[spaceshipone (OP)]

I have a homework question for my meteorology class. What is a baroclinic wave and what energy conversion is associated with it. I've scoured the internet and I don't really have a clue of what that is. If any smart people out there would like to chime in it would be greatly appreciated. Thanks!

[paul.fr]

OK, Firstly we realy don't do homework questions, but we can give you somewhere to start...a little nudge in the right direction.

A standard definition of a baroclinic wave is:

"(a baroclinic wave) Describes the synoptic-scale disturbance that grows in midlatitudes due to baroclinic instability."

But i am guessing that your teacher wants more than that.

So you may want to research the following terms:  synoptic-scale, baroclinic disturbance., stratification, barotropy, and baroclinity.

When you have that sorted, then you will find these links to wikipedia useful.

http://en.wikipedia.org/wiki/Rossby_wave
http://en.wikipedia.org/wiki/Baroclinic
http://en.wikipedia.org/wiki/Barotropic

This does seem rather advanced for school homework, may i ask what country you are in and an age?

[spaceshipone (OP)]

paul.fr thank you for your response. I am 20 taking a 100 level college meteorology class in the US. I actually did find that definition but was wondering if maybe you could explain that in lamens terms.

[paul.fr]

Hi again,
Firstly, i hope you will become a regular visitor to the site, not only asking but answering some questions as well. Now should you become a regular, you will find that I am pretty useless at explinations, well they make sense to me...sometimes only me.

hence the below reply. I have sent you further information via the PM (personal message) system.


Baroclinic (short) waves

Short waves are associated with temperature advection and are, therefore, baroclinic. The height contours and isotherms are out-of-phase and cross, resulting in temperature advection. Short-wave wavelengths are generally less than 60° of longitude. Their speeds average about 20 knots per day in the summer while in the winter, the average speed increases to 30 knots per day due to the increased speeds associated with the polar-front jet (PFJ). If a short wave supports a baroclinic low, we call it a short-wave trough. If a short wave supports a baroclinic high, we call it a short-wave ridge.

Major short waves

A major short wave is a short wave that is large enough to distort the long-wave pattern. They also reflect through a large depth of the atmosphere (visible on more than one constant-pressure level) and support surface features such as baroclinic lows or baroclinic highs.

Minor short waves

A minor short wave is a small short wave that generally moves faster than a major short wave and causes very little distortion to the long wave. They may not be detectable at more than one level.

Terms associated with low-pressure systems

The following terms relate to low-pressure systems:

Baroclinic low.
Barotropic low.
Stable waves.
Unstable waves.
Mature waves.
Decaying waves.


Baroclinic low

When contours and isotherms are out-of-phase, advection is occurring and the atmosphere is described as baroclinic. In other words, a baroclinic low is a low that has temperature advection associated with it. In a baroclinic system the axis tilts with height. The baroclinic low resides in a region of strong thermal contrast. As a result, strong thermal advection exists around the low. The system tilts with height to a short-wave trough. The system stacks down toward the warm air or up to the cold air. The tilted stack of the system causes the wind to change direction with height, thus suggesting thermal advection.

Barotropic low

When contours and isotherms are in phase, the atmosphere is said to be equivalent barotropic¾ or simply barotropic. There is no temperature advection. Lows located in pockets of cold air are also called barotropic. Barotropic lows are vertically, or nearly vertically, stacked. This means that the upper tropospheric reflection (upper-level low) of the surface system is located directly above the surface system. These systems are not associated with a contrast in air masses and no fronts accompany them.

 
You can identify the baroclinic and barotropic lows by noting the relationship between the flow and the temperatures around the system. Notice the baroclinic situation has isotherms that cross the flow pattern (temperature advection is occurring). In the barotropic situation, the isotherms and flow pattern are parallel to each other (no temperature advection is occurring).

Stable waves

This low-pressure system is usually shallow, seldom seen above the 850-mb level, and lacks upper-air support. It has a closed-cyclonic circulation and is baroclinic. This system does not intensify nor does it occlude. As it begins to form, you’ll find parallel windflow in the opposite direction on either side of the stationary polar front.

Local convection or heating increases the thickness in the local area, causing pressure falls that induce cyclonic flow and vertical motion. The winds on the cold side turn northerly and the winds on the warm side become southerly. Due to the low-level warm-air advection ahead of the low center and cold-air advection behind it, you’ll find height and pressure falls and rises, respectively.

 
Stable waves tend to propagate along fronts but without changing intensity. Since there is no upper-air support, the movement of this wave depends on the low-level warm-air advection. The amplitude of the wave is small and the pressure rises and falls are of a comparatively small size. The wave can produce significant weather over a small area and often evolve into unstable waves.

