Abstract
The effect of a capping inversion that lies above a neutrally stratified Ekman boundary layer (EBL) on the stability of the EBL is investigated by solving eigenvalue problems and initial value problems. If the inversion layer is sufficiently high, a growing normal mode exists that corresponds to the inflection point instability. This normal mode is similar to that in the case without an inversion layer. However, the origin of the growing normal mode changes into the Holmboe instability as the height where the inversion layer is imposed is decreased. The growing normal mode finally disappears if the inversion layer is below a certain level. Even if there is no growing normal mode, there may exist non-modal perturbations that can grow transiently. We calculate the optimal perturbation that grows the fastest over a short time period. Unlike the normal mode, the properties of this short-term optimal perturbation are not affected qualitatively by the presence of the inversion layer. These results are consistent with the fact that dominant structures do not emerge, but evanescent smaller-scale streaks do in large eddy simulations performed by other researchers for a neutrally stratified EBL with an inversion layer.
