Deformation

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deformation

The change in shape of a fluid mass by spatial variations in the velocity field, specifically by stretching or shearing.

A linear analysis of the two-dimensional velocity field can express this field in terms of divergence, vorticity, and deformation (or, more strictly, the rate of deformation)
ams2001glos-De10
ams2001glos-De11
where the subscript "0" refers to a selected fixed origin, and where
ams2001glos-De12
A pure stretching deformation field (u = a0x, v = -a0y) is characterized by rectangular hyperbolic streamlines. It has two characteristic axes: an axis of dilatation toward which streamlines converge asymptotically, and an axis of contraction from which streamlines diverge asymptotically. A pure shearing deformation field (u = a0y, v = a0x) is also characterized by rectangular hyperbolic streamlines, but the characteristic axes are rotated 45° from the coordinate axes. The resultant deformation is a combination of the stretching and shearing deformation fields by the appropriate choice of coordinates, which define the principal characteristic axes. Deformation is a primary factor in the processes of frontogenesis and frontolysis.

Holton, J. R. 1992. An Introduction to Dynamic Meteorology. 3d edition, Academic Press, . 266–277.

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