Non-Hermitian spatiotemporal potentials for turbulence control in parabolic and fractional dispersion

Abstract

We investigate the effect of dynamic non-Hermitian potentials on the control of turbulence in nonlinear systems. The proposed mechanism consists on the introduction of a complex modulation both in space and time. The non-Hermitian potential is intended to asymmetrically affect the excitation cascade responsible of turbulence. We show how the system effectively promotes or opposes to the excitation cascade through wavenumbers depending on the interplay between the real and the imaginary parts of the temporal modulation. The proposal is proved on the universal Complex Ginzburg Landau Equation and its fractional counterpart.