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3 Basics of Nonhydrostatic Modelling
3.13 Exercise 7: Lee Waves
3.13.1 Task Description
We consider a model domain, 500 m in length and 100 m in depth, resolved by a
horizontal grid spacing of Δx = 5 m and a vertical grid spacing of Δz = 2 m
(Fig. 3.27). Lateral boundaries are cyclic. A small submarine sill is included of a
height of 40 m and a width of about 100 m. A cosine function is used for the creation of this sill. Forcing is provided via prescription of ambient barotropic pressuregradient force that is added as additional terms in the u-momentum equation as:
Forcing term = −g
∂η o
∂ x
where ∂η o /∂ x is a prescribed ambient sea-level gradient. This forcing, which operates to gradually accelerate the flow into the positive x-direction, is switched off
after 20 min of simulation.
Two different stratification scenarios are considered. The first scenario deals with
a water column in which density increases initially linearly with depth (Fig. 3.27a).
The background sea level is assumed to vary by 0.5 cm over the length of the model
domain. The stability frequency (squared) is varied in a range between N
2
= 0.5 ×
10
−4 s
−2 and N
2
= 5 × 10
−4 s
−2 . The second scenario deals with two superimposed
layers of different densities both 50 m in thickness (Fig. 3.27b). Each layer is slightly
stratified with a stability frequency squared of N
2
= 0.5 × 10
−4 s
−2 . A density
interface, also called pycnocline, separates both layer. Density stratification across
this interface corresponds to a stability frequency (squared) of N
2
= 4.8×10
−3 s
−2 ,
which is stronger than any stratification considered in Scenario 1. In this scenario,
Fig. 3.27 Different initial density configurations used in Exercise 7
3 Basics of Nonhydrostatic Modelling
3.13 Exercise 7: Lee Waves
3.13.1 Task Description
We consider a model domain, 500 m in length and 100 m in depth, resolved by a
horizontal grid spacing of Δx = 5 m and a vertical grid spacing of Δz = 2 m
(Fig. 3.27). Lateral boundaries are cyclic. A small submarine sill is included of a
height of 40 m and a width of about 100 m. A cosine function is used for the creation of this sill. Forcing is provided via prescription of ambient barotropic pressuregradient force that is added as additional terms in the u-momentum equation as:
Forcing term = −g
∂η o
∂ x
where ∂η o /∂ x is a prescribed ambient sea-level gradient. This forcing, which operates to gradually accelerate the flow into the positive x-direction, is switched off
after 20 min of simulation.
Two different stratification scenarios are considered. The first scenario deals with
a water column in which density increases initially linearly with depth (Fig. 3.27a).
The background sea level is assumed to vary by 0.5 cm over the length of the model
domain. The stability frequency (squared) is varied in a range between N
2
= 0.5 ×
10
−4 s
−2 and N
2
= 5 × 10
−4 s
−2 . The second scenario deals with two superimposed
layers of different densities both 50 m in thickness (Fig. 3.27b). Each layer is slightly
stratified with a stability frequency squared of N
2
= 0.5 × 10
−4 s
−2 . A density
interface, also called pycnocline, separates both layer. Density stratification across
this interface corresponds to a stability frequency (squared) of N
2
= 4.8×10
−3 s
−2 ,
which is stronger than any stratification considered in Scenario 1. In this scenario,
Fig. 3.27 Different initial density configurations used in Exercise 7