Direct numerical simulation of a two-dimensional jet using Galerkin spectral method

The applications of Chebyshev polynomials in the flow direction and Fourier polynomials in the normal direction are shown to provide quasi-steady solutions to the Navier-Stokes equations for turbulent flows. The problem considered is at the exit of a jet where the velocity is nonzero and the wall velocity vanishes. A Poiseuille flow is assumed, as are a periodic flow at the upper and low boundaries and a pair of upstream vortices followed by suction at the exit. Calculations are presented for various Re flows that yield quasi-stable solutions, i.e., temporarily stable. Physical causes of the instabilities and possible numerical approaches to account for them are discussed.