Kelvin wave

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Schematic representation of a Kelvin wave

The Kelvin wave , named after Lord Kelvin (1824–1907), is a wave that, unlike the water wave and Poincaré wave, does not spread freely over the entire surface of the water. Instead, it can only propagate in narrow belts ( waveguides ) along the topographical boundaries of rotating liquids, e.g. B. on coasts as well as along the equator in the ocean and in the atmosphere .

The tides propagate in the form of barotropic coastal Kelvin waves. The bow wave of a ship is also composed of Kelvin waves.

properties

Kelvin waves are created by pressure gradients of any shape , e.g. B. high and low pressure areas , excited parallel to the axis of a waveguide. Kelvin waves are characterized by the fact that they have a horizontal velocity component only parallel to the axis of the waveguide, i.e. they always propagate in such a way that the fixed edge of the waveguide is on the right in the direction of propagation in the northern hemisphere and on the left in the southern hemisphere. The amphidromic systems are formed by this property of circulating an ocean basin counterclockwise in the northern hemisphere (or with it in the southern hemisphere) .

The pressure gradient perpendicular to the axis of the waveguide is in equilibrium with the Coriolis force , which is caused by the horizontal velocity component.

Spatial expansion

The amplitude of a Kelvin wave falls exponentially with the distance to the coast. Kelvin waves can therefore only be observed within a characteristic distance from the coast; further away they become so flat that they can hardly be made out. This characteristic length, the Rossby radius , depends on the geographical latitude and grows from the pole to the equator:

  • Barotropic Kelvin waves (= on the surface of the water) have a Rossby radius of around 1500 kilometers at the pole and around 3000 kilometers at the equator.
  • baroclinic (= propagating between layers of water of different densities ) Kelvin waves have Rossby radii of typically 10 kilometers at the pole and 300 kilometers at the equator.

Phase velocity and dispersion

The phase velocity of a Kelvin wave is equal to that of a long wave on the non-rotating earth. Barotropic Kelvin waves are very fast, with phase velocities of around 200 meters per second, whereas baroclinic Kelvin waves typically have phase velocities of 0.5 to 3 meters per second. A baroclinic disturbance in the equatorial region near Indonesia would take two to three months to spread within the equatorial waveguide to South America.

In the case of Kelvin waves, group and phase velocities are the same for all frequencies , they are dispersionless. This means that a free Kelvin wave retains its original waveform (which it received at the time of its excitation) as it propagates along the axis of the waveguide.

species

Coastal Kelvin waves

Idealized idea: a low pressure area raises the water level on a coast and disappears. What remains is a mountain of water and thus a pressure gradient force with a component directed towards the open sea. As soon as the observed water particle prepares to flow away from the coast, the Coriolis force acts: to the right in the northern hemisphere, to the left in the southern hemisphere. The water particle is deflected accordingly until it only flows parallel to the coast: this is then on the right in the northern hemisphere in the direction of propagation, on the left in the southern hemisphere.

Equatorial Kelvin waves

At the equator there is the special case that the Coriolis force is zero. So there doesn't have to be a coast here, the equator takes on the role of a virtual coast. This allows two Kelvin waves, one in each hemisphere , to travel back to back. In the northern hemisphere, the Kelvin wave propagates with the equator on the right and in the southern hemisphere with the equator on the left. This means that the disturbances in the deflection of the water surface or the thermoclines move eastwards. The pressure disturbances associated with the equatorial Kelvin wave decay exponentially towards the pole with the square of the distance to the equator. The characteristic meridional width of the waveguide at the equator is approximately one equatorial Rossby radius in each hemisphere.

Occurrence and meaning

Baroclinic Kelvin waves play an important role in ENSO events (El Niño-Southern Oscillation). Here, as the trade winds ease in the western equatorial Pacific, the warm water mountain pent up in front of Indonesia migrates as an equatorial Kelvin wave towards South America (delayed oscillator theory). When they hit the eastern edge of the ocean basin, they are z. Some of them are converted into coastal Kelvin waves that propagate poleward on both sides of the equator along the coasts of the continents. During El Niño events, warm water anomalies were observed that were transported by Kelvin waves along the coast into the Gulf of Alaska . In addition, part of the equatorial Kelvin wave is reflected as long Rossby waves in the equatorial waveguide and propagates back to the west in it.

Kelvin waves also play an important role in shaping the upwelling phenomena on the coasts and at the equator: if upwelling is stimulated in a limited area, Kelvin waves propagate from both edges of the upwelling area along the coasts and the equator in the direction possible for Kelvin waves.

  • The seen from the shore (in the northern hemisphere) from the start end on the right edge of the lifting area buoyancy Kelvin wavefront ( upwelling ) exports the buoyancy in the non-excitation exposed region between the right border and the current position of the lift-Kelvin wavefront.
  • The downwelling Kelvin wave front (downforce) starting from the left edge of the upwelling area propagates into the upwelling area and there stops the upwelling and acceleration of the coastal jet between the left edge and the current position of the downwelling Kelvin wave front.

The lift behind the front of the Kelvin wave is stopped by the fact that the balance existing in front of the front switches: the coastal-vertical divergence of the Ekman transport , which is in equilibrium with the proportion of the vertical divergence of the lift behind the front, switches to the coastal parallel Divergence of the coastal jet stream. The divergence of the ekmank compensation current below the surface layer, perpendicular to the coast, is balanced by the coast-parallel divergence of an undercurrent opposite to the jet current in the surface layer.

At the equator, this undercurrent is particularly strong as the equatorial undercurrent ( flow velocity in the core ≈ 1 meter per second) and represents an essential branch of the oceanic circulation . Since the buoyancy is stopped last on the right edge, it is strongest there, as well this is where the coastal jet current is strongest. The area to the left of the upwelling area is not influenced by the Kelvin waves.

In the southern hemisphere, the asymmetry between the left and right edge of a finite area of ​​upwelling is reversed compared to that in the northern hemisphere.

swell

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