  The relationship between a decaying strong turbulence and kinetic
instabilities in a slowly expanding plasma is investigated using
two-dimensional (2-D) hybrid expanding box simulations. We impose an initial
ambient magnetic field perpendicular to the simulation box, and we start with a
spectrum of large-scale, linearly-polarized, random-phase Alfv\'enic
fluctuations which have energy equipartition between kinetic and magnetic
fluctuations and vanishing correlation between the two fields. A turbulent
cascade rapidly develops, magnetic field fluctuations exhibit a Kolmogorov-like
power-law spectrum at large scales and a steeper spectrum at ion scales. The
turbulent cascade leads to an overall anisotropic proton heating, protons are
heated in the perpendicular direction, and, initially, also in the parallel
direction. The imposed expansion leads to generation of a large parallel proton
temperature anisotropy which is at later stages partly reduced by turbulence.
The turbulent heating is not sufficient to overcome the expansion-driven
perpendicular cooling and the system eventually drives the oblique firehose
instability in a form of localized nonlinear wave packets which efficiently
reduce the parallel temperature anisotropy. This work demonstrates that kinetic
instabilities may coexist with strong plasma turbulence even in a constrained
2-D regime.
