  We present constraints on Ks-band emission from one of the nearest short hard
gamma-ray bursts, GRB 160821B, at z=0.16, at three epochs. We detect a reddened
relativistic afterglow from the jetted emission in the first epoch but do not
detect any excess kilonova emission in the second two epochs. We compare upper
limits obtained with Keck I/MOSFIRE to multi-dimensional radiative transfer
models of kilonovae, that employ composition-dependent nuclear heating and LTE
opacities of heavy elements. We discuss eight models that combine toroidal
dynamical ejecta and two types of wind and one model with dynamical ejecta
only. We also discuss simple, empirical scaling laws of predicted emission as a
function of ejecta mass and ejecta velocity. Our limits for GRB 160821B
constrain the ejecta mass to be lower than 0.03 Msun for velocities greater
than 0.1c. At the distance sensitivity range of advanced LIGO, similar
ground-based observations would be sufficiently sensitive to the full range of
predicted model emission including models with only dynamical ejecta. The color
evolution of these models shows that I-K color spans 7--16 mag, which suggests
that even relatively shallow infrared searches for kilonovae could be as
constraining as optical searches.
