Deformation in the wind field

In a changing wind field four different kind of variations can affect elements flowing in the field (such as clouds and humid areas): translation, divergence, vorticity and deformation. The correspondent changes in clouds and humid areas are:

variation in the wind field	change to the cloud
Translation	location
Divergence	area
Vorticity	orientation
Deformation	shape

• Translation shifts elements
• Divergence either contracts (convergence) or expands (divergence) elements
• Vorticity rotates elements either cyclonically (positive vorticity) or anticyclonically (negative vorticity)
• Deformation changes the shape of the elements

Mathematically the deformation D can be written as a sum of two components, stretching and shearing deformation (Dst and Dsh) as follows:

D = √Dst² + Dsh² , where in a (x,y)-plane

Dst = ∂u/∂x - ∂v/∂y and
Dsh = ∂u/∂y + ∂v/∂x,

u being the wind component in x-direction, v in y-direction.

The effect of stretching and shearing terms can be represented schematically as follows: In the schematics above it can be seen that a col (saddle surface) and a confluent zone are required for the deformation to occur.

In the satellite images the stretching and shearing deformation can be pictured as follows:

The col surface can also be half of a saddle, which leads to the formation of a "mushroom pattern" (a curved cloud band):

Typical locations for Deformation Bands

Deformation zones are generated by opposing flows. Typical situations in which deformation occurs, are those in which the cloud bands of two synoptic or meso-scale cloud systems are brought close to each other. Once they start merging, the elongation of the cloud band becomes obvious.

The location of deformation is most often a col (see sketches before). The maximum of a deformation field is nearly always in the confluent area of the wind field, on the colder side of it. At the saddle point the deformation is non-existent.

The most likely location is the area near the pole ward boundary of Warm Front and Occlusion cloud bands. Often a cold front approaches this cloud area from the north. The cloud bands merge, then they start to elongate. In the end the cloud band breaks somewhere in the middle of the band, and the rest of the cloudiness dissipates.

Deformation zones are seen as linear structures with diverging moisture parcels along the line. The intensity of the deformation zone is proportional to the contrast in moisture gradient across the zone.

The moisture gradient is typically sharpest pole wards of the Deformation Band. Dry sinking air coming from the north is advected towards the axis of dilatation, which can be seen as a dark area in WV imagery. The contrast between dry and moist air is enhanced by the transportation of moist air from the south by the moist upper level conveyor belt.

Deformation Bands and Frontogenesis

Deformation is a primary factor in frontogenesis and frontolysis.

The full frontogenesis function F_t consists of three components: F_t = F_h + F_v + F_q, where F_t is frontogenesis caused by horizontal wind field, F_v frontogenesis by vertical motions and F_q frontogenesis by diabatic heating. The contribution from F_h is necessary for the formation of synoptic scale fronts. It can be expressed as:

where D_tot is the total deformation, D is the horizontal wind divergence and b the angle between the axis of dilatation and the isentropes.

Frontogenesis can occur when cos2b > 0, which means that 2b < 90° or b < 45°. Frontolysis can occur when 45° < b < 90°.
Frontogenesis is strongest in the confluence zone, and zero in the saddle point, where there is no wind.

The effect of vorticity on the deformation field is shown the following diagram:

Deformation Bands and Jet Fibres

Deformation Bands have a somewhat similar appearance to Jet Fibres towards the end their life cycle (see Jet Fibres ). Their origins and often also the locations with respect to jet streams, however, are different. The similarities and differences can be briefly listed as follows:

• Jet Fibres occur only in the vicinity of an upper level jet. Deformation Bands extends to areas with weak winds, usually a col.
• Jet fibres associated with a Cold Front occur only on the cold side of the front, whereas Deformation Bands are more likely on the warm side of a Cold Front.
• Jet Fibres have a typical life cycle ranging from 8 hours up to 24 hours. Deformation Bands have shorter life-cycles, due to the strong sinking motion that takes place at the poleward side of the cloud band. Typical life cycle for Deformation Band cloudiness is 6-9 hours.
• Both Jet Fibres and Deformation Bands have a dark stripe in WV imagery along the cold side of the cloudiness due to sinking motion at upper and middle troposphere.
• Jet Fibres experience deformation when they are brought into a deforming wind field. They should in this case be still classified as Jet Fibres due to their origin.

The example below illustrates a case showing Jet Fibres and Deformation Band over the Atlantic Ocean. The Deformation Band is within weak, but confluent upper level flow, whereas the Jet Fibres, more to the south, are clearly associated with a polar front jet streak.