The unstable modes of natural convection boundary layer

The instability of natural convection boundary layer around a vertical heated flat plate is analyzed theoretically in this paper. The results illustrate that the “loop” in the neutral curve is not a real loop but a twist of the curve in the frequency-wave number-Grashof number space, and there is only one unstable mode at small Prandtl numbers. Specially, when the Prandtl number is large enough two unstable modes will be found in the “loop” region. Along the amplyfying surface intersection the two unstable modes have the same Grashof number, wave number and frequency but different amplifying rates. Their instability characteristics are analyzed and the criterion for determining the existence of the multi-unstable modes is also discussed.