A temperature adjustment process of stratified fluid induced simultaneously by sidewall thermal variation and vertical through-flow

An analytical study is made of transient adjustment process of an initially stationary, stably-stratified fluid in a square. The boundary walls are highly-conducting. The overall Rayleigh number Ra is large. Considerations are given to both opposing (δω/δΤ>0) and cooperating (δω/δΤ<0) configurations. The flow character in opposing configuration can be classified into (a) a forced-convection dominant mode (δω/δΤ>1/√2), (b) a buoyancy-convection dominant mode (0<δω/δΤ<1/√2), and (c) a static mode (δω/δΤ≅1/√2). Global evolutionary processes are depicted, and physical rationalizations are provided