Subcritical autooscillations and nonlinear neutral curve for Poiseuille flow

Abstract

In the present paper an asymptotic solution of initial problem for disturbances of laminar flow obtained in [8] is employed for analysis of autooscillations. Numerical calculation has shown that there are two autooscillating regimes at values of the wave number α with the range 0.9649 ⩽ α ⩽ 1.0765 in subcritical region. The first regime is a well-known unstable limit cycle, and the second one is a stable autooscillating regime coming from the beyond-critical region. Cycles interflow at some critical value of the supercriticity parameter δ 1. The nonlinear critical value of Reynolds number R H (α) corresponds to this value. All disturbances are quenching at values of α, R lying to the left of nonlinear neutral curve. There exist critical amplitudes A 1(α, R) in the region between nonlinear and linear neutral curves. Increasing disturbances are stabilized at amplitude values equal to A 2(α, R). Within the linear neutral curve all disturbances increase up to the amplitude A 2(α, R).