Transient buoyant flows of a stratified fluid in a vertical channel

A theoretical analysis is performed to describe the qualitative behavior of transient buoyant flows in a vertical channel. Consideration is given to t he case of a fluid with a pre-existing stratification, The fluid motion is generated by giving impulsive anti-symmetric step-changes in temperature at the vertical left and right sidewalls. The qualitative character of the fl ow is shown to be classified in the Rayleigh number (R-a)-Prandtl number (s igma) diagram. The transitory approach to the steady state tan be monotonic or oscillatory, depending on (sigma -1)(2)pi (4)< (>)4 sigmaR(a). The prom inent characteristics of time-dependent flow are discussed for large R-a. T he profiles of temperature and velocity in the transient phase are depicted , which disclose distinctive time scales of motion. The transient process i s shown to be sensitive to the Prandtl number. The detailed evolutions of f low and temperature fields are illustrated for large R-a.