In this note, we derive (to third order in derivatives of the fluid velocity)
a 2+1 dimensional theory of fluid dynamics that governs the evolution of
generic long-wavelength perturbations of a black brane or large black hole in
four-dimensional gravity with negative cosmological constant, applying a
systematic procedure developed recently by Bhattacharyya, Hubeny, Minwalla, and
Rangamani. In the regime of validity of the fluid-dynamical description, the
black-brane evolution will generically correspond to a turbulent flow.
Turbulence in 2+1 dimensions has been well studied analytically, numerically,
experimentally, and observationally as it provides a first approximation to the
large scale dynamics of planetary atmospheres. These studies reveal dramatic
differences between fluid flows in 2+1 and 3+1 dimensions, suggesting that the
dynamics of perturbed four and five dimensional large AdS black holes may be
qualitatively different. However, further investigation is required to
understand whether these qualitative differences exist in the regime of fluid
dynamics relevant to black hole dynamics.Comment: 16 pages, LaTeX, v2: caveat regarding relativistic vs
non-relativistic fluids added v3: typos correcte