## 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) where the subscript "0" refers to a selected fixed origin, and where A pure stretching deformation field (

*u*=*a*_{0}*x*,*v*= -*a*_{0}*y*) 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*=*a*′_{0}*y*,*v*=*a*′_{0}*x*) 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.