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The Stokes I, Q, U and V parameters. The Stokes parameters are a set of values that describe the polarization state of electromagnetic radiation.They were defined by George Gabriel Stokes in 1851, [1] [2] as a mathematically convenient alternative to the more common description of incoherent or partially polarized radiation in terms of its total intensity (I), (fractional) degree of ...
When the Womersley parameter is low, viscous forces tend to dominate the flow, velocity profiles are parabolic in shape, and the center-line velocity oscillates in phase with the driving pressure gradient. [2] Starting with Navier–Stokes equation for Cartesian flow:
Examples of degenerate cases—with the non-linear terms in the Navier–Stokes equations equal to zero—are Poiseuille flow, Couette flow and the oscillatory Stokes boundary layer. But also, more interesting examples, solutions to the full non-linear equations, exist, such as Jeffery–Hamel flow , Von Kármán swirling flow , stagnation ...
In fluid dynamics, Stokes' law gives the frictional force – also called drag force – exerted on spherical objects moving at very small Reynolds numbers in a viscous fluid. [1] It was derived by George Gabriel Stokes in 1851 by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations .
Poincaré sphere, on or beneath which the three Stokes parameters [S 1, S 2, S 3] (or [Q, U, V]) are plotted in Cartesian coordinates Depiction of the polarization states on Poincaré sphere. Often the total beam power is not of interest, in which case a normalized Stokes vector is used by dividing the Stokes vector by the total intensity S 0:
When the bases are rotated by 45 degrees around the viewing axis, the definition of the third Stokes component becomes equivalent [dubious – discuss] [clarification needed] to that of the second, that is the difference in field intensity between the horizontal and vertical polarizations. Thus, if the instrument is rotated out of plane from ...
In fluid mechanics, non-dimensionalization of the Navier–Stokes equations is the conversion of the Navier–Stokes equation to a nondimensional form. This technique can ease the analysis of the problem at hand, and reduce the number of free parameters. Small or large sizes of certain dimensionless parameters indicate the importance of certain ...
The input stokes parameters q and u are then with respect to North but in the altitude-azimuth frame. We can easily unwrap q assuming it is in the +altitude direction. From the basic definition we know that +Q is an angle of 0° and -Q is an angle of 90°. Therefore, Q is calculated from a sine function.