Kelvin Waves

Introduction

Kelvin waves are a type of wave in fluids that are confined to the boundary of the fluid, such as a coastline or the equator of the Earth’s atmosphere or oceans. They are named after the physicist William Thomson, 1st Baron Kelvin, who first described these waves in 1879.

The Basics of Waves

In physics, a wave is an oscillation that travels through space and matter. Waves transfer energy from one point to another, often with no permanent displacement of the particles of the medium—they oscillate around relatively stable positions.

The Coriolis Effect and Geostrophic Balance

Understanding Kelvin waves requires a grasp of the Coriolis effect and the concept of geostrophic balance. The Coriolis effect refers to the apparent deflection of the path of an object moving in a rotating system. On Earth, this deflection is to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.

Geostrophic balance is a balance of forces between the pressure gradient force and the Coriolis effect. This balance is what keeps large-scale weather systems and ocean currents from collapsing under the force of their own pressure gradients.

Definition of Kelvin Waves

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 the equator. A key 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 energy of the wave packet.

Mathematical Representation

The phase speed of a Kelvin wave can be represented as:

where is the acceleration due to gravity and is the undisturbed fluid depth.

Types of Kelvin Waves

There are two types of Kelvin waves: coastal Kelvin waves and equatorial Kelvin waves.

1. Coastal Kelvin Waves: These waves propagate along the boundary of a coastline. They can be forced by wind stress, pressure anomalies, or other external forces.
2. Equatorial Kelvin Waves: These waves propagate along the equator. They have a maximum amplitude at the equator and diminish as they move towards the poles.

Importance and Applications

Kelvin waves play a significant role in the Earth’s climate system, particularly in the dynamics of El Niño and La Niña phenomena in the Pacific Ocean. By transporting heat along the equator from the western Pacific to the eastern Pacific, they contribute to significant climatic variability.

Observing Kelvin Waves

Kelvin waves are typically observed through satellite altimetry or in situ oceanic observations. They can also be identified in atmospheric pressure and wind data.

Conclusion

Kelvin waves are a fascinating result of the interplay between Earth’s rotation and fluid dynamics, with significant implications for oceanic and atmospheric phenomena. Understanding these waves is key to predicting weather and climate patterns, making them a vital part of Earth’s climate study.

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