Is fluid dynamics a true physics subject?

[MagnetoBLI]

Are fundamental discoveries made in fluid dynamics currently, or is it just particular solutions based upon known fundamentals? From reviewing journal literature, it appears that either application based problems have been studied (engineering), or fluids under certain conditions that form a collective behavior (engineering-science). However I believe, much like plasma physics, collective behaviors themselves are not by definition fundamental and are understood through the application of known physics; therefore it is not pure physics.

Any thoughts on the matter?

Thanks.

 

[boneh3ad]

Well my first thought it what does it matter? My second thought is that of course it is a true field of physics. There are still a whole lot of fundamental things we don't know (e.g. the origin of turbulence) that are actively sought that are not application-specific and not limited to certain conditions.

I would make the argument, however, that studying the collective behavior of certain classes of problems is absolutely fundamental physics because there is no other way to investigate physics. Experimental physics relies on observation of phenomena under highly controlled and specific conditions in the hopes of learning something that can later be broadened to a greater number of conditions until you have eventually described the more general phenomenon. After all, you can't let all variables remain independent at once in an experiment. You must always have all but one controlled per group if you are to isolate the parameters that are truly important to the physics and develop the more general law.

 

[MagnetoBLI]

I'm asking due to a potential career move. However, I wanted to know how scientific fluid dynamics is as I'm really not so interested in engineering i.e. parametric design, application based studies and the like. I'm really hoping fluids are as scientific as I'd like!

I agree completely that turbulence is fundamental, but when I search for these/other types of research I find all the usual variables and science being used i.e. density and buoyancy, stratification etc... However, I presume in pure physics new particles and variables are being created to describe non-collective behaviors, such as subatomic research? I understand and agree with your comment on isolating variables of interest, it's just there must be a reason why engineering uni's dominate the teaching of this field.

Here is a typical sentence from the Cambridge fluid journal:

**Deviations from neutral behaviour occurred when these two lengthscales became of the same order, after the initially larger inertial forces associated with the initial kinetic energy had become weaker and buoyancy forces became important. **

What do you think?

 

[Khashishi]

Since when does a field have to be about fundamental physics to be considered "true" physics?

 

[Antiphon]

I think that sounds like physics. And you'll find those same parametric studies at a particle accelerator.

It's engineering when the goal is to build something new using known principles. It's physics when the goal is to understand how something works when the principles are unclear or uncertain.

 

[0xDEADBEEF]

You are using the words all wrong. Biology for example is very scientific, although a bee is not described as a set of equations. Experimental physics requires a lot of "dirty work" and you need to work like an engineer, often under worse conditions because no one ever cared if their glue works a 4K of if you could spot weld those two metals... it's amazing what engineers have achieved when there was an industrial application for it.

Fluid dynamics is based on a set of equations called the Navier-Stokes equations. We believe they are correct, they look simple but mathematically they are so difficult to handle that you can get a millennium price of a million dollars if you can mathematically show under what conditions there is a solution to them. There is a research community doing computational fluid dynamics. They are not bad at getting the qualitative aspects right, and they can even build air planes or formula 1 cars with it. But turbulent flow is a very complicated field, because it is kind of fractal. Large eddies contain small eddies containing smaller eddies and so on until somehow it's not an eddy any more but an increased temperature. Unfortunately the small eddies influence the large eddies (the "butterfly effect") so after a short time a model will look very different from reality. Because of microscopic differences in the starting conditions and other effects, even if it is qualitatively correct.

There is a whole lot of things like non linear effects (non Newtonian liquids) and I don't think you can really practically model from first principles say the damping effect of carpet on a sound wave, and I have yet to see a good metric that measures how good a simulation approximates reality.

 

[MagnetoBLI]

Yes my wording is poor and I understand a true division between levels of physics doesn't exist. I am trying to understand the difference between collective behaviour and matter/properties ie. The discovery of electrons vs the boundary layer. For me electrons exist under many conditions i.e. very fundamental, where as a boundary layer is very specific and exists only under certain boundary conditions. Do you see what I'm getting at? They are both physics but different. The N/S equations are a fundamental recognition of fluid motion but numerically solving them seems to be a process of understanding collective behavior alone.

