Kelvin wave
The Kelvin wave, named after Lord Kelvin (1824-1907), is a wave in contrast to the water wave and Poincaré wave does not propagate freely over the whole surface, but only in narrow belts ( waveguides ) along topographical boundaries of rotating fluids, can spread, such as in coastal areas and along the equator in the ocean and in the atmosphere. Also, the bow wave of a ship consists of Kelvin waves.
The Kelvin wave propagates in the waveguide always so that its edge is fixed in the propagation direction for right / left hand on the Nord-/Südhalbkugel. Their phase velocity is equal to that of a long shaft on the non-rotating earth. The Kelvin wave is not dispersive, that is, the phase velocity of the wave is equal to its group velocity for all frequencies. This means that it maintains its original waveform for propagation along the axis of the waveguide. In addition, it is characterized in that it has only a horizontal component of velocity parallel to the axis of the waveguide and the pressure gradient is perpendicular to this direction caused by the Coriolis force horizontal component of velocity in equilibrium. The pressure field of the Kelvin wave sounds exponentially perpendicular to the axis of the waveguide with the scale of the Rossbyradius from. Kelvin waves are excited by means of any pressure gradient formed in parallel to the axis of the waveguide.
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Properties
Coastal Kelvin waves
Idealized presentation: A low pressure increases on a coast the water level and disappears. What remains is a mountain of water and thus a pressure gradient with a directional component to the open sea. As soon as the water particles considered is preparing to flow away from the coast, the Coriolis force acts; on the Northern Hemisphere (Southern Hemisphere ) to the right (left). The water particles is deflected to the right ( left) until it just flows parallel to the shore and the resulting Coriolis force balances the pressure gradient perpendicular to the coast. The pressure disturbance propagates within a riparian zone, which is referred to as a coastal waveguide and whose characteristic width is equal to the Rossbyradius. The phase speed of the Kelvin wave is equal to that of a long shaft on the non-rotating earth. The Kelvin wave can only propagate so that the coast on the Nord-/Südhalbkugel in the propagation direction is to her right / left.
Equatorial Kelvin waves
At the equator, however, there is a special case, which no longer requires the presence of a coast. The Coriolis force is zero at the equator and the equator assumes the role of a virtual coast. This may be two Kelvin waves, each move in one hemisphere, back to back. In the northern hemisphere, the Kelvin wave propagates from the equator to the right and in the southern hemisphere with the equator on the left with the phase speed of a long wave on the non-rotating earth. This implies that the noise in the deflection of the water surface or the thermoclines east hike. The costs associated with the equatorial Kelvin wave sound pressure disturbances poleward exponentially with the square of the distance to the equator. The characteristic meridional width of the waveguide at the equator in each hemisphere is about an equatorial Rossbyradius.
Spatial extent
The amplitude of the Kelvin wave decays exponentially with the distance to shore. Kelvin waves are therefore observable only within a characteristic distance from the coast, farther away from the coast, they are so flat that they can be identified any more. This characteristic length is known as the Rossby radius, it depends on the latitude and grows from the pole to the equator. Therefore, the spatial extent of a Kelvin wave is dependent on the latitude. Kelvin waves on the water surface ( barotropic ) at the equator have a Rossby radius of about 3,000 kilometers and at a pole of about 1,500 kilometers. Baroclinic ( = between water layers of different density propagating ) Kelvin waves exhibit Rossby radii of typically 300 km at the equator and 10 kilometers at the pole on.
Dispersion and phase velocity
For Kelvin waves agree Groups and match phase velocity, they are dispersionless. This means that a free Kelvin wave propagates in the form that they received at the time of stimulation. Surface Kelvin waves are very fast, with phase velocities of about 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 in Indonesia would need so two to three months, to propagate within the equatorial waveguide to South America.
Occurrence and significance
The tides propagate in the form of barotropic coastal Kelvin waves. To circulate through their property, an ocean basin in the northern hemisphere ( southern hemisphere ) against ( the ) clockwise, the amphidromischen systems form.
But Kelvin waves can also be excited by high - and low-pressure areas.
Play an important role baroclinic Kelvin waves with ENSO events ( El Niño - Southern Oscillation ), where by a decline of the trade winds in the western equatorial Pacific the pent-up off Indonesia warm water mountain as a Kelvin wave towards South America travels (delayed oscillator theory ). Since equatorial Kelvin waves are converted when striking the eastern edge of the ocean basin in coastal Kelvin waves in part that propagate both sides of the equator along the coasts of the continents poleward, were in El Niño events by Kelvin waves transported hot water anomalies along the coast to the Gulf of Alaska observed inside. In addition, a portion of the equatorial Kelvin wave as long Rossby waves, reflected in the equatorial waveguide and propagated in it back to the west.
Kelvin waves also play an important role in the formation of the upwelling along the coasts and on the equator. If buoyancy excited in a limited area, Kelvin waves propagate from both edges of the lifting area along the coast and the equator in the potential for Kelvin wave direction. The seen from the shore to the northern hemisphere from the right of the lift area takeoff lift Kelvin wavefront exports the buoyancy in the non -exposed area of the excitation between the right edge and the current position of the lift Kelvin wave front. The from the left edge of the buoyant region blasting down welling Kelvin wave front propagates into the upwelling region and stops the lift and the acceleration of the coastal jet stream (English: coastal jet) between the left edge and the current position of the down welling Kelvin wave front. The impetus behind the Kelvin wave front is thus stopped that existing before the front balance between the coastal vertical divergence of the Ekman transport and the share of vertical divergence of buoyancy behind the front switches to a balance between the divergence of the Ekmantransports and the coast parallel divergence of the coastal jet stream. The vertical divergence of the coast Ekmankompensations stream below the top layer is balanced by the divergence parallel to the coast for a beam current in the top layer opposite undercurrent. At the equator, this undercurrent as Equatorial Undercurrent particularly strongly developed ( flow velocity in the core ≈ 1 meter per second) and represents an important branch of ocean circulation dar. Since the lift is on the right side last stopped, he is there most strongly pronounced, as well as here, the coast beam current is greatest. The area located left from the upwelling area is not affected by the Kelvin waves. In the southern hemisphere, the asymmetry of a finite lift area is compared to the reversed in the northern hemisphere between left and right margins.