82
4 Long Waves in a Channel
place well above sea level! The plume dynamics are influence by the steepness of
the hill, which the reader can easily verify.
Fig. 4.15 Exercise 6. Scenario 2. Snapshots of sea-level elevation after 60, 90, 120 and 180 s of
simulation
4.5 The Multi-Layer Shallow-Water Model
4.5.1 Basics
Under the shallow-water assumption, we can formulate a dynamical model for a
water column consisting of multiple layers each of a certain density. Figure 4.16
gives the configuratio of a multi-layer model. Layers are numbered from top to
bottom and the surface layer carries the index 1. The momentum equation for a
layer i is given by:
∂u i
∂t
= −
1
ρ i
∂ P i
∂ x
(4.22)
where i is the layer index. Dynamic pressure in the layers is given by:
P 1 = ρ 1 g η 1
P 2 = P 1 + (ρ 2 − ρ 1 ) g η 2
4 Long Waves in a Channel
place well above sea level! The plume dynamics are influence by the steepness of
the hill, which the reader can easily verify.
Fig. 4.15 Exercise 6. Scenario 2. Snapshots of sea-level elevation after 60, 90, 120 and 180 s of
simulation
4.5 The Multi-Layer Shallow-Water Model
4.5.1 Basics
Under the shallow-water assumption, we can formulate a dynamical model for a
water column consisting of multiple layers each of a certain density. Figure 4.16
gives the configuratio of a multi-layer model. Layers are numbered from top to
bottom and the surface layer carries the index 1. The momentum equation for a
layer i is given by:
∂u i
∂t
= −
1
ρ i
∂ P i
∂ x
(4.22)
where i is the layer index. Dynamic pressure in the layers is given by:
P 1 = ρ 1 g η 1
P 2 = P 1 + (ρ 2 − ρ 1 ) g η 2