Stability analysis of thermal progression due to Ekman pumping

Abdolmajid Mohammadian, Yarzar Tun

Friday 3 july 2015

8:00 - 9:00h

Themes: (T) Special session

Parallel session: Miscalleneous

The process of how instabilities develop and become amplified in fluids, which eventually leads to turbulence, is still a major research area. Hydrodynamic stability theory is a branch of scientific knowledge which mathematically describes the tendency for a fluid flow in certain conditions to become unstable and evaluate the behavior of the instabilities. In traditional linear stability analysis, the governing equations are rewritten into an eigenvalue problem with the assumption that the added small disturbances take the form of waves. By calculating the eigenvalues, one can predict the behavior of the instabilities. However, some type of fluid flows are known to show instabilities even when the eigenvalue analysis predicts that the flow is stable. This paper describes the pseudospectral method as an alternative/addition to the eigenvalue analysis with Rayleigh-Benard convection as an example application. Singular vectors are also shown to calculate finite time instabilities. The ongoing work and future plans on applying this method to oceanic problems can also found in this paper.