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 the 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 flow is shown to be classified in the Rayleigh number (R-a)-Prandtl number (sigma) diagram. The transitory approach to the steady state tan be monotonic or oscillatory, depending on (sigma -1)(2)pi (4)< (>)4 sigmaR(a). The prominent characteristics of time-dependent flow are discussed for large R-a. The profiles of temperature and velocity in the transient phase are depicted, which disclose distinctive time scales of motion. The transient process is shown to be sensitive to the Prandtl number. The detailed evolutions of flow and temperature fields are illustrated for large R-a.