In 1967, Stuart [J. Fluid Mech. 29, 417 (1967)] found an exact nonlinear solution of the inviscid, incompressible two‐dimensional Navier–Stokes equations, representing an infinite row of identical vortices which are now known as Stuart vortices. In this Brief Communication, the corresponding result for an infinite row of counter‐rotating vortices, i.e., a row of vortices of alternating sign, is presented. While for Stuart’s solution, the streamfunction satisfied Liouville’s equation, the streamfunction presented here satisfies the sinh–Gordon equation [Solitons: An Introduction (Cambridge U.P., London, 1989)]. The connection with Stuart’s solution is discussed.
REFERENCES
1.
J. T.
Stuart
, “On finite amplitude oscillations in laminar mixing layers
,” J. Fluid Mech.
29
, 417
(1967
).2.
L. M. Milne-Thomson, Theoretical Hydrodynamics, 4th ed. (MacMillan, New York, 1960), p. 386.
3.
P. G. Drazin and R. S. Johnson, Solitons: An Introduction (Cambridge U.P., London, 1989).
4.
R. Mallier, “Stuart vortices in a stratified mixing layer. I: the Garcia model,” submitted to Geophys. Astrophys. Fluid Dyn. (1993).
5.
R. T.
Pierrehumbert
and S. E.
Widnall
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,” J. Fluid Mech.
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L. P. Wang, M. R. Maxey, and R. Mallier, “Structure of stratified shear layers at high Reynolds number,” submitted to Geophys. Astrophys. Fluid Dyn. (1993).
7.
R. Mallier, “The nonlinear stability of a bounded mixing layer,” submitted to Acta Mech. (1993).
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© 1993 American Institute of Physics.
1993
American Institute of Physics
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