Thanks for all your replies by the way, much appreciated!

 

[boneh3ad]

I don't really see what you are getting at. If you are trying to find fundamental particles, you should look elsewhere. On the other hand, discovering the nature of a fluid's path from the beginning of the boundary layer all the way to turbulence is one of the oldest unsolved problems in physics; one that even Feynman described as "the most important unsolved problem of classical physics." Shoot, when Werner Heisenberg died, he said "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first."

The boundary layer is very fundamental to fluid mechanics, as it occurs any time there is viscosity and a surface moving with respect to a fluid. This is the situation in nearly every conceivable situation short of working with superfluids, which at present are only a scientific curiosity rather than something useful.

Numerically solving the Navier-Stokes equations has nothing to do with understanding collective behavior. It is simply an exercise in numerical methods as they apply to partial differential equations. The problem is that the equations are highly nonlinear, and a real fluid flow will frequently involve both laminar and turbulent flows, meaning that to really capture the behavior, you need a numerical mesh that can capture everything from the full scale of the problem to the Kolmogorov scales in the flow. Presently, this is outside the realm of the power of the modern computer, so you see people trying to make various turbulence models and approximations. It has nothing to do with just understanding the collective behavior, whatever that even means.

Of course after writing all of this, I suppose I still don't understand what you are trying to get at... By collective behavior are you trying to describe what is commonly called the continuum approximation?

 

[0xDEADBEEF]

The connection between the Navier-Stokes and single molecules is done in statistical mechanics. There is the Boltzmann-Equation describing single molecules statistically and with a proof taking up just one page or two you can derive the Navier-Stokes equations. Within the framework of statistical mechanics there is also a lot of interesting research depending on the allowed interactions between the particles. Maybe you find that stuff interesting. I find the derived continuum mechanics and thermodynamics much more exciting because it relates much more directly to the world around me.

 

[Studiot]

@magneto,

This idea that it's all been done, bar the tidying up by the engineers, is pretty narrow.

Fluids is a subject that has spawned two whole new branches of mathematics in the last few decades. And the work was from a meteorologist for chaos theory.

Then of course the classical physics of fluids cannot handle transients.
Can you (or any theoretical physicist) offer any insights into what happens to a gas distribution network if a major disruption occurs to one of the main high pressure feeders?

Can you model the solar prominences?

 

[Jarfi]

I don't really see what you are getting at. If you are trying to find fundamental particles, you should look elsewhere. On the other hand, discovering the nature of a fluid's path from the beginning of the boundary layer all the way to turbulence is one of the oldest unsolved problems in physics; one that even Feynman described as "the most important unsolved problem of classical physics." Shoot, when Werner Heisenberg died, he said "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first."

The boundary layer is very fundamental to fluid mechanics, as it occurs any time there is viscosity and a surface moving with respect to a fluid. This is the situation in nearly every conceivable situation short of working with superfluids, which at present are only a scientific curiosity rather than something useful.

Numerically solving the Navier-Stokes equations has nothing to do with understanding collective behavior. It is simply an exercise in numerical methods as they apply to partial differential equations. The problem is that the equations are highly nonlinear, and a real fluid flow will frequently involve both laminar and turbulent flows, meaning that to really capture the behavior, you need a numerical mesh that can capture everything from the full scale of the problem to the Kolmogorov scales in the flow. Presently, this is outside the realm of the power of the modern computer, so you see people trying to make various turbulence models and approximations. It has nothing to do with just understanding the collective behavior, whatever that even means.

Of course after writing all of this, I suppose I still don't understand what you are trying to get at... By collective behavior are you trying to describe what is commonly called the continuum approximation?

I'm kind of crashing the party here.. never really studied fluid dynamics.

What exactly is the deal with turbulence? why does it scare you guys so much, to me all it is is waves, disorted waves and the transfer of kinetic energy trough a medium. So if the medium is not solid the kinetic energy will spread in a very complex manner because there are billions of atoms, but it will all make common sense when you'd see it spreading, maybe hooks in molecules would disort a stream and it would all start spinning, or a wave would meet small dust particles and be disorted and disorting itself in a snowball effec.. but what's the deal, I know this is complicated but there's nothing about the fundementals I see that's weird.

