Climate as a compressible gas under gravity (RealNSE). A perfect gas fills an extended rectangle, heated from below (hot wall T_hot) and cooled on top (cold wall T_cold), under a constant downward gravity g; the side walls are periodic, the top/bottom walls free-slip and impermeable. Heated gas at the bottom becomes buoyant and rises, cooled gas at the top sinks — the deterministic equations organise this into convection cells, the overturning that carries heat upward in every real atmosphere.   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 e = gamma rho T, gamma = 1. Colour = temperature (blue cold → red hot); white dots = tracers.   Vertical profiles (horizontal averages vs height, value increasing rightward): temperature (red), density (cyan), turbulent dissipation (yellow).