Enhanced energy fluxes via phase precession in forced Burgers equation

We present a study of phase dynamics in the non-linear forced Burgers' equation. We uncover a connection between energy flux across scales and the evolution of triad phase combinations in Fourier space\footnote{M. Buzzicotti, B. P. Murray, L. Biferale and M. D. Bustamante, \textit{EPJE} \textbf{39(3)}, (2016)}. As this energy is dissipated at small scales, real-space shock structures are associated with entangled correlations amongst the phase precession dynamics and the amplitude evolution of triads in Fourier space. We compute precession frequencies of the triad phases, which show a non-Gaussian distribution with multiple peaks and fat tails, with significant correlation between precession frequencies and amplitude growth. The observed fat tails and non-zero precession frequencies are two key criteria for enhancing energy fluxes via precession resonance\footnote{ M. D. Bustamante, B. Quinn, and D. Lucas, \textit{Phy. Rev. Let.} \textbf{113(8)}, (2014)}. We search for this resonance by varying the forcing strength and frequency and, additionally, by modifying the dimension of the underlying system via fractal Fourier decimation.