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### 3.4.5 The Saffman-Spalding KE-VO model

### (a) Origin

In 1968, Saffmann and Spalding independently proposed the use of a two-equation model
of which the first dependent variable was the energy, KE, and the second, here referred to
as VO, was a measure of the fluctuations of vorticity.

Since it was two-dimensional boundary-layer flows which were chiefly thought of at that
time, it was the direction of the vorticity which was thought of was that normal both to
the main flow and to the plane in which it was confined. However, this assumption had no
effect on the form of the equations.

### (b) The effective-viscosity presumption

In accordance with the requirements of dimensional analysis, then efective-viscosity
formula took the form:

EV = const * KE / VO**0.5

### (c) Implementation in PHOENICS

### (d) References

PG Saffmann (1970) "A model for inhomogeneous turbulent flow"; Proc Roy Soc
London vol A317 pp 417-433

DB Spalding (1969) "The prediction of two-dimensional steady turbulent elliptic
flows" ICHMT Seminar, Herceg Novi, Yugoslavia

Some discussion of the model will be found in the following:

BE Launder and DB Spalding (1972) "Mathematical Models of Turbulence",
Academic Press

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