6.5 Exercise 16: Topographic Steering
131
Fig. 6.5 Exercise 16. Scenario 1. Snapshot of fl w f eld (arrows, averaged over 5×5 grid cells) and
Eulerian tracer concentration (crowded lines) after 20 days of simulation. Bathymetric contours are
overlaid
ξ = f
h o + Δh
h o
− 1
(6.35)
where h o is the initial thickness of the water column, and Δh is the change in thickness of the water column along the f ow trajectory.
In Scenario 1, water-column squeezing over the bottom escarpment leads to a
fl w whose relative vorticity matches the curvature of bathymetric contours. The
propagation direction of topographic Rossby waves is the same as that of the ambient fl w, so that these waves propagate rapidly away from their generation zone.
Surprisingly, something different happens in Scenario 2 (Fig. 6.6). Here, watercolumn squeezing over the bottom escarpment creates relative vorticity of opposite
sign to that of Scenario 1. In response to this, the f ow crosses bathymetric contours
into deeper water. This initiates a standing topographic Rossby wave of a wavelength such that its phase speed (given by Eq. 6.28) is compensated by the speed
of the ambient fl w. For the configuratio of this exercise, the resultant wave pattern attains a horizontal amplitude of 20 km and a wavelength of 50 km. Obviously,
situations in which the ambient fl w runs opposite to the propagation direction of
topographic Rossby waves support the creation of such standing waves. Despite the
Fig. 6.6 Exercise 16. Same as Fig. 6.5, but for Scenario 2
131
Fig. 6.5 Exercise 16. Scenario 1. Snapshot of fl w f eld (arrows, averaged over 5×5 grid cells) and
Eulerian tracer concentration (crowded lines) after 20 days of simulation. Bathymetric contours are
overlaid
ξ = f
h o + Δh
h o
− 1
(6.35)
where h o is the initial thickness of the water column, and Δh is the change in thickness of the water column along the f ow trajectory.
In Scenario 1, water-column squeezing over the bottom escarpment leads to a
fl w whose relative vorticity matches the curvature of bathymetric contours. The
propagation direction of topographic Rossby waves is the same as that of the ambient fl w, so that these waves propagate rapidly away from their generation zone.
Surprisingly, something different happens in Scenario 2 (Fig. 6.6). Here, watercolumn squeezing over the bottom escarpment creates relative vorticity of opposite
sign to that of Scenario 1. In response to this, the f ow crosses bathymetric contours
into deeper water. This initiates a standing topographic Rossby wave of a wavelength such that its phase speed (given by Eq. 6.28) is compensated by the speed
of the ambient fl w. For the configuratio of this exercise, the resultant wave pattern attains a horizontal amplitude of 20 km and a wavelength of 50 km. Obviously,
situations in which the ambient fl w runs opposite to the propagation direction of
topographic Rossby waves support the creation of such standing waves. Despite the
Fig. 6.6 Exercise 16. Same as Fig. 6.5, but for Scenario 2