New Theories on Boundary Layer Transition and Turbulence Formation

Figure 38

(a) Whole domain is symmetric and periodic ---𝑎×cos2𝑦 (the period = 𝜋; spanwise domain is −𝜋<𝑦<𝜋), (b) symmetric and asymmetric—redrectangular: periodic and symmetric at 𝑦=−𝜋/2, 0, 𝜋/2, that is, 𝑓(−𝜋/2−𝑦) = 𝑓(−𝜋/2+𝑦), 𝑓(−𝑦) = 𝑓(𝑦), 𝑓(𝜋/2−𝑦) = 𝑓(𝜋/2+𝑦); yellow diamond: periodic, 𝑓(𝑦+𝜋) = 𝑓(𝑦), period = 𝜋; but asymmetric 𝑓(−𝑦)≠𝑓(𝑦); the spanwise domain is −𝜋<𝑦<𝜋, (c) periodic but asymmetric—yellow diamond: periodic, period = 𝜋; black box: periodic but period = 2𝜋; the spanwise domain is −𝜋<𝑦<𝜋. (d) Periodic but asymmetric—all black boxes: periodic but asymmetric (period=2𝜋); the spanwise domain is −𝜋<𝑦<𝜋.

(a)

(b)

(c)

(d)