Oceanic density/pressure gradients and slope currents

Eastern boundary currents are some of the most energetic features of the global ocean, contributing significantly to meridional mass, heat and salt transports. We take a new look at the form of an oceanic slope current in equilibrium with oceanic density gradients. We depth-integrate the linearised x and y momentum and continuity equations, assume an equilibrium force balance in the along-slope direction (no along-slope variation in the along-slope flow) and zero cross-slope flow at a coastal boundary. We relate the bottom stress to a bottom velocity via a simple boundary friction law (the precise details are easily modified), and then derive an expression for the slope current velocity by integrating upwards including thermal wind shear. This provides an expression for the slope current as a function of depth and of cross-slope coordinate, dependent on the oceanic density field and surface and bottom stresses. This new expression for the slope current allows for more general forms of oceanic density fields than have been treated previously. Wind stress is also now considered. The emphasis here is on understanding the simplified equilibrium force balance rather than the evolution towards that balance. There is a direct relationship between the slope current strength, friction and along-slope forcing (e.g. wind); also between the total along-slope forcing and bottom Ekman transport, illustrating that “slippery” bottom boundaries in literature are a direct consequence of unrealistically assuming zero along-slope pressure gradient. We demonstrate the utility of the new expression by comparison with a high resolution hydrodynamic numerical model.