ANGULAR MOMENTA OF MODELED OCEAN GYRES

Total angular momentum of fluid within an ocean basin consists of a part due to center of mass of the fluid rotating about Earth's axis and a part due to relative motion within the basin. In rotating planar geometry (f plane) the relative angular momentum due to motion within a basin can be expressed as an integral of mass transport stream function. This simple relationship is used to examine the consistency of free-slip "sidewall" boundary conditions applied to a homogeneous ocean model with viscous interior. One finds that the fluid exchanges angular momentum with the basin by means of the normal component of viscous stress, so that a closed angular momentum budget is recovered despite the use of free-slip boundary conditions. Cases of flow in an enclosed rectangular basin and in an open (infinite) channel are considered. Resolution of budget questions for these idealized cases opens a question concerning real ocean gyres: How is wind-supplied angular momentum disposed?