A three‐dimensional instability in mixed convection with streamwise periodic heating

Three‐dimensional numerical simulations of flow through a channel with spatially periodic temperature boundary conditions in the streamwise direction have been carried out. A spectral method employing Fourier series expansion in the streamwise and spanwise directions and Chebyshev expansion in the vertical direction is used. A supercritical bifurcation to three‐dimensional flow is found to occur before the onset of unsteadiness. The bifurcation to unsteady three‐dimensional flow is also found to be supercritical. The unsteady three‐dimensional flow oscillates at a slightly lower frequency than the two‐dimensional flow, and introduces a slightly higher incommensurate frequency causing quasiperiodic flow and a slow spanwise wave motion.