This work develops scaling and governing equations for mixing processes in large interconnected enclosures under stratified conditions. Injected buoyant jets, plumes from heat sources, and wall jets from heat transfer to structures can generate such mixing. Using the hierarchical two-tiered scaling analysis method, criteria are developed for the prediction of ambient enclosure fluid stratification due to temperature and/or concentration gradients. Simplified governing equations for mass, energy, and species conservation result. In their simplified form, the governing equations allow both scaling and simplified modeling and analysis of integral system behavior. The application to numerical analysis of mixing is illustrated with an example related to nuclear reactor containment mixing.