Skip to main content
    • Aa
    • Aa

Vorticity structure and evolution in a transverse jet


Transverse jets arise in many applications, including propulsion, effluent dispersion, oil field flows, and V/STOL aerodynamics. This study seeks a fundamental, mechanistic understanding of the structure and evolution of vorticity in the transverse jet. We develop a high-resolution three-dimensional vortex simulation of the transverse jet at large Reynolds number and consider jet-to-crossflow velocity ratios r ranging from 5 to 10. A new formulation of vorticity-flux boundary conditions accounts for the interaction of channel wall vorticity with the jet flow immediately around the orifice. We demonstrate that the nascent jet shear layer contains not only azimuthal vorticity generated in the jet pipe, but wall-normal and azimuthal perturbations resulting from the jet–crossflow interaction. This formulation also yields analytical expressions for vortex lines in the near field as a function of r.

Transformation of the cylindrical shear layer emanating from the orifice begins with axial elongation of its lee side to form sections of counter-rotating vorticity aligned with the jet trajectory. Periodic roll-up of the shear layer accompanies this deformation, creating complementary vortex arcs on the lee and windward sides of the jet. Counter-rotating vorticity then drives lee-side roll-ups in the windward direction, along the normal to the jet trajectory. Azimuthal vortex arcs of alternating sign thus approach each other on the windward boundary of the jet. Accordingly, initially planar material rings on the shear layer fold completely and assume an interlocking structure that persists for several diameters above the jet exit. Though the near field of the jet is dominated by deformation and periodic roll-up of the shear layer, the resulting counter-rotating vorticity is a pronounced feature of the mean field; in turn, the mean counter-rotation exerts a substantial influence on the deformation of the shear layer. Following the pronounced bending of the trajectory into the crossflow, we observe a sudden breakdown of near-field vortical structures into a dense distribution of smaller scales. Spatial filtering of this region reveals the persistence of counter-rotating streamwise vorticity initiated in the near field.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

A. Eroglu & R. E. Breidenthal 2001 Structure, penetration, and mixing of pulsed jets in crossflow. AIAA J. 39 (3), 417423.

L. L. Yuan & R. L. Street 1998 Trajectory and entrainment of a round jet in crossflow. Phys. Fluids 10 (9), 23232335.

A. J. Chorin 1973 Numerical study of slightly viscous flow. J. Fluid Mech. 57, 785796.

G.-H. Cottet & P. D. Koumoutsakos 2000 Vortex Methods: Theory and Practice. Cambridge University Press.

R. M. Kelso & A. J. Smits 1995 Horseshoe vortex systems resulting from the interaction between a laminar boundary-layer and a transverse jet. Phys. Fluids 7 (1), 153158.

J. U. Schlüter & T. Schönfeld 2000 LES of jets in cross flow and its application to a gas turbine burner. Flow Turbulence Combust. 65 (2), 177203.

P. Huq & M. R. Dhanak 1996 The bifurcation of circular jets in crossflow. Phys. Fluids 8 (3), 754763.

J. Andreopoulos & W. Rodi 1984 Experimental investigation of jets in a cross-flow. J. Fluid Mech. 138, 93127.

A. J. Chorin 1993 Hairpin removal in vortex interactions II. J. Comput. Phys. 107, 19.

A. J. Chorin 1994 Vorticity and Turbulence. Springer.

O. S. Eiff & J. F. Keffer 1997 On the structures in the near-wake region of an elevated turbulent jet in a crossflow. J. Fluid Mech. 333, 161195.

Y. Kamotani & I. Greber 1972 Experiments on a turbulent jet in a cross flow. AIAA J. 10, 14251429.

O. M. Knio & A. F. Ghoniem 1990 Numerical study of a three-dimensional vortex method. J. Comput. Phys. 86, 75106.

Y. M. Marzouk & A. F. Ghoniem 2005 K-means clustering for optimal partitioning and dynamic load balancing of parallel hierarchical N-body simulations. J. Comput. Phys. 207, 493528.

S. H. Smith & M. G. Mungal 1998 Mixing, structure, and scaling of the jet in crossflow. J. Fluid Mech. 357, 83122.

G. S. Winckelmans & A. Leonard 1993 Contributions to vortex particle methods for the computation of three-dimensional incompressible unsteady flows. J. Comput. Phys. 109 (2), 247273.

