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| | '''Deformation''' is the rate of change of shape of fluid bodies. Meteorologically, this quantity is very important in the formation of [[Weather fronts|atmospheric fronts]], in the explanation of [[cloud]] shapes, and in the diffusion of materials and properties.<ref name="Djurić, D 1994">Djurić, D: "Weather Analysis". Prentice Hall, 1994. ISBN 0-13-501149-3.</ref> |
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| | ==Equations== |
| | The deformation of horizontal wind is defined as <math> \operatorname{def} \mathbf{V} = \sqrt{A^2 + B^2}</math>, where <math>\ A = \frac{\partial v}{\partial x} + \frac{\partial u}{\partial y}</math> and <math>\ B = \frac{\partial u}{\partial x} - \frac{\partial v}{\partial y}</math>, representing the derivatives of wind component. Because these derivatives vary greatly with the rotation of the coordinate system, so do <math>\ A</math> and <math>\ B</math>.<ref name="Djurić, D 1994" /> |
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| | ==Stretching direction== |
| | The deformation elements <math>\ A</math> and <math>\ B</math> (above) can be used to find the ''direction of the dilatation axis'', the line along which the material elements stretch (also known as the ''stretching direction''). Several flow patterns are characteristic of large deformation: confluence, diffluence, and shear flow. '''{{visible anchor|Confluence}}''', also known as ''stretching'', is the elongating of a fluid body along the flow (streamline convergence). '''{{visible anchor|Diffluence}}''', also known as ''shearing'', is the elongating of a fluid body normal to the flow (streamline divergence).<ref name="Djurić, D 1994" /> |
| | |
| | ==See also== |
| | *[[Wind shear]] |
| | *[[Convergence zone]] |
| | *[[Divergence]] |
| | |
| | ==References== |
| | {{Reflist}} |
| | |
| | {{DEFAULTSORT:Deformation (Meteorology)}} |
| | [[Category:Vector calculus]] |
Revision as of 14:11, 2 November 2013
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Deformation is the rate of change of shape of fluid bodies. Meteorologically, this quantity is very important in the formation of atmospheric fronts, in the explanation of cloud shapes, and in the diffusion of materials and properties.[1]
Equations
The deformation of horizontal wind is defined as , where and , representing the derivatives of wind component. Because these derivatives vary greatly with the rotation of the coordinate system, so do and .[1]
Stretching direction
The deformation elements and (above) can be used to find the direction of the dilatation axis, the line along which the material elements stretch (also known as the stretching direction). Several flow patterns are characteristic of large deformation: confluence, diffluence, and shear flow. Template:Visible anchor, also known as stretching, is the elongating of a fluid body along the flow (streamline convergence). Template:Visible anchor, also known as shearing, is the elongating of a fluid body normal to the flow (streamline divergence).[1]
See also
References
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- ↑ 1.0 1.1 1.2 Djurić, D: "Weather Analysis". Prentice Hall, 1994. ISBN 0-13-501149-3.