# 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 ?
Also shown are observed patterns of the 5-day mean anomalies during the period P in (d) DSW (shading), sea level pressure (contours; 1.0-hPa interval), and surface winds (vectors) and (e) OLR (shading) and 500-hPa streamfunction (contours; 2 x [10.sup.6] [m.sup.2] [s.sup.-1] interval).
Figure 7 showed the temporal evolutions of the anomalous streamfunction averaged over the Philippine Sea (120-150[degrees]E, 10-20[degrees]N) at 850 hPa (S850), composed from PE years, PI years, and PEI years, respectively.
The nondimensional streamfunction f(s, [eta]) is related to the streamfunction [psi](x, y) through
(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  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.
Overlaid in (a) are the total 200-hPa streamfunction field (contours, interval: 5 x [10.sup.6] [m.sup.2] [s.sup.-1]) and the 200-850 hPa layer mean wind vectors (m [s.sup.-1]) representing the steering current.
Finally, we compare in Table 4.3 the position ([x.sub.c],[y.sub.c]) of the main vortex and the values of the streamfunction [[PHI].sub.mine] and of the vorticity [w.sub.c], in the ([x.sub.c], [x.sub.y]).
(e) The impact of the Polzin parameterization in the GFDL CM2G coupled climate model: (top) the Indo-Pacific meridional overturning streamfunction (Sv; 1 Sv = [10.sup.6] [m.sup.3] [s.sup.-1]; averaged over the final 100 years of a 1000-yr simulation) using the Polzin (2009) parameterization and (bottom) the differences in Indo- Pacific meridional overturning streamfunction (Sv) between the simulations with the Polzin (2009) parameterization and the St.
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.

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