A variational approach for the linear stability of the Antarctic circumpolar current

Under appropriate assumptions on the vorticity, we show that the critical points of the natural energy functional are traveling wave solutions to the governing equations for the dynamics of the Antarctic Circumpolar Current established from fundamental principles. A variational formulation that contributes to the stability of large-scale circulation motion is also given. Additionally, we analyze the second-order variation of the functional and derive some linear stability results.