Hi Carlos L. Janer

I don't study about your question but about "sound speed constantivity" you can test constantivity of coefitent of sound speed with dencity or Re number of sound speed.

Hope it help and

Hope your success

Dear Carlos,

reading carefully your question I think that your idea of how laminar-turbulent transition happens is not yet mature.

The matter can not be answered in short but I can give answers to your concise questions.

Sound does not play too much of a role. If incompressible laminar flow is considered the sound velocity is infinitely large but it does not matter. Instead, in one scenario with very low background disturbances in the flow along a wall, a linear instability sets in amplifying exponentially so-called disturbances which are Tollmien-Schlichting waves for a 2-d baseflow. Those waves are vorticity waves and travel with about 1/3 of the velocity at the edge of the viscous layer, the boundary layer. If there is no longitudinal pressure gradient in the base flow, then the instabiliy mechanism is purely viscous, i. e. viscosity is the reason for amplification. If the modes reach amplitudes of say 1% then secondary instability sets in and slightly after everything gets fully nonlinear and turbulence sets in. The smallest eddy size in turbulent flow depends on the Reynolds number where viscosity is in.

Re_crit is defined where linear modal instability sets in. The flow can be turbulent before also, by large disturbances like roughness or strong background turbulence, or in special cases by non-modal growth. In channel flow Re_crit is about 5000 but the flow in careless experiments may be turbulent for Re>1000.

Decisive for instability is a local maximum of base flow vorticity. If it is situated within the flow then there is viscous and inviscid instability, the latter independent of Re; if it is at the wall there is only viscous instability.

It's not my fault. Thy're articles of a 2016 monograph from "Nature" on "Transition to Turbulence".

Markus J. Kloker ,

Thak you very much for your detalied answer, although I would be lying if I said I unterstood everything you said. However, after carefully reading your answer, what I have in mind is this (I may have got everything wrong):

I would be very grateful if you could recomend me a (readable, meaning short) monograph on transition to turbulence. I would also be very grateful if you could tell me if the questions in point 3. (boldface letters) make sense and if they do, if you could, please, answer them.

Kind Regards,

Carlos.

1. Tapan: thank you, similar holds for you.

2. Carlos:

"If the boundary surface were completely smooth, the critical ammount of vorticity is due to viscosity only and,,,, transient turbulence dissapears?"

Yes, but it is not that simple because the strength of the vorticity is largest near the plate's leading edge (max always at wall), behaving like sqrt( Re_unit/x), i.e. goes down with distance on the plate. Hence a high value of base-flow vorticity alone is not decisive for viscous instability, only for inviscid instability it governs the growth rate. "Transient turbulence" (intermittently) then is caused by large oncoming disturbances only.

"? the critical Re number for the stable transition to turbulence can be calculated?? "

In the sense of linear stability theory, Re_crit, the onset of modal disturbance amplification (Orr-Sommerfeld equation), can be calculated. Using the Reynolds-Orr equation (nonlinear), other important Re values may be gained (monotonically stable flow, …). Then it is about energy gain from the base flow and viscous dissipation for the disturbed flow.

"Temperature as a source of fluctuations plays no role at all in this transition?"

The thermal noise is a source of background disturbances that can never fall below the thermal noise level. Temperature gradients in the base flow play a role; for incompressible flow (no direct coupling of velocity and temperature) the alteration of viscosity with temperature is decisive. If it is positive (gas), wall cooling stabilizes the flow; vice versa for a liquid.

There are some books on transition (Tapan also wrote one recently to my knowledge). To start just read the relevant chapters of: White: Viscous Fluid Flow; Schlichting & al: Boundary-Layer Theory.

The matter is complicated, hence answers on the fly may be a source of an exponentially rising number of further questions.

Markus J. Kloker , Tapan K. Sengupta

Thank you very much for your kind help. I will take a close look at the suggested bibliography.

Kind Regards,

Carlos.

Markus J. Kloker , Tapan K. Sengupta

I've been thinking a lot about the critical condition in Percolation Models (directed or not). I think that what really defines the critical transition is the fact that there are long range correlations for any given physical observable in two different space-time points of the fluid. I also think that this is generally true in any Critical Phenomenon.

Apparently, in turbulent flows, the mean square velocity fluctuacions scales as (1/L)^(3/2) which is in almost perfect agreement with the beta critical exponent of the 3D-Percolation Model (beta=0.813\simeq sqroot(2/3)) and is a perfect example of long range correlation.

So, the question I was trying to ask and failed to properly formulate, would be something like:

1.- At what critical Re numbers do perturbations stop being short range and become long ranged?

2.- In Field Theoretical terms the question would be something like: At what Re number does the fluctuation propagator become massless?

Than you very much in advance for your interest.

Kind Regards,

Carlos Janer.

Hi Carlos ( Carlos L. Janer ),

could you please say a few more words for non-specialists (like myself) on what exactly do you mean under :

1) "long range pertrubations". Does it mean something non-local or action at a distance? How do they exchange by the information? Instanteneously?

2) "fluctuation propagator become massless". Does that mean that the field of something massless emerges (like phonons in solids)?

