Instability of supersonic cold streams feeding Galaxies - III. Kelvin-Helmholtz instability in three dimensions

We study the effects of Kelvin-Helmholtz instability (KHI) on the cold streams that feed high-redshift galaxies through their hot haloes, generalizing our earlier analyses of a 2D slab to a 3D cylinder, but still limiting our analysis to the adiabatic case with no gravity. We combine analytic modelling and numerical simulations in the linear and non-linear regimes. For subsonic or transonic streams with respect to the halo sound speed, the instability in 3D is qualitatively similar to 2D, but progresses at a faster pace. For supersonic streams, the instability grows much faster in 3D and can be qualitatively different due to azimuthal modes, which introduce a strong dependence on the initial width of the stream-background interface. Using analytic toy models and approximations supported by high-resolution simulations, we apply our idealized hydrodynamical analysis to the astrophysical scenario. The upper limit for the radius of a stream that disintegrates prior to reaching the central galaxy is ~70 per cent larger than the 2D estimate; it is in the range 0.5-5 per cent of the halo virial radius, decreasing with increasing stream density and velocity. Stream disruption generates a turbulent mixing zone around the stream with velocities at the level of ~20 per cent of the initial stream velocity. KHI can cause significant stream deceleration and energy dissipation in 3D, contrary to 2D estimates. For typical streams, up to 10-50 per cent of the gravitational energy gained by inflow down the dark matter halo potential can be dissipated, capable of powering Lyman α blobs if most of it is dissipated into radiation.