stream function

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Stream function

In fluid mechanics, a mathematical idea which satisfies identically, and therefore eliminates completely, the equation of mass conservation. If the flow field consists of only two space coordinates, for example, x and y, a single and very useful stream function ψ(x, y) will arise. If there are three space coordinates, such as (x, y, z), multiple stream functions are needed, and the idea becomes much less useful and is much less widely employed.

The stream function not only is mathematically useful but also has a vivid physical meaning. Lines of constant ψ are streamlines of the flow; that is, they are everywhere parallel to the local velocity vector. No flow can exist normal to a streamline; thus, selected ψ lines can be interpreted as solid boundaries of the flow.

Further, ψ is also quantitatively useful. In plane flow, for any two points in the flow field, the difference in their stream function values represents the volume flow between the points. See Creeping flow, Fluid flow

stream function

[′strēm ‚fəŋk·shən]
(fluid mechanics)
References in periodicals archive ?
Naeem and Ali, 1996), by introducing the streamfunction and the generalized energy function, transformed equations into a new system of equations and obtained some new solutions by employing some functional forms of the streamfunction.
Our aim is to initially eliminate the appearance of the pressure term in the equations, and to this end, we introduce streamfunction and vorticity formulae in two-dimensional coordinates to enable computation of the velocity components without any assumptions on the pressure.
In studying Riabouchinsky flows [4] the streamfunction is taken to be linear in one of the space dimensions.
We introduce the streamfunction and vorticity formulas in the two-dimensional cylindrical coordinates for the governing equations in order to avoid the explicit appearance of the pressure term.
The stochastic kinetic energy backscatter scheme (SKEBS) aims to represent model uncertainty arising from unresolved subgrid-scale processes and their interactions with larger scales by introducing random perturbations to the streamfunction and potential temperature tendencies.
If shows the 250 mb streamfunction and SST differences between low and high snow frequency years.
the references cited earlier), many stratospheric circulation indices, such as the northern annular mode (NAM), zonal mean zonal wind, polar vortex oscillation, eddy poleward heat flux (or the vertical component of the Eliassen-Palm flux), and streamfunction of the residual circulation inferred from the downward control principle, may bear long-lead precursor information (0-60 days) for surface temperature anomalies.
The 200-hPa streamfunction pattern also showed a typical El Nino signal, with anticyclonic anomalies across the subtropical Pacific Ocean in both hemispheres flanking the region of enhanced El Nino-related convection (see Fig.
An examination of the standardized streamfunction and vector wind anomalies associated with this wave pattern shows three ways in which it was a primary contributor to the observed north-south dipole patterns of vertical wind shear and upper-level divergence in the Atlantic basin.
The analysis is based upon ASO standardized streamfunction indices for the three regions shown in Fig.