This study evaluated three algebraic stress models for predicting turbulent stresses near the free surface in a free-surface jet at nonzero Froude number, by comparing to experiments. The models examined included one with no explicit near-surface modeling, one which specified model coefficients in terms of invariants of the anisotropy tensor, and a third model which employed a surface correction with an ad-hoc damping function. Experiment showed that at low Froude number, the anisotropy near the free surface did not attain the limiting behavior characteristic of two-dimensional turbulence and the anisotropy increased with streamwise distance. At high Froude number the surface can have little effect on the anisotropy. Far from the free surface, all the models performed well. For the model with no explicit free-surface modeling, the turbulence near the free surface was predicted to be isotropic. For the “anisotropy-invariant” model, the predicted anisotropy was too small and confined to locations too near the free surface. The model with the ad-hoc damping function captured the anisotropy near the free surface best, but specification of the decay constant in the damping function is an open question.

1.
Anthony
D. G.
, and
Willmarth
W. W.
,
1992
, “
Turbulence Measurements in a Round Jet Near a Free Surface
,”
Journal of Fluid Mechanics
, Vol.
243
, pp.
699
720
.
2.
Daly
B. J.
, and
Harlow
F. H.
,
1970
, “
Transport Equations of Turbulence
,”
Physics of Fluids
, Vol.
13
, p.
2634
2634
.
3.
Launder
B. E.
, and
Shima
N.
,
1989
, “
A Second Moment Closure for the Near-Wall Sublayer: Development and Application
,”
AIAA Journal
, Vol.
27
, pp.
1319
1325
.
4.
Launder
B. E.
,
Reece
G. J.
, and
Rodi
W.
,
1975
, “
Progress in Development of a Reynolds-Stress Closure
,”
Journal of Fluid Mechanics
, Vol.
68
, pp.
537
566
.
5.
Miner, E. W., Stewart, M. B., and Swean, T. F., 1993, “Modeling and Computation of Turbulent Free-Surface Jets,” AIAA Paper No. 93–0201.
6.
Miner, E. W., Swean, T. F., and Troesch, A. W., 1988, “Evaluation and Additional Documentation of the Parabolic Marching Code SURFWAKE,” NRL Memorandum Report 6331, Naval Research Laboratory, Washington, D.C.
7.
Naot
D.
, and
Rodi
W.
,
1982
, “
Calculation of Secondary Currents in Channel Flow
,”
Journal of the Hydraulics Division ASCE
, Vol.
108
, pp.
948
968
.
8.
Rodi, W., 1984, Turbulence Models and their Application in Hydraulics, IAHR, Delft.
9.
Rotta
J. C.
,
1951
, “
Statistiche Theorie nichtmonger Turbulenz
,”
Z. Physics
, Vol.
129
, p.
547
547
.
10.
Shir
C. C.
,
1973
, “
A Preliminary Model of Atmospheric Turbulent Flow in an Idealized Turbulent Boundary Layer
,”
Journal of Atmospheric Science
, Vol.
30
, pp.
1327
1329
.
11.
Speziale
C. G.
,
Sarkar
S.
, and
Gatski
T. B.
,
1991
, “
Modeling the Pressure-Strain Correlation of Turbulence: An Invariant Dynamical Systems Approach
,”
Journal of Fluid Mechanics
, Vol.
227
, pp.
245
272
.
12.
Swean, T. F., Leighton, R. I., Handler, R. A., and Swearingen, J. D., 1991, “Turbulence Modeling Near the Free Surface in Open Channel Flow,” AIAA Paper No. 91–0613.
13.
Swean
T. F.
,
Ramberg
S. E.
, and
Miner
E. W.
,
1991
, “
Anisotropy in a Turbulent Jet Near a Free Surface
,”
ASME JOURNAL OF FLUIDS ENGINEERING
, Vol.
113
, pp.
430
438
.
14.
Tahara, Y., Stern, F., and Rosen, B., 1991, “An Interactive Approach for Calculating Ship Boundary Layers and wakes for Nonzero Froude Number,” Eighteenth Symposium on Naval Hydrodynamics, National Academy Press, Washington, D.C, pp. 699–719.
15.
Walker
D. T.
,
Chen
C.-Y.
, and
Willmarth
W. W.
,
1995
, “
Turbulent Structure in Free-Surface Jet Flows
,”
Journal of Fluid Mechanics
, Vol.
291
, pp.
223
262
.
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