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The relationship between a decaying plasma turbulence and proton fire hoseinstabilities in a slowly expanding plasma is investigated usingthree-dimensional (3-D) hybrid expanding box simulations. We impose an initialambient magnetic field along the radial direction, and we start with anisotropic spectrum of large-scale, linearly-polarized, random-phase Alfvenicfluctuations with zero cross-helicity. A turbulent cascade rapidly develops andleads to a weak proton heating that is not sufficient to overcome theexpansion-driven perpendicular cooling. The plasma system eventually drives theparallel and oblique fire hose instabilities that generate quasi-monochromaticwave packets that reduce the proton temperature anisotropy. The fire hose waveactivity has a low amplitude with wave vectors quasi-parallel/oblique withrespect to the ambient magnetic field outside of the region dominated by theturbulent cascade and is discernible in one-dimensional power spectra takenonly in the direction quasi-parallel/oblique with respect to the ambientmagnetic field; at quasi-perpendicular angles the wave activity is hidden bythe turbulent background. These waves are partly reabsorbed by protons andpartly couple to and participate in the turbulent cascade. Their presencereduces kurtosis, a measure of intermittency, and the Shannon entropy butincreases the Jensen-Shannon complexity of magnetic fluctuations; these changesare weak and anisotropic with respect to the ambient magnetic field and it'snot clear if they can be used to indirectly discern the presence ofinstability-driven waves.

Turbulence vs. fire hose instabilities: 3-D hybrid expanding box simulations