Fluid parcel
Influid dynamics,afluid parcel,also known as afluid elementormaterial element,is aninfinitesimalvolumeof fluid, identifiable throughout its dynamic history while moving with the fluid flow.[1]As it moves, themassof a fluid parcel remains constant, while—in acompressible flow—its volume may change,[2][3]and its shape changes due to distortion by the flow.[1]In anincompressible flow,the volume of the fluid parcel is also a constant (isochoricflow).
Material surfacesandmaterial linesare the corresponding notions forsurfacesandlines,respectively.[1][4]
The mathematical concept of a fluid parcel is closely related to the description of fluid motion—itskinematicsanddynamics—in aLagrangian frame of reference.In this reference frame, fluid parcels are labelled and followed through space and time. But also in theEulerian frame of referencethe notion of fluid parcels can be advantageous, for instance in defining thematerial derivative,streamlines, streaklines, and pathlines;or for determining theStokes drift.[1]
The fluid parcels, as used incontinuum mechanics,are to be distinguished from microscopicparticles(molecules and atoms) inphysics.Fluid parcels describe theaveragevelocity and other properties of fluid particles, averaged over alength scalewhich is large compared to themean free path,but small compared to thetypical length scalesof the specific flow under consideration. This requires theKnudsen numberto be small, as is also a pre-requisite for the continuum hypothesis to be a valid one.[2][4][5]Further note, that unlike the mathematical concept of a fluid parcel which can be uniquely identified—as well as exclusively distinguished from its direct neighbouring parcels—in a real fluid such a parcel would not always consist of the same particles.Molecular diffusionwill slowly evolve the parcel properties.[2][4]
References
[edit]- ^abcdBatchelor (1973),pp. 71–72
- ^abcGill (1982),pp. 63–64
- ^Bennett (2006),pp. 25
- ^abcThompson (2006),pp. 1–2
- ^Batchelor (1973),pp. 4–6
Bibliography
[edit]- Batchelor, George K.(1973).An introduction to fluid dynamics.Cambridge: Cambridge University Press.ISBN978-0-521-09817-5.
- Gill, Adrian E. (1982).Atmosphere–ocean dynamics.New York: Academic Press.ISBN978-0-12-283522-3.
- Thompson, Michael (2006).An introduction to astrophysical fluid dynamics.Imperial College Press.ISBN978-1-86094-615-8.
- Bennett, Andrew (2006).Lagrangian fluid dynamics.Cambridge: Cambridge University Press.ISBN978-0-521-85310-1.
- Badin, G.; Crisciani, F. (2018).Variational Formulation of Fluid and Geophysical Fluid Dynamics - Mechanics, Symmetries and Conservation Laws -.Springer. p. 218.doi:10.1007/978-3-319-59695-2.ISBN978-3-319-59694-5.S2CID125902566.