Unstable waves

Unstable waves deepen and undergo cyclogenesis. This low is also baroclinic, but it is much deeper than the stable wave because it extends higher into the troposphere. This system has upper-air support (i.e., major short-wave trough), which helps intensify it, and may progress into an occlusion (mature wave).

The initial development of an unstable wave is very similar to the stable wave. The upper-air support (an upper-air trough) is the mechanism that intensifies the cyclone. The major short-wave trough and the wave on the frontal system amplify with time as self-development occurs.

 
The unstable wave is slower moving than the stable wave and the amplitude is much larger, as depicted in figure 3–23. As the cyclone intensifies, the cold air mass pushes further south and the warm air mass is pushed to the north. It also has a large magnitude of pressure rises and falls compared to the stable wave. It is an extensive weather producer, especially ahead of the warm front portion of the system.

Mature waves

As an unstable wave continues to amplify, the low deepens back into the cold air and migrates to the +n side of the jet. The term "+n" is from the three dimensional natural coordinate system that moves with the wind flow. It’s very useful in understanding the processes involved with atmospheric motions. The n axis is oriented perpendicular to the flow, with +n oriented to the left of the flow (cold side of the jet) and –n to the right of the flow (warm side of the jet).

At this point the unstable wave evolves into a mature wave. The surface low center becomes removed from the surface temperature contrast and separated from the warm and cold fronts.

As the cyclone develops to this stage, you must have three different air masses: cold, warm, and cool. For the wave to occlude, the cold front rotates around the cyclone faster than the warm front and eventually overtakes it. As the cold front overtakes the warm front, one front is forced up over the other; this forms an upper front. An occlusion extends from the surface fronts into the cold air mass. The location of the coldest air mass compared with the wave determines the type of occlusion that forms. The point of intersection of the surface warm front, cold front, and occlusion is called the triple point. Unfavorable weather conditions occur here. It is a favorable area for the development of a new low since cyclonic turning is already occurring at this point.

Decaying waves

 
Eventually, the warm air in the warm sector associated with the mature wave is pushed aloft. In being pushed aloft, the warm air is cut off from the cyclone. Then the cyclone becomes cold-core or barotropic and the low-pressure center begins to fill. This cold-core system is known as a decaying wave. The thermal gradient across the occlusion is gradually lost, washing out the occluded portion of the front. Figure 3–24 shows the placement of the air masses as the system washes out or dissipates. The wave then disappears and the stationary polar front reestablishes.

042. Baroclinic instability

Baroclinic instability (Holton, 1979) is a process by which short waves amplify (increase amplitude with time) by extracting energy from the north/south temperature gradient. We bypass a formal investigation of baroclinic instability theory and examine two implications. First, long waves are relatively stable. Second, major short waves are most likely to amplify due to baroclinic instability. The optimum growth rate occurs for wavelengths of 3000 to 4000 km.

Baroclinic instability process

Recall that differential heating leads to a strong north/south temperature gradient in the mid-latitudes. It also results in the long-wave pattern discussed previously. This gradient is the source of potential energy which baroclinic systems tap as they strengthen. In order for a major short wave to amplify significantly, there must be a large energy transfer from the temperature gradient to the wave. The potential energy of the north/south temperature gradient is transferred to the major short wave by thermal advection throughout the troposphere.

Aloft, the thermal wave and contour wave are out of phase. Cold-air advection occurs into the contour trough; warm-air advection occurs into the contour ridge. This thermal advection, coupled with advection around the well-developed baroclinic system on the surface, causes the upper-level wave to amplify. The greater the amplitude of a short wave, the more energy is associated with it. The well-developed baroclinic system on the surface must be present to ensure thermal advection throughout the troposphere.

As the potential energy is transferred from the temperature gradient to the short wave, the short wave uses the potential energy to develop the low-level circulation of the low or high. The low-level circulation (wind) is kinetic energy. Energy is made available to the system when warm air rises and cold air sinks, as is true in mid-latitude systems. Warm air moves northward ahead of a baroclinic low; behind a baroclinic high, it ascends. Cold air moves southward ahead of a baroclinic high; behind a baroclinic low, it descends.

Because the process proceeds without outside influences if conditions are right, we call it instability. As the cyclogenesis/anticyclogenesis proceeds, the thermal advection increases and more energy is transferred to the wave. The energy then strengthens the low-level circulation. The process continues, repeating itself.

We can draw an analogy to an absolutely unstable layer on a Skew-T. Once a parcel is forced to rise, it continues to rise on its own, drawing energy from the unstable atmosphere. Once a short wave begins to amplify, it continues to amplify by drawing energy from the north/south temperature gradient.

