The effect of topography on ocean flow
The rôle which topography plays in constraining ocean flow is investigated in several ways, mostly aimed at application to the Southern Ocean where topography is known to be important. The physics of topographic Rossby waves is discussed in some depth and a description of ocean flow in terms of a sum of topographic normal modes is developed. It is shown that the apparent incompleteness of topographic modes can often be circumvented by including a function which absorbs the nett input of potential vorticity. Some subtle problems with this description are dealt with, and a calculation of topographic modes for the Southern Ocean is presented, which shows that the modes are very localised, making the use of them to describe basin-wide flows difficult. The effect of interactions between stratification and topography is investigated in terms of a quasi-two-dimensional model which deals only with the depth-integrated flow, and the assumptions which go into the model are examined in detail both analytically and by calculating terms of interest from a data set produced by the Fine Resolution Antarctic Model. It is shown that advection of density in the Southern Ocean can be described to a first approximation as being due to a barotropic current with no vertical velocity, the horizontal component of the baroclinic flow producing very little effect. The balance of terms reveals interesting features in the modelled flow in the Southern Ocean, showing the value of this type of analysis. Finally, insight developed in the course of the investigation allows a simple model to be constructed representing the feedback between density advection and forcing due to density gradients. This model is used to provide an explanation for the fact that the FRAM model spins up linearly, where most simple models would predict a component of quadratic behaviour in the spin-up.