  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 modeling
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% larger than the 2D estimate; it is in the range (0.5-5)% 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% 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)% of the gravitational energy gained by inflow
down the dark-matter halo potential can be dissipated, capable of powering
Lyman-alpha blobs if most of it is dissipated into radiation.