Am I not getting the word turbulence, why do you say it's such a mystery? I mean it's a mystery mathematically because of all the variables(dust, shape of molecules, multiple waves and streams of medium disorting each other) so calculating 100% would need a sick computer... but in itself I don't see the complexity.

 

[MagnetoBLI]

The thermodynamic relations I currently use within aerospace engineering are dated and based upon particularly well-defined physics. This has made me desire a more undefined science where I can let my imagination play a larger role.

By collective behavior, I mean a phenomena rather than matter itself. For example, circulation provides aerofoil lift in viscous flow, yet circulation is still just fluid molecules being deflected,rotated and sheared in a collaborative and specific way to provide an overall force direction change. The smaller scale features collectively produce macroscopic phenomena.

However I understand that each scale has it's own system i.e. particles are systems in reality. Are new variables produced frequently in fluid dynamics, i.e equivalent to the fundamental ones like temperature or pressure? I thinking that temperature and vorticity are actually not too dissimilar now, hmm...

Ah yes statistical mechanics does sound interesting, I will certainly investigate that further, but can definitely see the attraction to phenomena seen by the human eye also.

The first paragraph of the following link briefly attempts to explain why fluids aren't taught in physics undergrad usually. This is what got me questioning the potential in fluids as solving turbulence seems too intractable of a problem and I'm not a pure mathematician!

http://www.ap.smu.ca/~dclarke/PHYS4380/documents/introduction.pdf

Cheers.

 

[boneh3ad]

What exactly is the deal with turbulence? why does it scare you guys so much, to me all it is is waves, disorted waves and the transfer of kinetic energy trough a medium. So if the medium is not solid the kinetic energy will spread in a very complex manner because there are billions of atoms, but it will all make common sense when you'd see it spreading, maybe hooks in molecules would disort a stream and it would all start spinning, or a wave would meet small dust particles and be disorted and disorting itself in a snowball effec.. but what's the deal, I know this is complicated but there's nothing about the fundementals I see that's weird.

Am I not getting the word turbulence, why do you say it's such a mystery? I mean it's a mystery mathematically because of all the variables(dust, shape of molecules, multiple waves and streams of medium disorting each other) so calculating 100% would need a sick computer... but in itself I don't see the complexity.

It isn't that it is scary, per se. The breakdown to turbulence starts in the free stream of a flow, where there are, in all real flows, various disturbances (vortical, acoustic, etc.). The nature of these disturbances constitutes a relatively large parameter space to explore.

Next, these disturbances interact with the surface roughness on a surface through a process known as receptivity. The result is that, through wave diffraction, fluid dynamic and probably other unknown processes, the free stream disturbances are converted into wavelengths, frequencies and amplitudes to which the boundary layer is receptive. This is a huge parameter space constituting the size and pattern of roughness on a surface, the nature of the free stream disturbances and the conditions of the boundary layer.

The boundary layer itself is similar to a forced mass-spring-damper system in that it is a dynamical system. However, it is, in general, a dynamical system consisting of multiple equations that are highly nonlinear in nature. Three of those equations are the Navier-Stokes equations, plus the energy equation, continuity equation, and (various) equation(s) of state. This complicated system has not even been proven to have a general solution (thus the millenium prize). The receptivity process provides the initial conditions by which the boundary layer is excited, and depending on a variety of parameters, these disturbances may grow, decay, or do a combination of the two. There are also a number of larger-scale phenomenon, such as crossflow or Görtler vortices, that can affect the stability of the system. For a detailed look at this whole process, check out Mack's 1984 AGARD Report titled "Boundary-Layer Linear Stability Theory".

Once those wave grow to a certain amplitude, they become nonlinear. From that point on, there is a potential interplay between any number of an infinite number of instability modes propagating through the given boundary layer, and there is no real one-size-fits-all theory to these interplays. For now, there are only some pretty good descriptions of this regime for a few select situations such as wind tunnels or flows with limited, known CFD inputs. Eventually, the nonlinear waves grow large enough that breakdown occurs to turbulence. The breakdown process is also quite unknown. This is also a nearly infinite parameter space.

