Recently, Mallier and Maslowe [Phys. Fluids A 5, 1074 (1993)] found an exact nonlinear solution of the inviscid, incompressible, two‐dimensional Navier–Stokes equations, representing an infinite row of counter‐rotating vortices, which extended the previous Kelvin–Stuart vortices. The aim of this work is to establish explicit sufficient conditions for the nonlinear stability of this solution. The result is derived with the energy‐Casimir stability method as a function of the parameters of the solution and the domain size. The size of the domain over which the street of vortices is unstable is exhibited.
Topics
Navier Stokes equations
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© 1994 American Institute of Physics.
1994
American Institute of Physics
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