Structures of dynamically unstable shear flows and their implications for shallow internal gravity waves

Summary

In this study, the response of a dynamically unstable shear flow with a critical level to periodic forcing is presented. An energy argument is proposed to explain the upshear tilt of updrafts associated with disturbances in two-dimensional stably stratified flows. In a dynamically unstable flow, the energy equation requires an upshear tilt of the perturbation streamfunction and vertical velocity whereU _z is positive. A stability model is constructed using an iteration method. An upshear tilt of the vertical velocity and the streamfunction fields is evident in a dynamically unstable flow, which is required by energy conversion from the basic shear to the growing perturbation wave energy according to the energy argument. The momentum flux profile indicates that the basic flow is decreased (increased) above (below) the critical level. Thus, the shear instability tends to smooth the shear layer. Following the energy argument, a downshear tilt of the updraft is produced in an unstably stratified flow since the perturbation wave energy is negative. The wave energy budget indicates that the disturbance is caused by a thermal instability modified by a shear flow since the potential energy grows faster than the kinetic energy.