  We present 13.9-18.2 GHz observations of the Sunyaev-Zel'dovich (SZ) effect
towards Abell 2146 using the Arcminute Microkelvin Imager (AMI). The cluster is
detected with a peak SNR ratio of 13 sigma in the radio source subtracted map.
Comparison of the SZ and X-ray images suggests that they both have extended
regions which lie approximately perpendicular to one another, with their
emission peaks significantly displaced. These features indicate
non-uniformities in the distributions of the gas temperature and pressure,
indicative of a cluster merger. We use a Bayesian cluster analysis to explore
the high-dimensional parameter space of the cluster-plus-sources model to
obtain cluster parameter estimates in the presence of radio point sources,
receiver noise and primordial CMB anisotropy; the probability of SZ + CMB
primordial structure + radio sources + receiver noise to CMB + radio sources +
receiver noise is 3 x 10^{6}:1. We compare the results from three different
cluster models. Our preferred model exploits the observation that the gas
fractions do not appear to vary greatly between clusters. Given the relative
masses of the two merging systems in Abell 2146, the mean gas temperature can
be deduced from the virial theorem (assuming all of the kinetic energy is in
the form of internal gas energy) without being affected significantly by the
merger event, provided the primary cluster was virialized before the merger. In
this model we fit a simple spherical isothermal beta-model, despite the
inadequacy of this model for a merging system like Abell 2146, and assume the
cluster follows the mass-temperature relation of a virialized, singular,
isothermal sphere. We note that this model avoids inferring large-scale cluster
parameters internal to r_200 under the widely used assumption of hydrostatic
equilibrium. We find that at r_200 M_T= 4.1 \pm 0.5 x 10^{14} h^{-1}M_sun and
T=4.5 \pm 0.5 keV.
