In this short webinar we really really flew at a fast pace around very deep topics like the history of transition beginning with Reynolds and Orr-Sommerfeld, but also after noting ?Rayleigh and Fjo’rtof and 2D inviscid laminar flows criterions moved to 3D base flows and saw indications for baseflow profiles which arrive to a turbulent state without having an inlection point, that led us to the option of searching an answer in interacting mechanism of both Orr-Sommerfeld and Squire equation, and not stick with modal groth, with Ellingsen and Palm (1983) we have found transient algebraic growth, and introduced the reynolds-Orr Equation and learned firmly that the grothh rate of a final inviscid flow transition and and the inflection point and Fj’ortof Criterion. Modal stability analysis and the Orr-Sommerfeld/Squire equations, Landahl’sLift-up effect (1980 MIT school), and its huge contribution.

(highly) non-normal linearity Vs.non-linear normality where explained in a couple of ways,

“bootstrapping debate” (Fabian Walleffe clearly quite harshly criticizing the school of thought originating in MIT and spreading to KTH). At the time was fully engrossed with non-normal operators and linear transient growth mechanisms… Than it hit me that Walleffe has it very nicely explained, a rush of confusion went through my body. It made me review how much we do not notice our tendency for confirmation bias (in a big way unconsciously).

I think that if one listens well the concepts of streaks becomes almost fully explained.

secondary instability theory and Floquet analysis, the concept of pseudospectra “(read

his book like crazy – one of my best involving math and physics) and LLOyd Trephten

operator is where we aim to investigate. that the level of non-normality could be

represented represented by a condition number, of which the non-normal matrix

behaviour dependents strongly, we simply don’t have the same behaviour for the

resolvent of a normal Vs. a non-normal operator… and if we understood the essence we

MUST acknowledge that in the case of transient growth of non-normal operators things

like shpe (the obliqueness of Dan Henningson (KTH), the Landahl’s effect, and

‘bootstraping” redistributing energy in orthogonal direction back and forth) play a huge

role and it is not the exponentially modal eigenvalue that is not most susceptible to

growth just enough to excite non-linear mechanisms.

We saw that a spectra of an undisturbed initial flow to a infinitesimal disturbance is

modaly stable or perhaps unstable by way such a way that we shall find the flow

turbulent way before the representing Reynolds number of the unstable orthogonal

mode happens (such as waiting for orszag (1971) to find that at 5777.2 while in actuality

transition arrives whey before distabilation…). trying to communicate the essence

without deriving (albeit sometimes getting a glimpse at the frightening equations to stay

attached to the core)…

Then get a short but well posed acquaintance with types of transition mechanisms, (K-H-

O-N-TS…) the evolving literature in the studying fine grained coherent structures and self

sustained turbulence cycles, and watch cool KTH (by one of my favorite dissertations

ever of Phillip Christian Schlatter…) and P. MOIN LES and DNS.

It was really hard to organize communicating such an intrinsically intricate topic in two

hours. So I must admit I had some live difficult time… 🙏 (Forgive me if I got a little

confusion, you know this rarely happens to me… Love me 😋)…

 ✨There is room for a second webinar on the topic. Next week seems cool…✨

There is room for a second webinar on the topic. Next week seems cool…✨