# 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:
- Journal Article: 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.
```

```
@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 = {Tue Mar 06 00:00:00 EST 2018},

month = {Tue Mar 06 00:00:00 EST 2018}

}