Abstract
In this paper the thermal instability to infinitesimal disturbances in horizontal two dimensional shear flows with a negative vertical temperature gradient is investigated. The fluid is confined between horizontal planes, the lower of which is maintained warmer than the upper. The problem is treated analytically with the method of successive approximation for the case of very small Reynolds number (R<1), and obtain the neutral stability curves for stationary transverse rolls. Existence of transverse rolls in the range of subcritical Rayleigh number of Rayleigh-Bénard problem is clarified. Therefore, transverse rolls will be observed in this range of Reynolds number.
