Holography, hydrodynamics and flows

Hydrodynamic phenomena seem to be ubiquitous in the universe. Hydrodynamics provides an effective, long-wavelength description of both classical and quantum systems. We study the universal spatial features of certain non-equilibrium steady states corresponding to flows of strongly correlated fluids over obstacles. We identify spatial collective modes of the strongly coupled many body system. These modes can be both hydrodynamical or non-hydrodynamical. Analytic examples can be found in the large-dimension limit of the bulk theory, but in three dimensions as well. We construct the general first-order hydrodynamic theory invariant under time translations, the Euclidean group of spatial transformations and preserving particle number. Such theories are important in many situations, from hydrodynamics of graphene to flocking behaviour of birds and motion of self-propelled organisms. We apply our non-boost invariant model of hydrodynamics to concrete flow configurations - the Poiseuille, Couette and Taylor-Couette flows. We also test the instability of the Poiseuille flow