Abstract
Linear stability analysis was performed for channel flow with two ribs attached to one wall. Effects of perturbations with an infinitely small amplitude on a fundamental steady flow in the channel were numerically investigated. The fundamental flow corresponds to one of the steady solutions of the Navier-Stokes equations. Time-asymptotic solutions of the perturbation equations reach the least stable mode of the channel flow. Growth or decay of the perturbations was supposed to occur everywhere in the flow with a constant amplification factor, since the logarithmic value of the maximum transverse perturbation velocity of the least stable mode changed linearly with time at all monitoring locations in the channel. In addition, a direct numerical calculation was performed using the two-dimensional Navier-Stokes equations to investigate the characteristics of nonlinear stability, the results of which showed a similar growth pattern to those derived from the perturbation equations. The flow instability with an increase of the Reynolds number was found to depend on the value of the source functioning term of the perturbation vorticity equation derived from the perturbation equations.
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