  We present a new 400ks Chandra X-ray observation and a GMRT radio observation
at 325MHz of the merging galaxy cluster Abell 2146. The Chandra observation
reveals detailed structure associated with the major merger event including the
Mach M=2.1+/-0.2 bow shock located ahead of the dense subcluster core and the
first known example of an upstream shock (M=1.6+/-0.1). Surprisingly, the deep
GMRT observation at 325MHz does not detect any extended radio emission
associated with either shock front. All other merging galaxy clusters with
X-ray detected shock fronts, including the Bullet cluster, Abell 520, Abell 754
and Abell 2744, and clusters with candidate shock fronts have detected radio
relics or radio halo edges coincident with the shocks. We consider several
possible factors which could affect the formation of radio relics, including
the shock strength and the presence of a pre-existing electron population, but
do not find a favourable explanation for this result. We calculate a 3sigma
upper limit of 13mJy on extended radio emission, which is significantly below
the radio power expected by the observed P_{radio}-L_{X} correlation for
merging systems. The lack of an extended radio halo in Abell 2146 maybe due to
the low cluster mass relative to the majority of merging galaxy clusters with
detected radio halos.
