Three-Dimensional Features of Thermal Convection in a Plane Couette Flow

Abstract

An investigation is made of some features of perturbation superimposed in a plane Couette flow with unstable stratification. A set of linearized Boussinesq equations governing the perturbation is solved numerically employing a finite-difference technique. First, stability characteristics of the perturbations are shown. These characteristics are discussed for various Richardson numbers and wavenumbers and are compared with those obtained analytically by Kuo. It is confirmed that constant shear has a stabilizing effect on the perturbation and the effect is striking for perturbations of short wavelength and of transverse modes whose wavelengths in the direction perpendicular to the basic flow are longer than those in the direction parallel to the basic flow. Second, a dynamical structure of unstable perturbations and the associated energy conversions are discussed. Conversion between kinetic energy of the basic flow and that of the perturbation takes place as well as conversion of potential energy to kinetic energy. In particular, vertical transfer of horizontal momentum, which results in conversion between both the kinetic energies of the basic flow and of the perturbation, is crucially controlled by the three dimensionality of the perturbations. The vertical momentum transfer tends to intensify the shear of the basic flow when a perturbation is transverse, while it reverses for a longitudinal pertubation whose wavelength in the direction parallel to the basic flow is longer than that in the direction perpendicular to the basic now.