Turbulence control by non-Hermitian Potentials

The phenomenon of the turbulence is, and has been for a long time, an interesting and challenging topic for scientists from many fields. Turbulence appears in a wide range of disciplines, from fluids to business and optics. In optics for instance, turbulence represents one of the main drawbacks for laser sources. Increasing the laser power, the spatial stability of the homogeneous solution is lost through the Modulation Instability (MI), which leads to the onset of the turbulence. Generally, in turbulent flows, the energy is being continuously transferred from large to small spatial scales up to the viscosity range. Such energy cascade is at the root of the celebrated Kolmogorov theory for scaling laws in fully developed turbulence. 

We have proposed the introduction of a non-Hermitian potentials to control the turbulence. We see that the simultaneous spatio-temporal periodic modulation of the refractive index and gain/loss leads to an asymmetric or even unidirectional coupling between the spatial modes, allowing stabilizing/destabilizing effects. Moreover we are studying the effect of the introduction of these complex potentials in the stabilisation of periodic solutions of dissipaitive systems.

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