Lecture

Shallow Water Equations: Stability and Analysis

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In course

PHYS-203: Computational physics I

Aborder, formuler et résoudre des problèmes de physique en utilisant des méthodes numériques simples. Comprendre les avantages et les limites de ces méthodes (stabilité, convergence). Illustrer différents sujets de physique traités dans d'autres cours. ...

Description

This lecture covers the shallow water equations, von Neuman stability analysis, excitation of eigen modes, stability limit CFL, and variable phase speed (tsunami). It explores digital and analytic methods, including explicit diagrams and WKB approximation.

Instructor

Laurent Villard

Teaching & PhD Past EPFL PhD Students Matteo Maccio, Olivier Fischer, Gloria Luisa Falchetto, Paolo Angelino, Sébastien Jolliet, Xavier Lapillonne, Thibaut Vernay, Julien Stanislas Pierre Dominski, Gabriele Merlo, Emmanuel Lanti, Noé Ohana, Moahan Murugappan

Official source

Related concepts (32)

Tsunami

A tsunami ((t)suːˈnɑːmi,_(t)sʊˈ- ; from 津波, tsɯnami) is a series of waves in a water body caused by the displacement of a large volume of water, generally in an ocean or a large lake. Earthquakes, volcanic eruptions and other underwater explosions (including detonations, landslides, glacier calvings, meteorite impacts and other disturbances) above or below water all have the potential to generate a tsunami.

P wave

A P wave (primary wave or pressure wave) is one of the two main types of elastic body waves, called seismic waves in seismology. P waves travel faster than other seismic waves and hence are the first signal from an earthquake to arrive at any affected location or at a seismograph. P waves may be transmitted through gases, liquids, or solids. The name P wave can stand for either pressure wave (as it is formed from alternating compressions and rarefactions) or primary wave (as it has high velocity and is therefore the first wave to be recorded by a seismograph).

S wave

NOTOC In seismology and other areas involving elastic waves, S waves, secondary waves, or shear waves (sometimes called elastic S waves) are a type of elastic wave and are one of the two main types of elastic body waves, so named because they move through the body of an object, unlike surface waves. S waves are transverse waves, meaning that the direction of particle movement of a S wave is perpendicular to the direction of wave propagation, and the main restoring force comes from shear stress.

Longitudinal wave

Longitudinal waves are waves in which the vibration of the medium is parallel to the direction the wave travels and displacement of the medium is in the same (or opposite) direction of the wave propagation. Mechanical longitudinal waves are also called compressional or compression waves, because they produce compression and rarefaction when traveling through a medium, and pressure waves, because they produce increases and decreases in pressure.

Surface wave

In physics, a surface wave is a mechanical wave that propagates along the interface between differing media. A common example is gravity waves along the surface of liquids, such as ocean waves. Gravity waves can also occur within liquids, at the interface between two fluids with different densities. Elastic surface waves can travel along the surface of solids, such as Rayleigh or Love waves. Electromagnetic waves can also propagate as "surface waves" in that they can be guided along with a refractive index gradient or along an interface between two media having different dielectric constants.

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