When the wavelength is considerably more than the fluid layer thickness, there exists an unstable mode that travels against the main flow at a speed comparable to the antisymmetric Krauklis wave speed, which is almost the same as the nondispersive Rayleigh wave speed.
Figure4b shows that the growth rate of the antisymmetric solution at M = 0.4, traveling against the main flow at a speed of about -1.3, is still negative, but this solution becomes almost neutrally stable at M = 0.8.
Since the recirculation zone anchored in the cavity is not exposed to the main incoming flow, stable combustion is achieved, even in the presence of a high speed main flow as typically expected in Ramjets and Scramjets.
In the classical Poiseuille flow (δ = 0), the phase velocity is twice the peak speed of the main flow, and it is 3 ≃ 1.73 times greater than the speed of the symmetric Krauklis wave, which can be inferred from (40) or (41).
The wave propagating at a speed slightly slower than the peak speed of the main flow is known as the Tollmien-Schlichting wave, which is generally excited in the instability of a viscous shear layer (e.g., Schlichting and Gersten2000).
This is slower than the main flow of traffic and limits the speed with which goods can be delivered.
This increase in flow speed behind the main DF is also observed in the THEMIS P1 event, with a peak speed of nearly 1000 km/s observed 45 s after the main DF.
This means that enhanced flow speed is not a main factor in controlling a Pi2 power.
We have found that the critical flow speed can be significantly reduced when the main flow has a nonparabolic velocity profile, driven by nonuniform forcing in the fluid.
As M increases, the symmetric solution traveling against the main flow (Re c) ≃ -0.59) becomes more stabilized, and the wave speed slightly increases.
