120
4 2.5D Vertical Slice Modelling
Fig. 4.18 Illustration for implementation of lateral boundary conditions. Vertical arrows indicate
the grid columns in which values of vertical velocity and of the nonhydrostatic part of dynamic
pressure q are set to zero
values of vertical eddy viscosity and diffusivity. The bottom friction parameter is
set to r = 0.001. The total simulation time is 50 days with half daily data outputs.
The pressure accuracy for the S.O.R. iteration is set to = 10
−3 Pa. The time step
is chosen at Δt = 90 s, using the free-surface version of the model.
4.6.4 Results: Scenario 1
The wind stress imposed (see Fig. 4.17a) creates a surface Ekman layer in the ocean.
Details of the vertical structure of this Ekman layer are not revolved by the relatively coarse vertical grid spacing of 20 m chosen. Nevertheless, the model captures
the resultant net horizontal movement, the so-called Ekman-layer transport. In the
Northern Hemisphere, Ekman-layer transport in the surface ocean is directed 90
◦ to
the right with respect to the wind direction. Its magnitude varies with the magnitude
of the wind stress. Consequently, the wind-stress forcing of Scenario 1 creates a
lateral divergence of surface Ekman-layer transports. With ignorance of flows below
the surface Ekman layer, this divergence would result in a drop of the sea surface at
a rate of:
w ek =
1
ρ o f
∂τ
wind
y
∂ x
(4.24)
called Ekman-pumping velocity. In this exercise, the Ekman-pumping velocity
attains a maximum value in the middle of the model domain of about 6 × 10
−3 mm/s
or 50 cm per day. The sea surface, however, does not drop at this rate, given that flow
divergence in the surface Ekman layer is partially compensated by a convergence
of lateral flow in the ocean underneath. Instead, the sea level rapidly approaches
a steady state, accompanied by a steady-state geostrophic flow in the surface layer.
As a consequence of this, the Ekman-pumping velocity translates now to the vertical
displacement speed of the pycnocline caused by lateral flow divergence in the ocean
interior. Accordingly, we can anticipate that the shape of the sea level mirrors the
horizontal distribution of the Ekman-pumping velocity; that is,
η ∝ w ek =
1
ρ o f
∂τ
wind
y
∂ x
= −π
τ o
ρ o f L
sin (π x/L)
(4.25)
4 2.5D Vertical Slice Modelling
Fig. 4.18 Illustration for implementation of lateral boundary conditions. Vertical arrows indicate
the grid columns in which values of vertical velocity and of the nonhydrostatic part of dynamic
pressure q are set to zero
values of vertical eddy viscosity and diffusivity. The bottom friction parameter is
set to r = 0.001. The total simulation time is 50 days with half daily data outputs.
The pressure accuracy for the S.O.R. iteration is set to = 10
−3 Pa. The time step
is chosen at Δt = 90 s, using the free-surface version of the model.
4.6.4 Results: Scenario 1
The wind stress imposed (see Fig. 4.17a) creates a surface Ekman layer in the ocean.
Details of the vertical structure of this Ekman layer are not revolved by the relatively coarse vertical grid spacing of 20 m chosen. Nevertheless, the model captures
the resultant net horizontal movement, the so-called Ekman-layer transport. In the
Northern Hemisphere, Ekman-layer transport in the surface ocean is directed 90
◦ to
the right with respect to the wind direction. Its magnitude varies with the magnitude
of the wind stress. Consequently, the wind-stress forcing of Scenario 1 creates a
lateral divergence of surface Ekman-layer transports. With ignorance of flows below
the surface Ekman layer, this divergence would result in a drop of the sea surface at
a rate of:
w ek =
1
ρ o f
∂τ
wind
y
∂ x
(4.24)
called Ekman-pumping velocity. In this exercise, the Ekman-pumping velocity
attains a maximum value in the middle of the model domain of about 6 × 10
−3 mm/s
or 50 cm per day. The sea surface, however, does not drop at this rate, given that flow
divergence in the surface Ekman layer is partially compensated by a convergence
of lateral flow in the ocean underneath. Instead, the sea level rapidly approaches
a steady state, accompanied by a steady-state geostrophic flow in the surface layer.
As a consequence of this, the Ekman-pumping velocity translates now to the vertical
displacement speed of the pycnocline caused by lateral flow divergence in the ocean
interior. Accordingly, we can anticipate that the shape of the sea level mirrors the
horizontal distribution of the Ekman-pumping velocity; that is,
η ∝ w ek =
1
ρ o f
∂τ
wind
y
∂ x
= −π
τ o
ρ o f L
sin (π x/L)
(4.25)