Vorticity
87
We will focus now on variations in the flow on a time scale τ , a horizontal
velocity scale U and a length scale L.
b. Estimate the order of magnitude of the terms in the vorticity equation.
Let f =2 Ω . There is a special type of flow in case τ ≫ 1/f and
ǫ = U/(fL) ≪ 1.
c. Why is this case so special when considering the vorticity equation?
d. In an initially motionless layer, a sphere of radius R, with R
ǫ ≪ 1.Makeasketchofthisflow .
(4.4) Topographic steering
For large-scale flows in the deep ocean at locations for away from the equator,
the relative vorticity can be neglected with respect to the planetary vorticity.
a. Argue why this holds and show that for a constant density flow, the shallowwater potential vorticity Π reduces to
Π=
f
H
where H is the thickness of the layer and f = f 0 + β 0 y is the Coriolis parameter on the β plane.
Consider now the east to west flow over a seamount as sketched in the figure
below.
b. Describe the path of a watercolumn in this flow.
87
We will focus now on variations in the flow on a time scale τ , a horizontal
velocity scale U and a length scale L.
b. Estimate the order of magnitude of the terms in the vorticity equation.
Let f =2 Ω . There is a special type of flow in case τ ≫ 1/f and
ǫ = U/(fL) ≪ 1.
c. Why is this case so special when considering the vorticity equation?
d. In an initially motionless layer, a sphere of radius R, with R
ǫ ≪ 1.Makeasketchofthisflow .
(4.4) Topographic steering
For large-scale flows in the deep ocean at locations for away from the equator,
the relative vorticity can be neglected with respect to the planetary vorticity.
a. Argue why this holds and show that for a constant density flow, the shallowwater potential vorticity Π reduces to
Π=
f
H
where H is the thickness of the layer and f = f 0 + β 0 y is the Coriolis parameter on the β plane.
Consider now the east to west flow over a seamount as sketched in the figure
below.
b. Describe the path of a watercolumn in this flow.