Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-01-09T21:36:59.489Z Has data issue: false hasContentIssue false
  • English
  • Français

Entrainment of an eddy at the edge of a jet

Published online by Cambridge University Press:  26 April 2006

Melvin E. Stern
Melvin E. Stern
Affiliation:
Department of Oceanography, Florida State University, Tallahassee, FL 32306, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

An inviscid two-dimensional eddy (with maximum circulation $\hat{\Gamma}$ and uniform vorticity $\hat{\zeta}_2 > 0$, surrounded by irrotational fluid is initially located near the edge of a jet, on the other side of which the vorticity $\hat{\zeta}_1(< \hat{\zeta}_2)$ increases. The interaction causes the eddy to move towards the edge and into the shear flow. Eventually the eddy and the ambient (irrotational) fluid are surrounded by the jet fluid. An average entrainment velocity is computed for a variety of relevant conditions, and found to scale mainly with $(\hat{\Gamma}_1)^{\frac{1}{2}}$. The approximate proportionality constant is somewhat larger than the measured value for three-dimensional (turbulent) jets, suggesting that the two-dimensional mechanism may be qualitatively relevant. The results may also be generalized to study the role of mesoscale eddies in the lateral entrainment of ambient fluid into oceanic jets.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 228 , July 1991 , pp. 343 - 360
Copyright
© 1991 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Corcos, J. M. 1981 The deterministic description of the coherent structure of free shear layers. In The Role of Coherent Structures in Modelling Turbulence and Mixing (ed. J. Jimenez). Lecture Notes in Physics, vol. 136, pp. 10–40. Springer.
Dritschel, D. G 1988 The repeated filamentation of two-dimensional vorticity interfaces. J. Fluid Mech. 194, 511–517.Google Scholar
Hussain, A. K. M. F. 1981 Coherent structures of perturbed and unperturbed jets. In The Role of Coherent Structures in Modelling Turbulence and Mixing (ed. J. Jimenez). Lecture Notes in Physics, vol. 136, pp. 252–291. Springer.
Ikeda, M. & Lygre, K. 1989 Eddy-current interactions using a two layer quasi-geostrophic model. In Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence (ed. J. C. J. Nihoul & B. M. Jamart), vol. 50, pp. 277–291. Elsevier.
Melander, M. V., Overman, E. A. & Zabusky, N. J. 1986 Computational vortex dynamics in two and three dimensions In Proc. Workshop on Numerical Fluid Dynamics. North-Holland.
Pozrikidis, C. & Higdon, J. J. 1985 Nonlinear Kelvin Helmholtz instability of a finite vortex layer. J. Fluid Mech. 157, 225–263.Google Scholar
Pullin, D. I. 1981 The nonlinear behaviour of a constant vorticity layer at a wall. J. Fluid Mech. 108, 401–421.Google Scholar
Richardson, P. L. 1985 Average velocity and transport of the Gulf Stream near 55 W. J. Mar. Res. 73, 83–111.Google Scholar
Rockwell, D. O. & Niccolls, W. O. 1972. Natural breakdown of planar jets, Trans. ASME D: Basic Engng, 94, 720–730.Google Scholar
Roshko, A. 1981 The plane mixing layer. In The Role of Coherent Structures in Modelling Turbulence and Mixing (ed. J. Jimenez). Lecture Notes in Physics, vol. 136, pp. 208–217.
Smith, D. C. & Bird, A. A. 1989 Factors influencing asymmetry and self advection in ocean eddies. In Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence (ed. J. C. J. Nihoul & B. M. Jamart), vol. 50, pp. 211–224. Elsevier.
Stern, M. E. 1985 Lateral wave breaking and shingle formation in shear flow. J. Phys. Oceanogr. 15, 1274–1283.Google Scholar
Stern, M. E. & Flierl, G. R. 1987 On the interaction of a vortex with a shear flow. J. Geophys. Res. 92, (C10), 10733–10744.Google Scholar
Stern, M. E. & L, J. Pratt 1985 Dynamics of vorticity fronts. J. Fluid Mech. 161, 513–532.Google Scholar
Wygnanski, I. & Fiedler, H. 1969 Some measurements in the self preserving jet. J. Fluid Mech. 38, 577–612.Google Scholar
Zabusky, N. J., Hughes, M. H. & Roberts, K. V. 1979 Contour dynamics for the Euler equations in two dimensions. J. Comput. Phys. 30, 96–106.Google Scholar