Divergence equation: Difference between revisions
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<div class="definition"><div class="short_definition">An equation for the rate of change of [[horizontal divergence]] on a [[parcel]] (in analogy to the [[vorticity equation]]).</div><br/> <div class="paragraph">For frictionless flow this equation is <div class="display-formula"><blockquote>[[File:ams2001glos-De36.gif|link=|center|ams2001glos-De36]]</blockquote></div> where ∇<sub>''p''</sub> · '''u''' is the horizontal divergence, ''J''(''u'', ''v'') is the [[Jacobian]], ω is the material rate of change of [[pressure]], β is the [[Rossby parameter]], ζ is the [[vertical vorticity]], and φ is the [[geopotential]]. All horizontal differentiations are carried out in a [[constant-pressure surface]]. The divergence equation is derived by taking the [[divergence]] of the vector [[equation of motion]]. When the two terms in the divergence are neglected, this equation becomes the [[balance equation]].</div><br/> </div> | <div class="definition"><div class="short_definition">An equation for the rate of change of [[horizontal divergence]] on a [[parcel]] (in analogy to the [[vorticity equation]]).</div><br/> <div class="paragraph">For frictionless flow this equation is <div class="display-formula"><blockquote>[[File:ams2001glos-De36.gif|link=|center|ams2001glos-De36]]</blockquote></div> where ∇<sub>''p''</sub> · '''u''' is the horizontal divergence, ''J''(''u'', ''v'') is the [[Jacobian]], ω is the material rate of change of [[pressure]], β is the [[Rossby parameter]], ζ is the [[vertical vorticity]], and φ is the [[geopotential]]. All horizontal differentiations are carried out in a [[constant-pressure surface]]. The divergence equation is derived by taking the [[divergence]] of the vector [[equations of motion|equation of motion]]. When the two terms in the divergence are neglected, this equation becomes the [[balance equation]].</div><br/> </div> | ||
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Latest revision as of 15:49, 25 April 2012
divergence equation
An equation for the rate of change of horizontal divergence on a parcel (in analogy to the vorticity equation).
For frictionless flow this equation is where ∇p · u is the horizontal divergence, J(u, v) is the Jacobian, ω is the material rate of change of pressure, β is the Rossby parameter, ζ is the vertical vorticity, and φ is the geopotential. All horizontal differentiations are carried out in a constant-pressure surface. The divergence equation is derived by taking the divergence of the vector equation of motion. When the two terms in the divergence are neglected, this equation becomes the balance equation.
