**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Kelvin wave

Summary

A Kelvin wave is a wave in the ocean or atmosphere that balances the Earth's Coriolis force against a topographic boundary such as a coastline, or a waveguide such as the equator. A feature of a Kelvin wave is that it is non-dispersive, i.e., the phase speed of the wave crests is equal to the group speed of the wave energy for all frequencies. This means that it retains its shape as it moves in the alongshore direction over time.
A Kelvin wave (fluid dynamics) is also a long scale perturbation mode of a vortex in superfluid dynamics; in terms of the meteorological or oceanographical derivation, one may assume that the meridional velocity component vanishes (i.e. there is no flow in the north–south direction, thus making the momentum and continuity equations much simpler). This wave is named after the discoverer, Lord Kelvin (1879).
In a stratified ocean of mean depth H, perturbed by some amount η, free waves propagate along coastal boundaries (and hence become trapped in the vicinity of the coast itself) in the form of internal Kelvin waves on a scale of about 30 km. These waves are called coastal Kelvin waves, and have propagation speeds of approximately 2 m/s in the ocean. Using the assumption that the cross-shore velocity v is zero at the coast, v = 0, one may solve a frequency relation for the phase speed of coastal Kelvin waves, which are among the class of waves called boundary waves, edge waves, trapped waves, or surface waves (similar to the Lamb waves). The (linearised) primitive equations then become the following:
the continuity equation (accounting for the effects of horizontal convergence and divergence):
the u-momentum equation (zonal wind component):
the v-momentum equation (meridional wind component):
If one assumes that the Coriolis coefficient f is constant along the right boundary conditions and the zonal wind speed is set equal to zero, then the primitive equations become the following:
the continuity equation:
the u-momentum equation:
the v-momentum equation:
The solution to these equations yields the following phase speed: c2 = gH, which is the same speed as for shallow-water gravity waves without the effect of Earth's rotation.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related courses (2)

CIVIL-527: Selected topics in mechanics of solids and structures

The class covers the fundamentals of wave dynamics and fracture mechanics. The aim is to deepen their knowledge in advanced topis in mechanics of solids and structures and discuss current research top

PHYS-755: Introduction to topological phases

This course introduces the elementary topological concepts and tools that recently spread from condensed matter physics to various quantum and classical wave systems.

Related lectures (16)

Related concepts (4)

Kelvin-Helmholtz and Rayleigh Taylor Instabilities

Explores Kelvin-Helmholtz and Rayleigh Taylor instabilities, kinematic conditions, linearized equations, and normal mode expansion.

Instability: parallel flow concepts

Explores fluid flow instabilities, including Rayleigh-Taylor and Kelvin-Helmholtz, and parallel flow concepts like normal mode decomposition and Squire's transformation.

Instability of 2D fluid flow

Covers the stability analysis of a 2D fluid flow and various instabilities.

In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise (or counterclockwise) rotation, the force acts to the right. Deflection of an object due to the Coriolis force is called the Coriolis effect.

A Kelvin wave is a wave in the ocean or atmosphere that balances the Earth's Coriolis force against a topographic boundary such as a coastline, or a waveguide such as the equator. A feature of a Kelvin wave is that it is non-dispersive, i.e., the phase speed of the wave crests is equal to the group speed of the wave energy for all frequencies. This means that it retains its shape as it moves in the alongshore direction over time.

In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction, it is said to be a traveling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a standing wave.