We present a self-consistent model for the excitation of the extranucl
ear emission line filaments in Centaurus A. Interaction of the norther
n radio jet of Centaurus A with a dense cloud of material at the locat
ion of the filaments causes shock waves with velocities approximately
200-450 km s-1. The shocks produce a strong flux of EUV and soft X-ray
radiation which photoionize the visible knots. We show that the mecha
nical flux of a mildly supersonic low-density jet is sufficient to ene
rgize the shock waves through the production of supersonic turbulent v
elocities in the dense cloud via the Kelvin-Helmholtz instability. Fur
thermore, the expected instability growth time scales, turbulent veloc
ities, and characteristic wavelengths are all in agreement with the ob
servations. Detailed models of cloud-cloud collisions, using the new M
APPINGS II shock and photoionization code, produce a very good fit to
the observed spectra when allowance is made for shock instabilities an
d cloud-cloud density contrasts. The high-excitation and low-excitatio
n forbidden lines are reproduced along with the Hbeta luminosity and t
emperature-sensitive [O III] lambda4363/(5007+4959) ratio. We predict
the presence of a radio jet in the vicinity of the inner filaments and
the presence of strong ultraviolet line fluxes in the spectrum of the
filaments. The latter prediction is in contrast to the beamed photoio
nization models. We conclude that a narrow ionizing radiation beam is
not required to produce the observed phenomena. Moreover, many propert
ies of the knots, such as the velocity field, are deduced in the model
presented here whereas they are ad hoc assumptions in a simple beamed
radiation model. Similar models involving shocks with velocities grea
ter than or similar to 200 km s-1 may also be relevant to the extended
and nuclear line emission from a wide variety of active galaxies.