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An invariant object on the laminar-turbulent boundary in phase space called the "edge state" is investigated for the pressure-driven flow through a square straight duct. For a long duct with the streamwise period of 8πb_* (b_*: half the duct side), the edge trajectory settles down to a flow with streamwise localized disturbances. The localized edge state is converged into the travelling wave by using the Newton-GMRES method.
Shinya Okino (Wed,) studied this question.