  We employ a two-dimensional grid-based hydrodynamic model to simulate upper
atmospheric dynamics on extrasolar giant planets. Our model is well-suited to
simulate the dynamics of the atmospheres of planets with high orbital
eccentricity that are subject to widely-varying irradiation conditions. We
identify six such planets, with eccentricities between $e=0.28$ and $e=0.93$
and semimajor axes ranging from $a=0.0508$ A.U. to $a=0.432$ A.U., as
particularly interesting objects for study. For each of these planets, we
determine the temperature profile and resulting infrared light curves in the
8-$\mu$m Spitzer bands. Especially notable are the results for HD 80606b, which
has the largest eccentricity ($e=0.9321$) of any known planet, and HAT-P-2b,
which transits its parent star, so that its physical properties are
well-constrained. Despite the variety of orbital parameters, the atmospheric
dynamics of these eccentric planets display a number of interesting common
properties. In all cases, the atmospheric response is primarily driven by the
intense irradiation at periastron. The resulting expansion of heated air
produces high-velocity turbulent flow, including long-lived circumpolar
vortices. Additionally, a superrotating acoustic front develops on some
planets; the strength of this disturbance depends on both the eccentricity and
the temperature gradient resulting from uneven heating. The specifics of the
resulting infrared light curves depend strongly on the orbital geometry. We
show, however, that the variations on HD 80606 b and HAT-P-2b should be readily
detectable at 4.5 and 8 $\mu$m using the Spitzer Space Telescope. Indeed, these
two objects present the most attractive observational targets of all known
high-$e$ exoplanets.
