The Equilibrium State of the Finite Disturbance in Free Flows

Abstract

The equilibrium state of periodic, quasi-neutral disturbance with finite amplitude in free flows is investigated for large values of the Reynolds number R.
The equilibrium amplitude of the disturbance is obtained as, for c_i<R^−1⁄3,
|A|=K₁c_i^1⁄2R^−1⁄6(1+K₂Rc_i)^−1⁄2,
and for c_i>R^−1⁄3,
|A|=K₃c_i²,
where K₁, K₂ and K₃ are numerical constants depending upon the form of the velocity distribution of the basic flow, and c₁ the amplification factor due to the linear theory.
In the sub-critical state, the flow is stable even for the disturbance of finite amplitude.