Rossby adjustment over a slope in a homogeneous fluid

The adjustment of ocean currents initially traveling over a topographic change in depth has previously been investigated in the limit of a discontinuous depth change. The present work is an extension to a linear, continuous depth change. Differences in the time-dependent flow are shown to follow from the different properties of double Kelvin waves over steps and slopes. Over a slope, double Kelvin waves have a series of cross-slope modes and can have group speeds in both directions along the slope. Thus, energy propagates both ways along the slope. The steady state over a linear slope is argued to be similar to that for a step escarpment. The slope separates the streamlines, isolating the dow on the two sides of the slope. The results of a series of numerical experiments are given in order to describe the transient Bow and to examine the effect of varying the two governing parameters: the nondimensional gradient of the slope and the nondimensional slope width. The slope gradient is found to define the timescale of formation of the tongue and the slope width to define the cross-sectional shape.