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The Eulerian specification of the flow field is a way of looking at fluid motion that focuses on specific locations in the space through which the fluid flows as time passes. [ 1 ] [ 2 ] This can be visualized by sitting on the bank of a river and watching the water pass the fixed location.
Thanks to these vector identities, the incompressible Euler equations with constant and uniform density and without external field can be put in the so-called conservation (or Eulerian) differential form, with vector notation: {+ (+) = + =, or with Einstein notation: {+ (+) = + =,
In continuum mechanics, the material derivative [1] [2] describes the time rate of change of some physical quantity (like heat or momentum) of a material element that is subjected to a space-and-time-dependent macroscopic velocity field. The material derivative can serve as a link between Eulerian and Lagrangian descriptions of continuum ...
Continuity in the Eulerian description is expressed by the spatial and temporal continuity and continuous differentiability of the flow velocity field. All physical quantities are defined this way at each instant of time, in the current configuration, as a function of the vector position x {\displaystyle \mathbf {x} } .
In fluid dynamics and plasma physics, the Clebsch representation provides a means to overcome the difficulties to describe an inviscid flow with non-zero vorticity – in the Eulerian reference frame – using Lagrangian mechanics and Hamiltonian mechanics.
In scientific visualization, Lagrangian–Eulerian advection is a technique mainly used for the visualization of unsteady flows. The computer graphics generated by the technique can help scientists visualize changes in velocity fields. This technique uses a hybrid Lagrangian and Eulerian specification of the flow field.
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases.It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of water and other liquids in motion).
For very small particle diameter the latter is locally a constant whose value is given by the undisturbed Eulerian field evaluated at the location of the particle center, () = ((),). The small particle size also implies that the disturbed flow can be found in the limit of very small Reynolds number, leading to a drag force given by Stokes' drag .