Particle image velocimetry (PIV) experiments have been conducted to study the velocity flow fields in the developing flow region of high-speed jets. These velocity distributions were examined to determine the entrained mass flow over a range of geometric and flow conditions, including overpressured cases up to an overpressure ratio of 2.83. In the region near the jet exit, all measured flows exhibited the same entrainment up until the location of the first shock when overpressured. Beyond this location, the entrainment was reduced with increasing overpressure ratio, falling to approximately 60% of the magnitudes seen when subsonic. Since entrainment ratios based on lower speed, subsonic results are typically used in one-dimensional volcanological models of plume development, the current analytical methods will underestimate the likelihood of column collapse. In addition, the concept of the entrainment ratio normalization is examined in detail, as several key assumptions in this methodology do not apply when overpressured.

References

References
1.
Solovitz
,
S. A.
, and
Mastin
,
L. G.
, 2009, “
Experimental Study of Near-Field Air Entrainment by Subsonic Volcanic Jets
,”
J. Geophys. Res.
,
114
(
B10203
).
2.
Kaminski
,
E.
,
Tait
,
S.
, and
Carazzo
,
G.
, 2005, “
Turbulent Entrainment in Jets With Arbitrary Buoyancy
,”
J. Fluid Mech.
,
526
, pp.
361
376
.
3.
Ogden
,
D. E.
,
Wohletz
,
K.
,
Glatzmaier
,
G. A.
, and
Brodsky
,
E. E.
, 2008, “
Numerical Simulations of Volcanic Jets: Importance of Vent Overpressure
,”
J. Geophys. Res.
,
113
(
B02204
).
4.
Morton
,
B. R.
,
Taylor
,
G.
, and
Turner
,
J. S.
, 1956, “
Turbulent Gravitational Convection From Maintained and Instantaneous Sources
,”
Proc. R. Soc. London, Ser. A
,
234
, pp.
1
23
.
5.
Fischer
,
H. B.
,
Imberger
,
J.
,
List
,
E. J.
,
Koh
,
R. C. Y.
, and
Brooks
,
N. H.
, 1979,
Mixing in Inland and Coastal Waters
,
Academic
,
New York
, pp.
315
389
.
6.
Turner
,
J. S.
, 1986, “
Turbulent Entrainment: The Development of the Entrainment Assumption, and its Application to Geophysical Flows
,”
J. Fluid Mech.
,
173
, pp.
431
471
.
7.
Mastin
,
L.G.
, 2007, “
A User-Friendly One-Dimensional Model for Wet Volcanic Plumes
,”
Geochem., Geophys., Geosyst.
,
8
.
8.
Sparks
,
R. S. J.
,
Bursik
,
M. I.
,
Carey
,
S. N.
,
Gilbert
,
J. S.
,
Glaze
,
L. S.
,
Sigurdsson
,
H.
, and
Woods
,
A. W.
, 1997,
Volcanic Plumes
,
Wiley
,
Chichester
, pp.
88
116
.
9.
Pope
,
S.
, 2000,
Turbulent Flows
,
Cambridge University Press
:
Cambridge, UK
,
pp.
96
111
.
10.
Kieffer
,
S. W.
, and
Sturtevant
,
B.
, 1984, “
Laboratory Studies of Volcanic Jets
,”
J. Geophys. Res.
,
89
(
B10
), pp.
8253
8268
.
11.
Koyaguchi
,
T.
,
Suzuki
,
Y. J.
, and
Kozono
,
T.
, 2010, “
Effects of the crater on eruption column dynamics
,”
Journal of Geophysical Research,
115 (B07205).
12.
Saad
,
M. A.
, 1993,
Compressible Fluid Flow
,
2nd ed.
,
Prentice Hall
,
Englewood Cliffs, NJ
, pp.
199
227
, 340–341
.
13.
Smits
,
A. J.
, and
Dussauge
,
J.-P.
, 2006,
Turbulent Shear Layers in Supersonic Flow
,
Springer
,
New York
.
14.
Friedman
,
P. D.
,
Vadakoot
,
V. D.
,
Meyer
, Jr.,
W. J.
, and
Carey
,
S.
, 2007, “
Instability Threshold of a Negatively Buoyant Fountain
,”
Exp. Fluids
,
42
, pp.
751
759
.
15.
Liepmann
,
D.
, 1991, “
Streamwise Vorticity and Entrainment in the Near Field of a Round Jet
,”
Phys. Fluids A
,
31
(
5
), pp.
1179
1185
.
16.
Lourenco
,
L.
, and
Krothapalli
,
A.
, 1988, “
Particle Image Displacement Velocimetry Measurements of a Three-Dimensional Jet
,”
Phys. Fluids
,
31
(
7
), pp.
1835
1837
.
17.
Mi
,
J.
Kalt
,
P.
