**4. Various regimes of flow**

The various curves of Figure 1(b) permit to determine different regimes of the flow (Riahi & Lili, 2011). This figure shows that there is an increase in the turbulent kinetic energy when *Mg*0 increases for various cases considered A1,…,A10. In addition, when initial gradient Mach number increases, we observe a break of slope which is accentuated when the value of *Mg*<sup>0</sup> becomes more significant. It appears from this figure that the turbulent kinetic energy varies quasi-linearly in cases A1 and A2, where *Mg*0 takes respectively values 2.7 and 4. These two values of *Mg*0 correspond to the incompressible regime. A weak amplification of the turbulent kinetic energy shows that cases A4 (*Mg*0 = 12) and A10 (*Mg*0 = 66.7) correspond to the intermediate regime. From *Mg*0 = 16.5, the regime becomes compressible. Indeed, cases A5,…, A10 show a significant amplification of the total kinetic energy more and more marked when the initial gradient Mach number *Mg*0 increases.

These different regimes permit to better understanding compressibility effects on structure of homogeneous sheared turbulence and to analyze the causes of turbulence structure modification generated by compressibility.

Several explanations were proposed these last years to analyze causes of the stabilising effect of compressibility which are still not cleared up.
