Prediction of three-dimensional breakdown of a longitudinal roll in a square duct.

Yuki Kato and Kaoru Fujimura, Theoretical and Applied Mechanics, Vol. 50, pp.327-333. (Proceedings of the 50th Japan National Congress on Theoretical and Applied Mechanics, 2001, ed. E. Watanabe).


abstract

Thermal convections in a square duct that is heated from below are studied. In the presence of a through flow, the roll aligning along the flow sets in because of the primary instability of the conduction state. The secondary instability of the longitudinal roll is analyzed to specify stability boundaries of the roll to three-dimensional disturbances. Three kinds of the instabilities are found. Among them, two instabilities with respect to symmetric disturbances make the longitudinal roll wavy. The other instability with respect to an anti-symmetric disturbance makes the roll thicker and thinner periodically. The breakdown occurring in relatively low Reynolds number is similar to the breakdown in available experimental results.