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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.
In a steady flow of an inviscid fluid without external forces, the center of curvature of the streamline lies in the direction of decreasing radial pressure. Although this relationship between the pressure field and flow curvature is very useful, it doesn't have a name in the English-language scientific literature. [25]
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.
The material derivative can serve as a link between Eulerian and Lagrangian descriptions of continuum deformation. [3] For example, in fluid dynamics, the velocity field is the flow velocity, and the quantity of interest might be the temperature of the fluid.
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} } .
Fluid kinematics is a term from fluid mechanics, [1] usually referring to a mere mathematical description or specification of a flow field, divorced from any account of the forces and conditions that might actually create such a flow.
In physics, one distinguishes different reference frames depending on where the observer is located, this is the basics for the Lagrangian and Eulerian specification of the flow field in fluid dynamics: The observer can be either in the Moving frame (as for a Lagrangian drifter) or in a resting frame.
Semi-Lagrangian schemes use a regular (Eulerian) grid, just like finite difference methods. The idea is this: at every time step the point where a parcel originated from is calculated. An interpolation scheme is then utilized to estimate the value of the dependent variable at the grid points surrounding the point where the particle originated from.