The evolution of coastal currents over a wedge-shaped escarpment

Abstract

This paper considers the evolution of a source-sink driven coastal current across an escarpment of finite non-zero width and semi-infinite length in an inviscid homogeneous uniformly rotating fluid. In plan view the escarpment is wedge-shaped with the apex lying on a vertical coastal wall. The axis of symmetry of the escarpment intersects the coastal wall orthogonally. Using conformal mapping techniques, an analytical solution is developed for the barotropic streamfunction, for an arbitrary (but monotonic) escarpment depth profile. The escarpment waveguide supports an infinite set of topographic Rossby waves which can transmit in either the off-shore or on-shore direction.

The direction of propagation of long wavelength escarpment modes determines the final steady solution. When the phase velocity is directed towards the coastal wall the steady solution consists of stagnant fluid above the escarpment, except at the apex, where all the fluid crosses at a singular point. When the phase velocity is directed off-shore the steady solution once again exhibits stagnant fluid above the escarpment, with cross-escarpment flow occurring at an infinite distance off-shore.

When the semi-vertical angle (∊) of the escarpment satisfies 0<∊≲0.1 the mode one escarpment mode dominates the solution and the flow evolution is almost indistinguishable from that over a step. Over wider escarpments (∊≳ 0.5) higher escarpment modes play a significant role in the adjustment of the coastal current.

Key Words:

• Coastal current
• escarpment
• Rossby waves
• wave guide