Some, including myself, believe that turbulence can ultimately be described as a sort of spatiotemporal chaos. Turbulent flow, however, has never been described in sufficient detail in a way that can confirm this. In general, design using turbulent flow assumptions occurs by using the general properties we know about it, such as increased skin friction and heat transfer. Often, this is done with what are called turbulence models, ant those are really kind of a blacksmith job that get you a good-enough answer. They improve all the time, but they don't really describe the full flow, but rather the properties of interest.

Turbulent flow itself is characterized by an energy cascade through a series of increasingly small length scales, starting with the integral length scales, which are determined by the dominant flow features in the mean flow and are highly anisotropic, going all the way down to the Kolmogorov microscales, which are locally isotropic and depend on the flow properties. These small scales are where energy dissipation finally takes place, so they are equally important to the larger flow scales, yet they are often the ones that must be modeled because computational grids simply can't be dense enough to solve those flows at reasonable conditions within a reasonable length of time. The bottom line is that in order to make the problem tractable to a computer, major assumptions must be made or else the flow conditions must be so unrealistic as to not include the transition phenomenon in detail. We won't crack the problem computationally for probably at least another half-century, according to a well-known practioner of direct numerical simulation with whom I am familiar. The computational meshes are simply too large and too fine to be solvable on today's computers.

So in essence, it isn't that the problem is scary, but rather than it is huge and takes a lot of time and effort to crack. Even when computers can solve it, we will still need to develop some theoretical framework to describe it. Experiments will be useful for validating computational solutions, but they cannot hope to get the kind of detail required to truly solve the problem, so they are limited to the validation role as far as I can see.

That said, the stability (or instability, rather) of boundary layers and the eventual transition to turbulence is an interesting problem, which is why I am personally drawn to it. It is also one of the more theoretical areas of study within fluid mechanics.

Wow that took a long time to type and is still just a very quick rundown, haha! :yuck:
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The thermodynamic relations I currently use within aerospace engineering are dated and based upon particularly well-defined physics. This has made me desire a more undefined science where I can let my imagination play a larger role.

That's fine, then move to a more theoretical course of study. However, basing the level of theory involved in a subject based on undergraduate classes, particularly in engineering, is somewhat foolhardy. Engineering is ultimately the application of physics and mathematics, and as such, the undergraduate classes are often a blend of theory and applications and don't get too close to the bleeding edge. When you move into the graduate level, things usually get considerably more theoretical.

By collective behavior, I mean a phenomena rather than matter itself.

The only fields where you will be dealing with matter itself are things like condensed matter physics and particle physics and any applied mathematics branches dealing with these fields. Otherwise, even most other physics fields are dealing with larger phenomena.

Are new variables produced frequently in fluid dynamics, i.e equivalent to the fundamental ones like temperature or pressure? I thinking that temperature and vorticity are actually not too dissimilar now, hmm...

You can't generally just create variables. The physical world only has certain properties, and after those properties have been described, you can't just pull others out of thin air. Even theoretical physics follows this pattern where most if not all the fundamental properties are known and it is a matter of proving our theories about those properties. The only variables that are ever really "produced" are things like similarity variables.

The first paragraph of the following link briefly attempts to explain why fluids aren't taught in physics undergrad usually. This is what got me questioning the potential in fluids as solving turbulence seems too intractable of a problem and I'm not a pure mathematician!

http://www.ap.smu.ca/~dclarke/PHYS4380/documents/introduction.pdf

Those points are valid. Basically, other disciplines have taken over as the prime caretakers of fluid mechanics as physicists have move on to other fields like quantum mechanics. That doesn't mean that fluid mechanics is not "true physics", but rather than it just is not en vogue with pure physicists of late. It is still a staple of engineering, mechanics and applied mathematics departments worldwide, and at the graduate level, can get very, very theoretical. Indeed, the entire field of perturbation methods for the solution of nonlinear equations evolved mid-century as a result of fluid mechanics and was later applied to theoretical physics.

