Molecular jets announce the successful birth of a protostar. We develo
p here a model for the jets and their environments, adapting a multi-d
imensional hydrocode to follow the molecular-atomic transitions of hyd
rogen. We examine powerful outflows into dense gas. The cocoon which f
orms around a jet is a very low density cavity of atomic gas. These at
oms originate from strong shocks which dissociate the molecules. The r
est of the molecules are either within the jet or swept up into very t
hin layers. Pulsed jets produce wider cavities and molecular layers wh
ich can grow onto resolvable jet knots. Three-dimensional simulations
produce shocked molecular knots, distorted and multiple bow shocks and
arclike structures. The resemblance of simulated images of the 1-0 S(
1) H-2 emission to recently observed deeply embedded outflows in HH 21
1, HH 212, HH 288 and L1634 is discussed. Spectroscopic and excitation
properties of the hydrogen molecules and CO maps are calculated. In t
he infrared, strong emission is seen from shocks within the jet (when
pulsed) as well as from discrete regions along the cavity walls. Excit
ation, as measured by line ratios, is not generally constant. Broad do
uble-peaked, shifted emission lines are predicted. Low-J CO emission i
s limb-brightened but spread over the whole outflow region. Some of th
ese signatures are shown to depend on the chosen jet conditions. We fi
nd that three-dimensional calculations are essential for numerical sim
ulations of strong cooling jets.