Holographic Turbulence in Einstein-Gauss-Bonnet Gravity at Large $D$

We study the holographic hydrodynamics in the Einstein-Gauss-Bonnet(EGB) gravity in the framework of the large $D$ expansion. We find that the large $D$ EGB equations can be interpreted as the hydrodynamic equations describing the conformal fluid. These fluid equations are truncated at the second order of the derivative expansion, similar to the Einstein gravity at large $D$. From the analysis of the fluid flows, we find that the fluid equations can be taken as a variant of the compressible version of the non-relativistic Navier-Stokes equations. Particularly, in the limit of small Mach number, these equations could be cast into the form of the incompressible Navier-Stokes equations with redefined Reynolds number and Mach number. By using numerical simulation, we find that the EGB holographic turbulence shares similar qualitative feature as the turbulence from the Einstein gravity, despite the presence of two extra terms in the equations of motion. We analyze the effect of the GB term on the holographic turbulence in detail.