Thanks,

Ilya

Carlos L. Janer

Ok, percolation theory. My feeling is that this is not useful for the bulk of standard laminar-turbulent transition scenarios but maybe for special cases. I think you are interested in the merging of (at first localized ) turbulent spots. Go to JFM https://www.cambridge.org/core/journals/journal-of-fluid-mechanics

and check for "turbulent spot merging" for instance. One, more recent paper that may be interesting to you in this respect is from JFM

Article Experiments on transient growth of turbulent spots

Good success.

Markus J. Kloker,

I will. Thank you very much for your time.

Kind Regards,

Carlos Janer.

@Ilya M. Peshkov

By long range perturbation propagation what I mean is a perturbation that propagates unattenuated at the speed of sound.

When I use the word massless propagator what I mean is the same thing as in Equilbrium Critical Phenomena (2nd order phase-transitions): The critical system is strongly correlated because fluctuations propagate without any attenuation. In QFT, this lack of attenuation is associated to a massless interacting field. If its mass is non null you get a short range interacting field (Yukawa-like).

Regards,

Carlos Janer.

Tapan K. Sengupta

It is true that I do not know almost anything about turbulence (I just did two semesters on fluid dynamics before I graduated 25 years ago), but I do not understand your statement. A fluid is a material that is perfectly capable of transmitting compression waves (sound). If density does not change much inside this material, the speed of sound should be roughly constant.

I vividly remember that when a sphere blocks the flow of a fluid, there is a limit speed above which stationary flow is no longer possible. I strongly suspect that this fact and the finiteness of the speed of sound are deeply rooted in the transition to turbulence. But, of course, you are right. I am not an expert (in this or any other field) and, very possibly, my suspicion is pure nonsense. But I can check wether or not this is just nonsense (and I will).

That's the beauty of physics.

Tapan K. Sengupta

I am still having difficulties trying to understand you. I think that you assume that I know things that I really don't.

My educated guess is that you are trying to tell me that turbulent flows do not propagate sound, that they just propagate entropy and vorticity.

Did I get it right?

Regards,

Carlos.

@Tapan K. Sengupta,

This conversation is becoming very difficult.

I am quite sure that you are an excellent researcher and that you are very famous in your field. That is something that is not in question and is not the subject of my previous lines. I never said anything about turbulence being or not a source of sound, but that is beside the point.

What I asked was if the following statement roughly explained what you were trying to tell me:

Regards,

Carlos Janer.

I didn't knew before, that Turbulence doesn't propagate sound waves! Really interesting! I have noticed that Light bends very differently in Turbulent water, compared to laminar water. To me this is a sign of surfaces inside the fluid. But It's would actually be as logical to the sound waves. If you put some steelbar pieces on the row, no matter how near each other, and how nicely the cuts are connected, they do not propagate sound much compared to single cable which has no broke's. Thanks for this input. I support your ideas, they merely have another approach/ view point compared to my thougts.

Carlos L. Janer

To your point 1:

Sound disturbances are not at all necessary for laminar-to-turbulent transition because the fundamental instability waves are vorticity waves bound to the advection speed of the base flow. If the disturbances reach nonlinear values, sound is generated by the process, as well as by full turbulence, and there can be feedback to vorticity (edge tone phenomenon for instance). A turbulent flow may "propagate" sound waves like a non-turbulent flow, but there is no essential connection. Also a distinction must be made between the "hydrodynamic" pressure fluctuations (hpf's) that are large in the turbulent core regions, and sound which is a directed, long range, effect and orders of magnitude smaller than the hpf's; they decay fast with distance. Sound waves have no vorticity in general; hpf's intrinsically do.

2. Right, turbulence is inherently made of a broad range of (vortical) eddies, the smallest ones dissipating kinetic energy.

Markus J. Kloker ,

Thank you very much for your answer. I will carefully read it as soon as I have some spare time at my job.

Tapan K. Sengupta

The more I read your comments the more I have the impression that this subject is becoming personal for you, that you think that we have become contenders in I'm not sure what kind of competition.

I will happily give up any ideas I may have regarding turbulence or any other scientific topic if they're proven wrong. All I care about is having an accurate description of the physical reality. For me, this is not about being either right or wrong. It is all about understanding Physics.

Carlos L. Janer I understand that things become frustrating sometimes in RG, but that is the beauty of science; that is my humble/romantic opinion. That makes perfect sense since the main contributors are professors (full professors most of the time) whose experience/knowledge is above the majority of the forum (I talk for myself). It takes 4 or 5 times more time for me to follow the discussions, but that does not mean we may react this way. Instead, I think we need to be thankful that such professors take their valuable time to engage in such discussions. Sorry for my "off topic" answer but I don't believe that professor Tapan K. Sengupta

Julio Mendez Tapan K. Sengupta

Tapan, Julio, thank you for your points. Of course the answer of Tapan K. Sengupta

OK guys, do whatever you like doing but I'm not gonna be involved in a conversation that revolves around the concep of "status" (profesional, social, whatever it may be). I'm completely unimpressed by status (yours or anybody elses).

If you like to think that I do not understand your answers, well, please be my guest. Think whatever you like to think. You're entitled to it. Please, don't let the fact that I have not even had the time to read them spoil your sense of imagined superiority.