A variational problem for the maximization of energy dissipation during turbulent fluid mixing in Boussinesq approximation

We study the Boussinesq approximation of the Rayleigh-Taylor instability with local energy inequality, within the convex integration plus variational selection criterion framework of arXiv:2505.03278. We show that, under an appropriate rescaling, the energy dissipation functionals obtained in said paper $\mathrm{\Gamma }$-converge, and that their limit has a unique maximizer, corresponding to the profile also obtained in arXiv:2008.08853.