  We study the effects of Kelvin Helmholtz Instability (KHI) on the cold
streams that feed massive halos at high redshift, generalizing our earlier
results to include the effects of radiative cooling and heating from a UV
background, using analytic models and high resolution idealized simulations. We
currently do not consider self-shielding, thermal conduction or gravity. A key
parameter in determining the fate of the streams is the ratio of the cooling
time in the turbulent mixing layer which forms between the stream and the
background following the onset of the instability, $t_{\rm cool,mix}$, to the
time in which the mixing layer expands to the width of the stream in the
non-radiative case, $t_{\rm shear}$. This can be converted into a critical
stream radius, $R_{\rm s,crit}$, such that $R_{\rm s}/R_{\rm s,crit}=t_{\rm
shear}/t_{\rm cool,mix}$. If $R_{\rm s}<R_{\rm s,crit}$, the non-linear
evolution proceeds similarly to the non-radiative case studied by Mandelker et
al. 2019a. If $R_{\rm s}>R_{\rm s,crit}$, which we find to almost always be the
case for astrophysical cold streams, the stream is not disrupted by KHI.
Rather, background mass cools and condenses onto the stream, and can increase
the mass of cold gas by a factor of $\sim 3$ within 10 stream sound crossing
times. The mass entrainment induces thermal energy losses from the background
and kinetic energy losses from the stream, which we model analytically. Roughly
half of the dissipated energy is radiated away from gas with $T<5\times
10^4{\rm K}$, suggesting much of it will be emitted in Ly$\alpha$.