Y. K. Chang & A. D. Vakili 1995 Dynamics of vortex rings in cross-flow. Phys. Fluids 7 (7), 15831597.

A. J. Chorin & O. H. Hald 1995 Vortex renormalization in three space dimensions. Phys. Rev. B 51 (17), 1196911972.

S. L. V. Coelho & J. C. R. Hunt 1989 The dynamics of the near-field of strong jets in crossflows. J. Fluid Mech. 200, 95120.

T. F. Fric & A. Roshko 1994 Vortical structure in the wake of a transverse jet. J. Fluid Mech. 279, 147.

E. F. Hasselbrink & M. G. Mungal 2001 Transverse jets and jet flames. Part 1. Scaling laws for strong transverse jets. J. Fluid Mech. 443, 125.

J. F. Keffer & W. D. Baines 1962 The round turbulent jet in a cross-wind. J. Fluid Mech. 15, 481496.

R. M. Kelso , T. T. Lim & A. E. Perry 1996 An experimental study of round jets in cross-flow. J. Fluid Mech. 306, 111144.

A. Leonard 1985 Computing three-dimensional incompressible flows with vortex elements. Annual Review of Fluid Mechanics 17, 523559.

L. Rosenhead 1931 The formation of vortices from a surface of discontinuity. Proc. R. Soc. Lond. A 134, 170192.

H. Y. Wang 1998 Short wave instability on vortex filaments. Phys. Rev. Lett. 80 (21), 46654668.

D. Wee & A. F. Ghoniem 2006 Modified interpolation kernels for diffusion and remeshing in vortex methods. J. Comput. Phys. 213 (1), 239263.

W. T. Ashurst & E. Meiburg 1988 Three-dimensional shear layers via vortex dynamics. J. Fluid Mech. 189, 87116.

J. T. Beale & A. Majda 1985 High-order accurate vortex methods with explicit velocity kernels. J. Comput. Phys. 58, 188208.

J. E. Broadwell & R. E. Breidenthal 1984 Structure and mixing of a transverse jet in incompressible-flow. J. Fluid Mech. 148, 405412.

A. J. Chorin 1996 Microstructure, renormalization, and more efficient vortex methods. ESAIM Proceedings: Vortex Flows and Related Numerical Methods II vol. 1, pp. 114.

A. J. Chorin & J. E. Marsden 1993 A Mathematical Introduction to Fluid Mechanics. Springer.

R. Fearn & R. P. Weston 1974 Vorticity associated with a jet in a cross flow. AIAA J. 12 (12), 16661671.

E. F. Hasselbrink & M. G. Mungal 2001 Transverse jets and jet flames. Part 2. Velocity and OH field imaging. J. Fluid Mech. 443, 2768.

B. A. Haven & M. Kurosaka 1997 Kidney and anti-kidney vortices in crossflow jets. J. Fluid Mech. 352, 2764.

A. R. Karagozian 1986 An analytical model for the vorticity associated with a transverse jet. AIAA J. 24, 429436.

A. Krothapalli , L. Lourenco & J. M. Buchlin 1990 Separated flow upstream of a jet in a cross-flow. AIAA J. 28 (3), 414420.

T. T. Lim , T. H. New & S. C. Luo 2001 On the development of large-scale structures of a jet normal to a cross flow. Phys. Fluids 13 (3), 770775.

K. Lindsay & R. Krasny 2001 A particle method and adaptive treecode for vortex sheet motion in three-dimensional flow. J. Comput. Phys. 172 (2), 879907.

S. Muppidi & K. Mahesh 2005 Study of trajectories of jets in crossflow using direct numerical simulations. J. Fluid Mech. 530, 81100.

S. Narayanan , P. Barooah & J. M. Cohen 2003 Dynamics and control of an isolated jet in crossflow. AIAA J. 41 (12), 23162330.

A. Rivero , J. A. Ferre & F. Giralt 2001 Organized motions in a jet in crossflow. J. Fluid Mech. 444, 117149.

R. I. Sykes , W. S. Lewellen & S. F. Parker 1986 On the vorticity dynamics of a turbulent jet in a cross-flow. J. Fluid Mech. 168, 393413.

L. L. Yuan , R. L. Street & J. H. Ferziger 1999 Large-eddy simulations of a round jet in crossflow. J. Fluid Mech. 379, 71104.

K. B. M. Q. Zaman & J. K. Foss 1997 The effect of vortex generators on a jet in a cross-flow. Phys. Fluids 9 (1), 106114.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *