Three-Dimensional Waves in Tilt Thermal Boundary Layers

We numerically and theoretically study the stabilities of tilt thermal boundary layers immersed in stratified air. An interesting phenomenon is revealed: the stationary longitudinal-roll mode becomes unstable to some oscillating state even when the Grashof number is smaller than its corresponding critical value. By stability analysis, this phenomenon is explained in terms of a new three-dimensional wave mode. The effect of the tilt angle on the stability of the boundary flows is investigated. Since the new three-dimensional wave is found to be the most unstable mode when the title angle is between 30 degrees and 64 degrees, it is expected to play an important role in the transition to turbulence.