  As part of our long-term campaign to understand how cold streams feed massive
galaxies at high redshift, we study the Kelvin-Helmholtz instability (KHI) of a
supersonic, cold, dense gas stream as it penetrates through a hot, dilute
circumgalactic medium (CGM). A linear analysis (Paper I) showed that, for
realistic conditions, KHI may produce nonlinear perturbations to the stream
during infall. Therefore, we proceed here to study the nonlinear stage of KHI,
still limited to a two-dimensional slab with no radiative cooling or gravity.
Using analytic models and numerical simulations, we examine stream breakup,
deceleration and heating via surface modes and body modes. The relevant
parameters are the density contrast between stream and CGM ($\delta$), the Mach
number of the stream velocity with respect to the CGM ($M_{\rm b}$) and the
stream radius relative to the halo virial radius ($R_{\rm s}/R_{\rm v}$). We
find that sufficiently thin streams disintegrate prior to reaching the central
galaxy. The condition for breakup ranges from $R_{\rm s} < 0.03 R_{\rm v}$ for
$(M_{\rm b} \sim 0.75, \delta \sim 10)$ to $R_{\rm s} < 0.003 R_{\rm v}$ for
$(M_{\rm b} \sim 2.25, \delta \sim 100)$. However, due to the large stream
inertia, KHI has only a small effect on the stream inflow rate and a small
contribution to heating and subsequent Lyman-$\alpha$ cooling emission.
