Turbulence of heterogeneous fluids (non-miscible fluids separated by an interface) are encountered in several natural and industrial situations. Most of available theoretical descriptions of such flows generally apply to the dispersed regime, when one phase is much more abundant than the other. When the two-phases are found in similar proportions (the dense regime), the shapes of fluid structures are much more contorted and cannot simply be described in terms of e.g. drop/bubble diameter distribution.