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Dynamics in asymptotically anti-de Sitter spacetimes with reflecting boundary conditions are characterized by reduced dissipation as compared to asymptotically flat spacetimes. Such spacetimes, thus, represent opportunities to study nonlinear gravitational interactions that would otherwise be quickly damped away. I will discuss two background spacetimes---large AdS black branes in d=4, and pure AdS---where small perturbations display turbulent behavior and energy cascades driven by nonlinear interactions. In each case, the presence of an unexpected conserved quantity---a gravitational "enstrophy" around the AdS black brane, and a "particle number" for pure AdS perturbations---significantly affects the energy flow direction throughout the cascade, and drives energy to longer distance scales. I will comment on implications for fundamental general relativity questions such as cosmic censorship, and potential for turbulence beyond AdS.