132
5 3D Level Modelling
The model is forced by initial prescription of a cylindrical patch of surface water
of 10 km in diameter and a thickness 200 m. This patch is initially 0.1 kg/m
3 lighter
compared with ambient water of a density of ρ o = 1,028 kg/m
3 . The associated density anomaly is linearly adjusted from zero to its final value during the first 2 hrs of
simulation.
The Coriolis parameter is set to f = 1 × 10
−4 s
−1 . We expect that geostrophic
adjustment creates frontal currents running around the rim of the low-density patch.
We also expect that the width of this current is of the order of the internal Rossby
radius of deformation, given by Eq. (4.12), which is approximately 3.4 km in this
exercise. Although the lateral grid spacing of 2 km does not adequately resolve this
length scale, the results will show that the model is able to capture key dynamical
aspects of the geostrophic adjustment process.
Wind forcing is not applied in this exercise. Horizontal eddy viscosity and eddy
diffusivity are set to uniform values of A h = K h = 1 m
2 /s. Kochergin’s turbulence
closure scheme, Eq. (4.22), is employed for calculation of variable vertical eddy viscosity and eddy diffusivity. The bottom-friction parameter in the assumed quadratic
bottom-friction law is set to r = 0.001.
The total simulation time is 60 hrs (2.5 days) with data outputs at hourly interval.
Data outputs are those of surface distributions of density, horizontal velocity components and sea-level elevation, and vertical transects of density and horizontal velocity components across the centre of the model domain at y = 25 km. The time step
is set to Δt = 5 s, using the free-surface version of the model. Pressure accuracy of
the S.O.R. iteration is set to = 0.01 Pa.
5.3.3 Results
The geostrophic adjustment process creates a high-pressure centre associated with
a sea-level elevation of 1 cm (not shown). This drives an anticyclonic geostrophic
surface eddy of approximately 20 cm/s in speed (Fig. 5.4) superimposed on which
are inertial oscillations. Instead of continued lateral spreading, the Coriolis force
operates to maintain the low-density surface patch as a circular feature that only
slowly dissipates owing to both lateral density diffusion and frictional effects. As
anticipated, a cyclonic eddy establishes in the bottom layer owing to water-column
stretching (Fig. 5.5). In summary, the three-dimensional model appears to capture
key dynamical aspects of the geostrophic adjustment process, even with a relatively
coarse spatial resolution. Note the striking similarity of the 3d findings with those
of the 2.5d application in Exercise 16 (see Sect. 4.2).
5.3.4 Additional Exercise for the Reader
Place a cylindrical patch of denser water at the bottom of the model domain and
explore the geostrophic adjustment process that follows for this configuration. Vary
5 3D Level Modelling
The model is forced by initial prescription of a cylindrical patch of surface water
of 10 km in diameter and a thickness 200 m. This patch is initially 0.1 kg/m
3 lighter
compared with ambient water of a density of ρ o = 1,028 kg/m
3 . The associated density anomaly is linearly adjusted from zero to its final value during the first 2 hrs of
simulation.
The Coriolis parameter is set to f = 1 × 10
−4 s
−1 . We expect that geostrophic
adjustment creates frontal currents running around the rim of the low-density patch.
We also expect that the width of this current is of the order of the internal Rossby
radius of deformation, given by Eq. (4.12), which is approximately 3.4 km in this
exercise. Although the lateral grid spacing of 2 km does not adequately resolve this
length scale, the results will show that the model is able to capture key dynamical
aspects of the geostrophic adjustment process.
Wind forcing is not applied in this exercise. Horizontal eddy viscosity and eddy
diffusivity are set to uniform values of A h = K h = 1 m
2 /s. Kochergin’s turbulence
closure scheme, Eq. (4.22), is employed for calculation of variable vertical eddy viscosity and eddy diffusivity. The bottom-friction parameter in the assumed quadratic
bottom-friction law is set to r = 0.001.
The total simulation time is 60 hrs (2.5 days) with data outputs at hourly interval.
Data outputs are those of surface distributions of density, horizontal velocity components and sea-level elevation, and vertical transects of density and horizontal velocity components across the centre of the model domain at y = 25 km. The time step
is set to Δt = 5 s, using the free-surface version of the model. Pressure accuracy of
the S.O.R. iteration is set to = 0.01 Pa.
5.3.3 Results
The geostrophic adjustment process creates a high-pressure centre associated with
a sea-level elevation of 1 cm (not shown). This drives an anticyclonic geostrophic
surface eddy of approximately 20 cm/s in speed (Fig. 5.4) superimposed on which
are inertial oscillations. Instead of continued lateral spreading, the Coriolis force
operates to maintain the low-density surface patch as a circular feature that only
slowly dissipates owing to both lateral density diffusion and frictional effects. As
anticipated, a cyclonic eddy establishes in the bottom layer owing to water-column
stretching (Fig. 5.5). In summary, the three-dimensional model appears to capture
key dynamical aspects of the geostrophic adjustment process, even with a relatively
coarse spatial resolution. Note the striking similarity of the 3d findings with those
of the 2.5d application in Exercise 16 (see Sect. 4.2).
5.3.4 Additional Exercise for the Reader
Place a cylindrical patch of denser water at the bottom of the model domain and
explore the geostrophic adjustment process that follows for this configuration. Vary