Stability analysis of natural convection in vertical cavities with lateralheating

Thermal convection of air in two-dimensional vertical cavities is considere d under the boundary conditions of the left and right vertical walls kept a t different temperatures and the top and bottom horizontal walls subject to thermal insulation. Linear stability analysis of thermal convection is mad e with the aid of the Galerkin method in which the field variables are expa nded in terms of Chebyshev polynomials and linear growth rates of steady st ates are computed using the QR algorithm. The results of the stability anal ysis for air with the Prandtl number 0.71 over the range of the cavity aspe ct ratio A from 1 to 10 show that with increase of the temperature differen ce between the two vertical walls the oscillatory motion first generated by the instability of steady convection is in the form of the Tollmien-Schlic hting or the internal gravity waves according as A > 3.65 or A < 3.41 while for 3.41 < A < 3.65 the internal gravity waves are first generated after t he preceding spatial flow transition of the hydraulic jump.