Wave growth and spreading of a turbulent spot in plane Poiseuille flow

摘要: Previous numerical simulations have shown that waves at the wing tips of plane Poiseuille spots grow rapidly as they are overtaken by turbulent region. Kinematic wave theory is used to investigate growth mechanism calculating amplitude along rays defined group velocity. A dispersion relation found solving an extended form Orr–Sommerfeld equation using spatially averaged mean velocity profiles. The results indicate because a combination energy focusing and ‘‘cross‐flow’’ instability. exponential resulting from inflectional profiles dominating factor. Good agreement obtained between characteristics calculated those in simulation.