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Kelvin and Rossby Waves

Krauss Chapter Nine

The Importance of Long Wavelength Waves

LongWaves

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Barotropic Waves:well mixed oceanisopycnal and isobaricsurfaces undulate in unisonwith the passage of thewave

Baroclinic Waves:stratified oceanisopycnal and isobaricsurfaces undulates in nearmirror image form withthe passage of the wave -except that the amplitudeat the surface is smallcompared to the that ofthe thermocline

Rossby Radius of Deformation (L) is the distance that aparticle or wave travels before being significantly

affected by the earth’s rotation.

If h is the depth of the upper ocean layer, we L theBAROCLINIC DEFORMATION RADIUS

If h is the depth of the ocean, we call L theBAROTROPIC DEFORMATION RADIUS

Note that L decreases with latitude (increasing f) so that a wave (orcurrent for that matter) at high latitude need only travel a shortdistance before being affected by Coriolis Force.

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Kelvin Waves(Coastal and Equatorial)

Coastal Kelvin Waves balance the Coriolis Force against a Topographic Boundary (i.e.,Coastline). They always propagate with the shoreline on the right in the northern and theleft in the southern hemisphere.

A Coastal Kelvin Wave moving northward along the coast is deflected to the right, but thecoast prevents the wave from turning right and instead causes water to pile up on the coast.The pile of water creates a pressure gradient directed offshore and a geostrophic currentdirected northward.

Kelvin Wave Amplitude is negligible at a distance offshore given by the Rossby Radius ofDeformation. For mid-latitude Kelvin Waves traveling on the ocean surface this is about200 km. For mid-latitude Kelvin Waves traveling in the thermocline this is about 25 km.Because of this rapid decay Coastal Kelvin waves appear to be Trapped Close to the Coast.

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Equatorial Kelvin waves are a special type of Kelvin wave thatbalances the Coriolis Force in the northern hemisphere against itssouthern hemisphere counterpart. This wave always propagateseastward and only exists on the equator.

Equatorial Kelvin Waves propagating in the thermocline have wavespeeds slow enough to give a Rossby Radius of Deformation that ison the order of 250 km and thus they appear to be trapped closeto the equator.

section view

plan view

An Example of an Equatorial Kelvin Wave

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Equatorial Kelvin Wave TravelingAlong the Thermocline

Rossby Waves

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The “RestoringForce” for aRossby Wave isthe Requirementto ConservePotential Vorticity

1500

100 m

Vertical Scale of Rossby Waves

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Latitudinal Variation of Rossby Wave Phase Speed

Latitudinal variation ofthe phase speeds ofnondispersive Rossbywaves obtained fromhistorical hydrographicdata based on theclassical theory (solid line)and from T/Pobservations in the Pacific(solid circles) and theAtlantic and Indian oceans(open circles).

AVISO News Letter #6

25 km/day

8 km/day

Krauss, page 228

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Time-Distance or “Hovmoller” Diagrams are Commonlyused to Depict Wave Propagation in the Ocean

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Kelvin-Rossby Wave Interactions

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A westward-propagating Rossbywave trough centered on theequator and extending tomidlatitudes in both hemispherescan be seen in the Pacific Ocean inthe April 13, 1993 frame. Therefracted shape that ischaracteristic of Rossby waves isdue to the latitudinal variation ofphase speed.

In the July 31, 1993 frame, thisRossby wave trough has impingedon the western boundary of thePacific and an equatorial Kelvinwave trough centered at about 140W has propagated rapidly eastwardmore than half way across thePacific, splitting a newly formedRossby wave crest that haspropagated westward from SouthAmerica.

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