Contents

82 4 Long Waves in a Channelplace well above sea level! The plume dynamics are influence by the steepness ofthe 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 ofsimulation4.5 The Multi-Layer Shallow-Water Model4.5.1 BasicsUnder the shallow-water assumption, we can formulate a dynamical model for awater column consisting of multiple layers each of a certain density. Figure 4.16gives the configuratio of a multi-layer model. Layers are numbered from top tobottom and the surface layer carries the index 1. The momentum equation for alayer 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 1P 2 = P 1 + (ρ 2 − ρ 1 ) g η 2