The $\beta$-plane approximation of the rotating shallow water equations is widely used to study the characteristics of equatorial atmospheric and oceanic waves. In this talk, I will draw the contrasts in the properties of waves between the approximated system and the system under the full spherical geometry. I will first consider the system in the framework of linear modal stability analysis which involves an eigen-decomposition of the governing operator into normal modes and summarising the spectrum and structure of the modes.
I will then shift the focus to my non-normal stability analysis which deals with an investigation of the response of the system to small perturbations for short time. I will highlight the fundamental difference between the property of the governing operator in the two systems to show that, contrary to the $\beta$-plane system, the spherical system exhibits a significant short time amplification of the perturbation energy.
Zoom link: https://icts-res-in.zoom.us/j/83122729524?pwd=VHpLTnNxZjFpSHZXSDI3YXJkeTh1UT09
Meeting ID: 831 2272 9524
Passcode: 191920