Nathan
,
G. J.
, and
Wong
,
C. Y.
, 2007, “
PIV Measurements of a Turbulent Jet Issuing From Round Sharp-Edged Plate
,”
Exp. Fluids
,
42
, pp.
625
637
.
18.
Yüceil
,
K. B.
,
Ötügen
,
M. V.
, and
Arik
,
E.
, 2000, “
Underexpanded Sonic Jets: A PIV Study
,”
Proceedings of the 10th International Symposium on the Applications of Laser Techniques to Fluid Mechanics
,
Calouste Gulbenkian Foundation
,
Lisbon, Portugal
.
19.
Liepmann
,
D.
, and
Gharib
,
M.
, 1992, “
The Role of Streamwise Vorticity in the Near-Field Entrainment of Round Jets
,”
J. Fluid Mech.
,
245
, pp.
643
668
.
20.
Hussein
,
H. J.
,
Capp
,
S. P.
, and
George
,
W. K.
, 1994, “
Velocity Measurements in a High-Reynolds-Number, Momentum-Conserving, Axisymmetric, Turbulent Jet
,”
J. Fluid Mech.
,
258
, pp.
31
75
.
21.
Raffel
,
M.
,
Willert
,
C. E.
, and
Kompenhans
,
J.
, 1998,
Particle Image Velocimetry: A Practical Guide
,
Springer
,
Berlin
.
22.
Kays
,
W. M.
, and
Crawford
,
M. E.
, 1993,
Convective Heat and Mass Transfer
, Second Edition,
McGraw-Hill
,
New York
.
23.
Chuech
,
S. G.
,
Lai
,
M.-C.
, and
Faeth
,
G. M.
, 1989, “
Structure of Turbulent Sonic Underexpanded Free Jets
,”
AIAA J.
,
27
(
5
), pp.
549
559
.
24.
Cumber
,
P. S.
,
Fairweather
,
M.
,
Falle
,
S. A. E. G.
, and
Giddings
,
J. R.
, 1994, “
Predictions of the Structure of Turbulent, Moderately Underexpanded Jets
,”
J. Fluids Eng.
,
116
, pp.
707
713
.
25.
Ladenburg
,
R.
,
Van Voorhis
,
C. C.
, and
Winckler
,
J.
, 1949, “
Interferometric Studies of Faster than Sound Phenomena. Part II. Analysis of Supersonic Air Jets
,”
Phys. Rev.
,
76
(
1
), pp.
662
677
.
26.
Falcone
,
A. M.
, and
Cataldo
,
J. C.
, 2003, “
Entrainment Velocity in an Axisymmetric Turbulent Jet
,”
J. Fluids Eng.
,
125
, pp.
620
627
.
27.
Davies
,
P.
,
Fisher
,
M.
, and
Barratt
,
M.
, 1963,
‘‘The Characteristics of the Turbulence in the Mixing Region of a Round Jet
,”
J. Fluid Mech.
,
15
, pp.
337
367
.
28.
Wygnanski
,
I.
, and
Fiedler
,
H.
, 1969,
‘‘Some Measurements in the Self-Preserving Jet
,”
J. Fluid Mech.
,
38
, pp.
577
612
.
29.
Agrawal
,
A.
, and
Prasad
,
A. K.
, 2003, “
Flow Profiles of Turbulent Jets, Plumes, and Wakes
,”
J. Fluids Eng.
,
125
, pp.
813
822
.
30.
Woods
,
A. W.
, 1993, “
Moist Convection and the Injection of Volcanic Ash into the Atmosphere
,”
J. Geophys. Res.
,
98
(
B10
), pp.
17627
17636
.
31.
Woods
,
A. W.
, and
Bower
,
S. M.
, 1995, “
The Decompression of Volcanic Jets in a Crater During Explosive Volcanic Eruptions
,”
Earth Planet. Sci. Lett.
,
131
, pp.
189
205
.
32.
Ricou
,
F. P.
, and
Spalding
,
D. B.
, 1961, “
Measurements of Entrainment by Axisymmetrical Turbulent Jets
,”
J. Fluid Mech.
,
11
, pp.
21
32
.
33.
Crow
,
S. C.
, and
Champagne
,
F. H.
, 1971, “
Orderly Structure in Jet Turbulence
,”
J. Fluid Mech.
,
48
, pp.
547
591
.
34.
Mastin
,
L. G.
, 2002, “
Insights into Volcanic Conduit Flow From an Open-Source Numerical Model
,”
Geochem., Geophys., Geosyst.
,
3
, pp.
1
18
.
35.
Simkin
,
T. L.
, and
Fiske
,
R. S.
, 1983,
Krakatau 1883: The Volcanic Eruption and its Effects
,
Smithsonian Institution Press
,
Washington, D.C
.
You do not currently have access to this content.