It has been demonstrated that, within the context of variable-density shear flows, the generation-destruction of vorticity by the baroclinic torque may substantially alter the transition dynamics of shear flows. The focus of the present contribution is on baroclinic effects beyond the Boussinesq approximation but uncorrelated to compressibility. The baroclinic torque results from the inertial component of the pressure gradient only. The vorticity evolves within a quasi-solenoidal velocity field without suffering from strong dilatationnal effects that scale with any relevant Mach number. This purely inertial influence of density variations is likely to occur in high Reynolds number mixing of fluids of different densities or in thermal mixing. The vorticity is redistributed to the benefits of the light-side vorticity braid, the other being vorticity depleted in a first stage and feeded with an opposite sign vorticity afterwards, as stressed by Reinaud et al. (1999). These two opposite-sign vorticity sheets are lying around the vanishing primary structure core, still figuring the center of this two-layers system. In three-dimensions the vorticity dynamics is also affected by the vortex stretching mechanism that enable circulation to travel among vorticity components through 3D instability modes. The consequences of the baroclinic redistribution of spanwise vorticity on the development of three-dimensionnal modes is the focus point of the present proposition. The interference with the pairing process and further subharmonics emergence is not yet considered
