We present observations from the Gaia-ESO Survey in the lines of H$alpha$, [N II], [S II] and He I of nebular emission in the central part of the Carina Nebula. We investigate the properties of the two already known kinematic components (approaching and receding, respectively), which account for the bulk of emission. Moreover, we investigate the features of the much less known low-intensity high-velocity (absolute RV $>$50 km/s) gas emission. We show that gas giving rise to H$alpha$ and He I emission is dynamically well correlated, but not identical, to gas seen through forbidden-line emission. Gas temperatures are derived from line-width ratios, and densities from [S II] doublet ratios. The spatial variation of N ionization is also studied, and found to differ between the approaching and receding components. The main result is that the bulk of the emission lines in the central part of Carina arises from several distinct shell-like expanding regions, the most evident found around $eta$ Car, the Trumpler 14 core, and the star WR25. Such shells are non-spherical, and show distortions probably caused by collisions with other shells or colder, higher-density gas. Part of them is also obscured by foreground dust lanes, while only very little dust is found in their interior. Preferential directions, parallel to the dark dust lanes, are found in the shell geometries and physical properties, probably related to strong density gradients in the studied region. We also find evidence that the ionizing flux emerging from $eta$ Car and the surrounding Homunculus nebula varies with polar angle. The high-velocity components in the wings of H$alpha$ are found to arise from expanding dust reflecting the $eta$ Car spectrum.
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