We demonstrate that relativistic conformal hydrodynamics in $2+1$ dimensions displays a turbulent behavior which cascades energy to longer wavelengths on both flat and spherical manifolds. Our motivation for this study is to understand the implications for gravitational solutions through the AdS/CFT correspondence. The observed behavior implies gravitational perturbations of the corresponding black brane/black hole spacetimes (for sufficiently large scales/temperatures) will display a similar cascade towards longer wavelengths.

• Received 1 November 2012

DOI:https://doi.org/10.1103/PhysRevD.86.126006