, September 1984

- Kato, Y.; Mima, K.; Miyanaga, N.
- Physical Review Letters, Vol. 53, Issue 11

##
On the analytical theory for stationary self-focusing of radiation

journal, April 1993

- Malkin, V. M.
- Physica D: Nonlinear Phenomena, Vol. 64, Issue 1-3

##
Statistical description of nonlinear wave fields

journal, October 1975

- Zakharov, V. E.; L'vov, V. S.
- Radiophysics and Quantum Electronics, Vol. 18, Issue 10

##
Kolmogorov and Nonstationary Spectra of Optical Turbulence

journal, June 1996

- Malkin, Vladimir M.
- Physical Review Letters, Vol. 76, Issue 24

##
Use of induced spatial incoherence for uniform illumination of laser fusion targets

journal, June 1983

- Lehmberg, R. H.; Obenschain, S. P.
- Optics Communications, Vol. 46, Issue 1

##
Inertial Ranges in Two-Dimensional Turbulence

journal, January 1967

- Kraichnan, Robert H.
- Physics of Fluids, Vol. 10, Issue 7

##
Wave kinetics of random fibre lasers

journal, February 2015

- Churkin, D. V.; Kolokolov, I. V.; Podivilov, E. V.
- Nature Communications, Vol. 6, Issue 1

##
Random distributed feedback fibre laser

journal, February 2010

- Turitsyn, Sergei K.; Babin, Sergey A.; El-Taher, Atalla E.
- Nature Photonics, Vol. 4, Issue 4

##
Inverse Energy Cascade in Forced Two-Dimensional Quantum Turbulence

journal, March 2013

- Reeves, Matthew T.; Billam, Thomas P.; Anderson, Brian P.
- Physical Review Letters, Vol. 110, Issue 10

##
Critical transitions in thin layer turbulence

journal, June 2017

- Benavides, Santiago Jose; Alexakis, Alexandros
- Journal of Fluid Mechanics, Vol. 822

##
Improved laser‐beam uniformity using the angular dispersion of frequency‐modulated light

journal, October 1989

- Skupsky, S.; Short, R. W.; Kessler, T.
- Journal of Applied Physics, Vol. 66, Issue 8

##
The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers

journal, July 1991

- Kolmogorov, A. N.
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 434, Issue 1890

##
Self-Modulation and Self-Focusing of Electromagnetic Waves in Plasmas

journal, July 1974

- Max, Claire Ellen; Arons, Jonathan; Langdon, A. Bruce
- Physical Review Letters, Vol. 33, Issue 4

##
Exceeding the leading spike intensity and fluence limits in backward Raman amplifiers

journal, December 2014

- Malkin, V. M.; Toroker, Z.; Fisch, N. J.
- Physical Review E, Vol. 90, Issue 6

##
Dissipation of Energy in the Locally Isotropic Turbulence

journal, July 1991

- Kolmogorov, A. N.
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 434, Issue 1890

##
Cascades in nonlocal turbulence

journal, April 2015

- Falkovich, Gregory; Vladimirova, Natalia
- Physical Review E, Vol. 91, Issue 4

##
Fast Compression of Laser Beams to Highly Overcritical Powers

journal, May 1999

- Malkin, V. M.; Shvets, G.; Fisch, N. J.
- Physical Review Letters, Vol. 82, Issue 22

##
The physics and applications of random lasers

journal, May 2008

- Wiersma, Diederik S.
- Nature Physics, Vol. 4, Issue 5

##
Extended Propagation of Powerful Laser Pulses in Focusing Kerr Media

journal, September 2016

- Malkin, V. M.; Fisch, N. J.
- Physical Review Letters, Vol. 117, Issue 13

##
Observation of the kinetic condensation of classical waves

journal, April 2012

- Sun, Can; Jia, Shu; Barsi, Christopher
- Nature Physics, Vol. 8, Issue 6

##
Beyond nonlinear saturation of backward Raman amplifiers

journal, June 2016

- Barth, Ido; Toroker, Zeev; Balakin, Alexey A.
- Physical Review E, Vol. 93, Issue 6

##
Discontinuous Transition from Direct to Inverse Cascade in Three-Dimensional Turbulence

journal, April 2017

- Sahoo, Ganapati; Alexakis, Alexandros; Biferale, Luca
- Physical Review Letters, Vol. 118, Issue 16

Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*