Lagrangian coordinates: Difference between revisions

Latest revision as of 16:18, 25 April 2012

Lagrangian coordinates

(Also called material coordinates.) 1. A system of coordinates by which fluid parcels are identified for all time by assigning them coordinates that do not vary with time.

Examples of such coordinates are 1) the values of any properties of the fluid conserved in the motion; or 2) more generally, the positions in space of the parcels at some arbitrarily selected moment. Subsequent positions in space of the parcels are then the dependent variables, functions of time and of the Lagrangian coordinates. Few observations in meteorology are Lagrangian; this would require successive observations in time of the same air parcel. Exceptions are the constant- pressure balloon observation, which attempts to follow a parcel under the assumption that its pressure is conserved, and certain small-scale observations of diffusing particles.
Compare Eulerian coordinates;
see also Lagrangian equations.
Same as generalized coordinates.

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-#<div class="definition"><div class="short_definition">(''Also called'' material coordinates.) 1. A system of coordinates by which  fluid parcels are identified for all time by assigning them coordinates that do not vary with time.</div><br/> <div class="paragraph">Examples of such coordinates are 1) the values of any properties of the fluid conserved in the  motion; or 2) more generally, the positions in space of the parcels at some arbitrarily selected  moment. Subsequent positions in space of the parcels are then the dependent variables, functions  of time and of the Lagrangian coordinates. Few observations in meteorology are Lagrangian; this  would require successive observations in time of the same [[air parcel]]. Exceptions are the [[constant-  pressure balloon]] observation, which attempts to follow a parcel under the assumption that its  [[pressure]] is conserved, and certain small-scale observations of diffusing [[particles]]. <br/>''Compare''  [[Eulerian  coordinates]]; <br/>''see also'' [[Lagrangian equations]].</div><br/> </div>
+#<div class="definition"><div class="short_definition">(''Also called'' material coordinates.) 1. A system of coordinates by which  fluid parcels are identified for all time by assigning them coordinates that do not vary with time.</div><br/> <div class="paragraph">Examples of such coordinates are 1) the values of any properties of the fluid conserved in the  motion; or 2) more generally, the positions in space of the parcels at some arbitrarily selected  moment. Subsequent positions in space of the parcels are then the dependent variables, functions  of time and of the Lagrangian coordinates. Few observations in meteorology are Lagrangian; this  would require successive observations in time of the same [[air parcel]]. Exceptions are the [[constant-level balloon|constant-  pressure balloon]] observation, which attempts to follow a parcel under the assumption that its  [[pressure]] is conserved, and certain small-scale observations of diffusing [[particles]]. <br/>''Compare''  [[Eulerian coordinates|Eulerian  coordinates]]; <br/>''see also'' [[Lagrangian equations]].</div><br/> </div>
 #<div class="definition"><div class="short_definition"><br/>''Same as'' [[generalized coordinates]].</div><br/> </div>
 </div>