Turbulence control by non-Hermitian potentials

Abstract

We propose a method to control turbulence by the introduction a non-Hermitian spatiotemporal modulation, based on the energy redirection from unstable to stable modes by the unidirectional coupling induced by these potentials and so, influence and slow down the excitation cascade of turbulence. The phenomenon of the turbulence is, and has been for a long time an interesting and challenging topic for scientist. Plenty of turbulent systems follow a quite general scenario, the excitation in a continuous system imposed on a large spatial scale, decreases in scale due to nonlinear wave-mixing processes until finally entering into a dissipative range, on a small spatial scale. Turbulence bridges these two spatial scales and results in an energy cascade through the wavenumbers. Turbulence appears in a wide range of disciplines, from fluids to business and optics. For this last case, turbulence represents one of the main inconvenience for laser source. These sources loss stability when power is increased through a instability of spatial character, the Modulation Instability (MI). Some techniques have been proposed to reduce and suppress the MI [1] . Aside, the introduction of non-Hermitian potentials has shown an asymmetric or even unidirectional coupling between modes allowing different spatial effects [2] – [3] .