高等大气动力学Rossbywave

11
Restoring force is the north-south gradient of background potential vorticity (f/H). That gradient can be due to either the variation in f with latitude, or to a variation in H (“topographic Rossby waves” and when trapped near the coast “continental shelf waves”). Note that Rossby waves are tranverse waves, that is the particles move perpendicular to the direction of propagation. Conserves PV = (f+ζ)/H.
White and red indicated higher than average levels; purple and magenta indicate lower than average levels. These scenes show eastward-moving Kelvin waves and westward-moving Rossby waves. Superimposed black circles show how the elevated sea surface moves east in April, then west as Rossby 10 waves during July and December.
Ocean
Mechanism of Rossby Wave
Rossby Waves
The most important class of large-scale atmospheric waves are called planetary waves, or Rossby waves. These waves are characterized by oscillations in the rotational part of the horizontal wind that are parallel to the horizontal gradient in the potential vorticity.
2
Wave
What is wave？
In physics, a wave is a disturbance that travels through space and time, usually accompanied by the transfer of energy. Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass transport. They consist, instead, of oscillations or vibrations around almost fixed locations.
16
Rossby wave propagation
In last section, we derived the properties of Rossby waves. Our key findings was that Rossby waves rely on the β-effect for their existence. We also discussed the mechanism for Rossby wave propagation through potential vorticity conservation.
Physics of Rossby Wave
Yihua Lin AOPP, Clarendon Laboratory University of Oxford, UK 4th, June, 2008
Outline
Wave Rossby wave in atmosphere & ocean Mechanism of Rossby wave Propagation & dispersion of Rossby wave
6
Atmosphere
• usually are 4-6 of them around the globe at a given time • wavelength varies between 4000-8000 km • are generally stationary - or move very slowly east or west
7
Surface pressure analysis; 03 March 2005 12Z.
Height Leabharlann f the 500hPa isobaric surface (dam), 03 March 2005 06Z.
8
9
The 2 small black circles off the coast of the Americas correspond to sea level highs on the trailing edge of Kelvin waves. The leading edge of this wave group has bounced off the coastline, creating Rossby waves whose rising and falling sea levels are marked by solid and dashed lines, respectively. In the July image, the circles are moving west with the Rossby waves. The "X" marks a relative sea level low caused by a Kelvin wave moving east. In December, the Rossby waves continue to move westward. The shapes of the solid and dashed lines indicate that the Rossby waves are moving away from the Americas faster at the equator than at higher latitudes.
The same thing will hold true on a slope ─ pushed towards shallower water will require decreased relative vorticity and vice versa ─ so shallower water is the analog of northward over a flat bottom and there are analogous waves generated on strong topographic slopes called topographic Rossby waves. H～f.
12
Sketch: northern hemisphere
13
Imagine that something pushes a water column perpendicular to the planetary vorticity. What will happen? The parcel will conserve total potential vorticity ─ (f+ζ/H). As it moves into a region of higher f, it will tend to decrease relative vorticity ─ a tendency to clockwise motion. Likewise if it were displaced towards lower relative vorticity, it will increase relative vorticity ─ a tendency towards counterclockwise motion.
14
Now let’s look at the Coriolis forces on the induced circulation pattern.
Size of restoring force (for a given displacement) is proportional to β= df/dy. PV equation: Dζ/Dt +15βv = 0
3
Mechanical wave, which propagates through a medium in which the substance of this medium is deformed. The deformation reverses itself owing to restoring forces resulting from its deformation. For example, sound waves.
Electromagnetic radiation (including visible light, ultraviolet radiation, infrared radiation, gamma rays, X-rays, and radio waves). This type wave can travel through a vacuum and consists of periodic oscillations in electrical and magnetic fields.