  The relationship between a decaying plasma turbulence and proton fire hose
instabilities in a slowly expanding plasma is investigated using
three-dimensional (3-D) hybrid expanding box simulations. We impose an initial
ambient magnetic field along the radial direction, and we start with an
isotropic spectrum of large-scale, linearly-polarized, random-phase Alfvenic
fluctuations with zero cross-helicity. A turbulent cascade rapidly develops and
leads to a weak proton heating that is not sufficient to overcome the
expansion-driven perpendicular cooling. The plasma system eventually drives the
parallel and oblique fire hose instabilities that generate quasi-monochromatic
wave packets that reduce the proton temperature anisotropy. The fire hose wave
activity has a low amplitude with wave vectors quasi-parallel/oblique with
respect to the ambient magnetic field outside of the region dominated by the
turbulent cascade and is discernible in one-dimensional power spectra taken
only in the direction quasi-parallel/oblique with respect to the ambient
magnetic field; at quasi-perpendicular angles the wave activity is hidden by
the turbulent background. These waves are partly reabsorbed by protons and
partly couple to and participate in the turbulent cascade. Their presence
reduces kurtosis, a measure of intermittency, and the Shannon entropy but
increases the Jensen-Shannon complexity of magnetic fluctuations; these changes
are weak and anisotropic with respect to the ambient magnetic field and it's
not clear if they can be used to indirectly discern the presence of
instability-driven waves.
