Climate as a 3D compressible gas under gravity (RealNSE). A perfect gas fills a box, heated from below (hot floor) and cooled on top (cold lid) under downward gravity g; the four side walls are periodic, the floor/lid free-slip and impermeable. Buoyant hot gas rises, cold gas sinks, and the deterministic equations organise this into three-dimensional convection cells. Shown: a vertical temperature slice through the mid-plane (blue cold → red hot). Vertical profiles (horizontal averages over the whole layer vs height): temperature (red), density (cyan), turbulent dissipation (yellow).   rho_t + div m = 0, m_t + div(m v) + grad p − nu lap v = rho g, e_t + div(e v) + p div v = nu|grad v|²; p = gamma rho T, gamma = 1.