Dear Muriel.

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There is only turbulence studies using only water. When the main unit of measurement was the hot film anemometer usually the fluid used was air or other gases.

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Measurements made by Helmut Eckelmann (The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow) the viscous sub-layer were performed in a channel full of CREAM PONDS (fragrance free). That is, in many experimental measurements are used many gases and liquids, not only water.

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Excuse me, but I think the controversy over the Reynolds number be or not be a limit for the transition is a bit misplaced, because the derivation of this assumes several simplifications that are weak in given situations.

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The Reynolds number, basically defined as a ratio of inertial forces and viscous forces, if we take into account all restrictions the Navier-Stokes equations, let aside several variables and non-linear characteristics of the fluids.

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I think this concern should be addressed at the source of the definition of the Reynolds number.

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Rogerio, you're absolutely right with your skepticism regarding the role of Reynolds numbers in the transition to turbulence. We know from various studies that the pathway to a steady state is critical so that we may observe many different flows for one and the same Re. This was discovered and well documented by Coles in 1965.

Amador, water is indeed a popular fluid (namely at present air temperatures of 30 degC here around) but very important also is various forms of oil because of its use for lubricating rotating machine parts, including your bycicle or whatever you prefer to go for swimming in the next lake ...HZB

For single-phase incompressible flow with no free surface (surface tension effects) and a Newtonian fluid (such as water, air, oil, and most fluids) it can be shown mathematically using dimensional analysis that the only relevant parameter is the Reynolds number.  

Dimensional analysis is both very simple  - and potentially very powerful.   For example, the few analytical results we known about turbulence can all be derived from dimensional analysis.   Google it for more info.  Many textbooks contain chapters on it.

Dimensional analysis tells you that any single fluid (either air, OR water, OR oil) is sufficient to understand the physics and behavior of ALL fluids (given the caveats listed above).  Air and water, and heavy water behave identically when the experiment or numerical simulation is performed at the same Reynolds number,

One thing that does vary slightly and is important in boundary layer  transition is the initial conditions (particularly if the outer flow is turbulent leading to bypass transition) and the boundary conditions.  For example small vibrations of the wall boundary (say from sound waves) can influence natural transition quite impressively.   Upstream conditions (fans, tunnel bends, etc) also have an impressive influence on natural (no free-stream turbulence transition to turbulence.

Hi Blair, your comments supports my view that, if THE classical turbulence problem has two components, (1) transition, (2) statistics for Re=> infty, then only (2) has a universal solution. Compenent (1) is too specific. For Taylor-Couette for instance the role of the route to steady state has classically been demonstrated more than 40 years ago. For (2) the solution is attached. Cheers, HZB

Identical critical Reynolds numbers for pipe flow for H2O and D2O is not true. The only study made on this was done by Novopashin, who is a ResearchGate member. If this experiment is verified, and should be, then the usual scaling arguments from NSE does not hold. This would be a fundamental problem. 

Possibility 1:   The experiments are not actually identical.  This is highly likely as transition is very very sensitive.  People have reported differences in the time of day (hypothesized to be due to differences in external traffic noise and vibration).  Different levels of degassing (due to different storage), etc.  The list of odd possibilities is quite large.  

Possibility 2:  Some other physics is acting (such as surface tension, comprehensibility, etc).   This new physics would have to be clearly identified and demonstrated to be convincing as an explanation.   

What I think is highly likely to withstand every and all debate is the scaling of the N.S. equations.  The math involved with set theory (from which dimensional analysis is a subset) is simpler even than addition/subtraction.    It would be very hard to find fault with it.

I think Occam's razor would apply very well here; "The simplest explanation is by far the most likely explanation."    In this case that would be #1.  

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Dear J. Blair Perot.

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As I work for 37 years in Experimental Fluid Mechanics, can strengthen your statements by saying that nowadays 99% of searchers do not know "clean" an essay of small side effects that disturb the results.

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The progression of CFD has made expert researchers in mathematical models perform some "experimental heresies". Likewise the CFD does not accept "neophytes" manipulating their more complex models physical experimentation is even more sensitive.

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When one day we get to perfect mathematical models, the degree of complexity in the operation of these models will be such that only the "initiated" can manipulate them.

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On the comment "Air and water, and heavy water behave identically when the experiment or numerical simulation is performed at the same Reynolds number,"Please see the paper by Novopashin on normal and heavy water using the same apparatus. Novopashin is a member of ResearchGate.

Amador, unfortunately the text that thou referes "Is the critical Reynolds number universal?" only have the abstract in ResearchGate, I'm asking the full text to be able to follow your line of reasoning. When you are ready, if you have any questions return.