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Mechanism of flow instability and transition to turbulence. (English) Zbl 1160.76353
Summary: A new mechanism of flow instability and turbulence transition is proposed for wall bounded shear flows. It is stated that the total energy gradient in the transverse direction and that in the streamwise direction of the main flow dominate the disturbance amplification or decay. Thus, they determine the critical condition of instability initiation and flow transition under given initial disturbance. A new dimensionless parameter $K$ for characterizing flow instability is proposed which is expressed as the ratio of the energy gradients in the two directions for the flow without energy input or output. It is suggested that flow instability should first occur at the position of ${K}_{max}$ which may be the most dangerous position. This speculation is confirmed by Nishioka et al.’s experimental data. Comparison with experimental data for plane Poiseuille flow and pipe Poiseuille flow indicates that the proposed idea is really valid. It is found that the turbulence transition takes place at a critical value of ${K}_{max}$ of about 385 for both plane Poiseuille flow and pipe Poiseuille flow, below which no turbulence will occur regardless the disturbance. More studies show that the theory is also valid for plane Couette flows which holds a critical value of ${K}_{max}$ of about 370.
##### MSC:
 76F06 Transition to turbulence
##### Keywords:
instability; transition; turbulence; energy gradient; energy loss