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.

Figure 1

The normalized transverse temperature of photons $y\left(x\right)$ (dashed line) and spectral flux of transverse energy $\mathcal{J}\left(x\right)$ (solid line) around the spectrum upper boundary $x=k_{\perp }/k_{\perp M}\sim 1$ at early evolution stage.

Figure 2

The normalized transverse temperature of photons $y\left(x\right)$ (dashed line) and spectral flux of transverse energy $\mathcal{J}\left(x\right)$ (solid line) around the spectrum upper boundary $x=k_{\perp }/k_{\perp M}\sim 1$ at advanced evolution stage.

Figure 3

Divisions of the parameter plane $(Q,P)$.