Abstract
Abstract Based on consideration of the perturbation enstrophy and energy equations, we have derived a general family of bounds on the growth rates of perturbations to non-parallel (vortex-like or wave-like) flow on the barotropic beta-plane, allowing for the effects of forcing, Ekman friction, and topography. The family of bounds generalizes Arnol’d's stability criterion. A number of specific applications of the family of bounds are explored. In particular, the formulas are used to demonstrate that the growth rate of the perturbations must vanish if the perturbation length-scale approaches zero or infinity. The distinction between transient and sustained growth of perturbation energy is discussed in light of our results. It is suggested that the bounds are most useful for estimating transient growth rates.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.