Kelvin wave

A Kelvin wave is a large-scale wave motion in the atmosphere or ocean that is strongly influenced by the Earth’s rotation and the Coriolis effect. It is characterised by its tendency to remain confined to a boundary—such as a coastline or the equator—where the Coriolis force and the boundary constraint balance each other. Named after the British physicist Lord Kelvin (William Thomson), who first described their behaviour in the 19th century, Kelvin waves play a vital role in the dynamics of oceanic and atmospheric circulation, climate variability, and weather phenomena such as El Niño.

Fundamental Concept and Mechanism

Kelvin waves arise due to the interplay between gravity, pressure gradients, and the Coriolis force. When a disturbance occurs in a rotating fluid, the Coriolis force (which deflects moving air or water due to Earth’s rotation) would normally cause the motion to curve. However, near certain boundaries such as coastlines or the equator, this effect is neutralised or balanced, resulting in a trapped wave that propagates in one preferred direction.
In essence, a Kelvin wave maintains geostrophic balance—a state where the Coriolis force is balanced by the pressure gradient force—except at the boundary where friction and gravity act to restore equilibrium.

Types of Kelvin Waves

Kelvin waves are broadly classified into two major types based on where they occur:

1. Coastal Kelvin Waves:
   • Confined to coastlines or continental boundaries.
   • The coast acts as a boundary, keeping the wave trapped to one side (for instance, the right-hand side in the Northern Hemisphere, left-hand side in the Southern Hemisphere).
   • They travel with the coast on their right (Northern Hemisphere) or left (Southern Hemisphere) when looking in the direction of propagation.
   • Typically generated by changes in wind stress, sea level, or atmospheric pressure.
   • Important for coastal oceanography, influencing sea level variations, storm surges, and upwelling.
2. Equatorial Kelvin Waves:
   • Confined to the equatorial region, where the Coriolis force is effectively zero but increases with latitude on either side.
   • This latitudinal variation acts as a restoring mechanism, trapping the wave near the equator.
   • They travel eastward along the equator, transporting energy and warm water across ocean basins.
   • Play a crucial role in El Niño–Southern Oscillation (ENSO) dynamics.

Characteristics of Kelvin Waves

• Propagation Direction:
  • Coastal Kelvin waves follow coastlines, while equatorial Kelvin waves propagate eastward along the equator.
• Speed:
  • Their phase speed depends on gravity and water depth; in the ocean, typical speeds range from 2 to 3 m/s for equatorial waves and somewhat slower for coastal waves.
• Restoring Force:
  • Primarily gravity, balanced by the Coriolis effect and pressure gradients.
• Structure:
  • The wave motion is asymmetric, with the greatest displacement near the boundary and decaying exponentially away from it.
• Non-dispersive Nature:
  • All components of the wave travel at the same speed, maintaining the shape of the disturbance over long distances.

Formation and Dynamics

Kelvin waves are typically generated by changes in wind patterns or atmospheric disturbances.

• In the Ocean:
  • Strong westerly wind bursts along the equator (often in the western Pacific) can trigger eastward-moving equatorial Kelvin waves.
  • As these waves travel, they cause sea surface height anomalies, temperature variations, and subsurface water movement.
• In the Atmosphere:
  • Equatorial atmospheric Kelvin waves are driven by convection and pressure changes, moving eastward through the tropical troposphere at speeds between 10 and 20 m/s.

The interaction between oceanic and atmospheric Kelvin waves forms a key feedback mechanism in tropical climate systems.

Role in El Niño and La Niña Phenomena

Equatorial Kelvin waves play a central role in the El Niño–Southern Oscillation (ENSO), one of the most significant sources of interannual climate variability.

• During El Niño development:
  • Westerly wind bursts in the western Pacific generate Kelvin waves that travel eastward.
  • These waves deepen the thermocline (the boundary between warm surface water and cold deep water) and raise sea surface temperatures in the eastern Pacific.
  • This redistribution of warm water suppresses upwelling off the South American coast, leading to global climatic impacts such as altered rainfall patterns and warmer global temperatures.
• During La Niña, the reverse process occurs:
  • Rossby waves (westward-moving) help restore the thermocline, and reflected Kelvin waves reinforce the cooling phase.

Thus, Kelvin waves act as a mechanism for energy and heat transfer across ocean basins, influencing weather and climate patterns on a planetary scale.

Atmospheric Kelvin Waves

In the atmosphere, Kelvin waves are observed primarily in the tropical troposphere and stratosphere. They are generated by convective disturbances and interact with larger-scale circulation patterns such as the Madden–Julian Oscillation (MJO) and quasi-biennial oscillation (QBO).
Key features include:

• Eastward propagation along the equator.
• Symmetric structure about the equator, with maximum amplitude at the equator.
• Typical speeds of 10–20 m/s and wavelengths of several thousand kilometres.
• Influence on tropical convection, rainfall distribution, and upper-atmospheric wind variability.

Atmospheric Kelvin waves can modulate monsoon systems, tropical cyclone formation, and stratospheric circulation.

Mathematical Representation

In simplified terms, the behaviour of a Kelvin wave can be described by the linear shallow-water equations on a rotating Earth, where:

• The Coriolis parameter (f) varies with latitude (β-effect).
• Boundary conditions (such as a coastline or the equator) constrain the flow.
• The resulting solutions show wave propagation with an exponential decay in amplitude away from the boundary.

The wave’s phase speed (c) is approximately given by:
c=gHc = \sqrt{gH}c=gH​
where g is gravitational acceleration and H is the equivalent depth of the fluid layer.

Significance in Climate and Oceanography

Kelvin waves are fundamental to understanding large-scale geophysical fluid dynamics. Their importance spans multiple fields:

• Climate Dynamics:
  • They are a crucial link between short-term weather variability and long-term climate phenomena such as ENSO and the MJO.
• Oceanography:
  • Coastal Kelvin waves affect sea-level rise, coastal flooding, and upwelling systems, influencing marine productivity and fisheries.
• Atmospheric Science:
  • Atmospheric Kelvin waves influence global teleconnections and tropical weather systems.
• Remote Sensing and Prediction:
  • Satellite altimetry and ocean buoys track Kelvin waves to improve El Niño forecasts and climate models.

Global Examples

• Equatorial Pacific Ocean: Dominant site for Kelvin wave generation associated with El Niño events.
• Indian Ocean: Plays a role in the Indian Ocean Dipole (IOD) and monsoon modulation.
• Atlantic Ocean: Supports smaller-amplitude Kelvin waves that influence regional sea-level changes.
• Coastal Regions: Observed along the coasts of South America, Africa, and Asia following major wind shifts or storm surges.