Baroclinic instability is the primary mechanism responsible for the development of mid-latitude synoptic-scale systems (baroclinic lows and highs). These systems help maintain the global heat balance by transporting warm air northward and cold air southward as the atmosphere attempts to gain equilibrium. Amazingly, only 0.5 percent of the total potential energy of the atmosphere is available for conversion to kinetic energy. Additionally, only 10 percent of that 0.5 percent converts to kinetic energy. Imagine the consequences if the atmosphere was more efficient!

043. The development of baroclinic lows

Cyclogenesis is favored by certain large-scale conditions. In the long-wave pattern, cyclogenesis typically occurs at, and just downstream from, a long-wave trough axis. Intense cyclogenesis normally occurs in troughs with a negative tilt (Sanders and Gyakum, 1980). Negatively-tilted troughs have an axis that is oriented northwest/southeast, cause stronger divergence, and, therefore, can support stronger cyclogenesis. Positively-tilted troughs have an axis that is oriented northeast/southwest and are more often associated with non-developing systems.

The relationship between the jet stream and cyclogenesis is also very important. Cyclogenesis typically occurs under difluent flow aloft. Supergradient winds deepen troughs and are associated with difluent flow. Upper-level troughs are likely to intensify when the wind speeds upstream from the trough axis are greater than the wind speeds downstream from the axis. The determination of whether the wind speeds are decreasing downstream or not is based on the contour spacing across the trough axis.

Short-wave troughs strengthen as they move into long-wave trough positions and become negatively-tilted downstream from the long-wave trough axis. Short-wave troughs intensify under difluent upper flow, which is common in negatively-tilted troughs. The negatively-tilted difluent major short-wave trough (six words to describe one trough!) stacks 1 to 3° latitude per standard level to a baroclinic low on the surface. This trough must be present to support the baroclinic low. The baroclinic low must be there to ensure temperature advection occurs throughout the troposphere, in order for the wave to amplify.

Baroclinic instability is the link between the upper-and lower-level features. You know that baroclinic instability converts the potential energy of the north-south temperature gradient to the kinetic energy of the disturbance. The strongest north-south temperature gradient occurs at the polar front. Consequently, baroclinic lows form along the polar front. Petterssen’s rule describes the initial interplay between the frontal system and the divergence associated with the major short-wave trough. Thus, all the mechanisms causing cyclogenesis are linked together

http://www.fas.org/spp/military/docops/afwa/atmos-U3.htm

[spaceshipone (OP)]

Wow... this was way more help then I could have ever asked for. Thanks a lot.

[spaceshipone (OP)]

I was wondering if you might be able to give me your take on how energy dispersion occurs in Rossby Waves.  I was wondering if Wave trains are any evidence of this or am I way off base.  THANK YOU SOOOOO MUCH!!!!

[paul.fr]

Are you way off base? I don't think so, I may be wrong but this is still an open question. I would be interested to hear whatever you teacher / lecturer has to say on the issue.

There was a paper written last year, that is really interesting;

"Tropical Cyclone Energy Dispersion in a Three-Dimensional Primitive Equation Model: Upper Tropospheric Influence", by Xuyang Ge, Tim Li, Yuqing Wang
Department of Meteorology and International Pacific Research Center, University
of Hawaii, Honolulu, HI
and
Melinda S. Peng, Naval Research Laboratory, Monterey, California.

The three-dimensional (3D) Rossby wave energy dispersion of a tropical cyclone
(TC) is studied using a baroclinic primitive equation model. The model is initialized with
a symmetric vortex on a beta-plane in an environment at rest. The vortex intensifies
while becoming asymmetric and moving northwestward due to the beta effect, and a
synoptic-scale wave train forms in its wake a few of days later. The energy-dispersion
induced Rossby wave train has a noticeable baroclinic structure with alternating
cyclonic-anticyclonic-cyclonic (anticyclonic-cyclonic-anticyclonic) circulations in the
lower (upper) troposphere.
A key feature associated with the 3D wave train development is a downward
propagation of the relative vorticity and kinetic energy. Due to the vertical differential
inertial stability, the upper level wave train develops faster than the lower level
counterpart. The upper anticyclonic circulation rapidly induces an intense asymmetric
outflow jet at the southeast quadrant, and then further influences the lower-level Rossby
wave train. On one hand, the outflow jet exerts an indirect effect on the lower-level wave
train strength through changing TC intensity and structure. On the other hand, it triggers
downward energy propagation that further enhances the lower level Rossby wave train.
A sudden removal of the diabatic heating may initially accelerate the energy dispersion
through the increase of the radius of maximum wind and the reduction of the lower level
inflow. The latter may modulate the group velocity of the Rossby wave train through the
Doppler shift effect. The 3D numerical results illustrate more complicated Rossby wave
energy dispersion characteristics than 2D barotropic dynamics.

I have a pdf version of the full paper if you are interested?

It may be an idea to post a question in the physics section in relation to wave trains, i am no physicist, and there are some pretty smart guys there.