Thermal Instability of a Shear Flow Turning the Direction with Height

Abstract

Thermal convection in a shear flow varying the direction as well as the speed with respect to height is investigated by means of the perturbation analysis under the Boussinesq approximation. A particular attention is focused on characteristic band structure of thermal convection in relation to the basic flow in which the convection is superimposed. Two different types of unstable perturbations may be found. One originates from thermal instability and the other is in essence of inertial origin. The thermal instability yields a preferred mode of convection roll along which the vertical shear of the velocity component of the basic flow perpendicular to the roll axis is a minimum.