Still, I am not sure what exactly it is that is concerning you here. It seems like either fluids just isn't your thing, or else you have some misguided notion about what constitutes "true" physics.

 

[MagnetoBLI]

First of all, thanks for the particularly thorough reply.

I am in my final year of an AE doctorate and have used some interesting theory over the course, although it is useful for me to know the potential in the theory of fluids as I'm hopefully going to be working in it for more than 3 years. Turbulence I must, say does sound very interesting.

The comment about 'similarity variables' is what I was most confused about; I knew relatively large scale properties were known but not the small scale properties, so that's interesting to hear. I was in general trying to target this issue; that properties are well understood and that focus is now on the phenomena/processes (collective behavior of properties and energy etc...). It seems a shame that almost only a couple of centuries were needed to uncover so many property based mysteries. I'm not entirely sure why I have this mental fixation on properties, they just seem pure and intrinsic.

However, I am intrigued by phenomena also. Out of interest, are there many other general solutions (rather than particular solutions) being devised or potential for existence for other fluid phenomena than turbulence? Most of what I've read are particular solutions mainly focusing on, as you said, building up to something bigger, and there must be infinite particular solutions i.e. less pure feeling. I always thought more complex was not always better.

Many thanks.

 

[boneh3ad]

If I had the answer to whether there were more general solutions, I'd be a much more famous human being. Haha.

 

[ZapperZ]

The assertion that collective behavior isn't physics is utterly ridiculous. This implies that all of condensed matter physics/solid state physics isn't physics or not fundamental. Anyone who thinks that way should read Robert Laughlin's Nobel Prize lecture.

Zz.

 

[twofish-quant]

,I know this is complicated but there's nothing about the fundamentals I see that's weird.

The problem is putting numbers to things. The standard way you break up a problem in physics is by doing spectral analysis. You break up turbulence into a set of waves at a given scale that interact with other waves. The trouble is that because the problem is non-linear, it turns out that all of the scales interact with other scales.

OK. So you cheat. You put in some fudge factor that redistributes energies from scale to scale. Trouble with that is that if you just put random fudge factors in there, you end up with non-physical situations (i.e. negative energies, unstable equations. etc. etc)

The fact that you end up with complex behavior even though the fundamental properties of the gas is known is interesting. Also, you could imagine a hypothetical computer in which you put in each atom and see it interact with other atoms, but in that situations you'd be seeing the trees and missing the forest.

Am I not getting the word turbulence, why do you say it's such a mystery? I mean it's a mystery mathematically because of all the variables(dust, shape of molecules, multiple waves and streams of medium disorting each other) so calculating 100% would need a sick computer... but in itself I don't see the complexity.

The equations themselves are non-linear. Suppose you calculate the flow over a wing. Since all scales interact with all other scales, you would in principle need to calculate the motion of every atom. You don't have the compute power to do that. What you try to do is to come up with equations for the large scale behavior that mimic the behavior at small scales, but that's easier said than done.

Then you get into the problem that things might be happening at atomic scales. You might have nuclear reactions, shock waves, radiation transfer.

And even if you could calculate something at the atomic level, you might me missing something. For example, if you have two gasses that are shearing against each other, they will form eddies, and with some simple scaling arguments you can come up with the length scale of the eddy. Similarly with dimensional arguments you can get a rough guess for how energy distributes itself in flows. It turns out that for 3-d flows, eddies tend to break up, but for 2-d flows small eddies tend to form big eddies, until you have one big eddy, which might be the great red spot of Jupiter.

 

[MagnetoBLI]

By providing such an initial statement (albeit incorrect), a discussion was stimulated that actually uncovered a lot of interesting information. The emergent phenomenon is spot on there, startlingly interesting. The link is below for any curious eyes. Thanks for all your replies and I hope this helps others with a similar thought pattern.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1998/laughlin-lecture.pdf

 

[twofish-quant]

For me electrons exist under many conditions i.e. very fundamental, where as a boundary layer is very specific and exists only under certain boundary conditions. Do you see what I'm getting at?

Yes, but it involves a 18th century view of physics that's wrong.

In modern particle physics, the electron exists as a field and in some sense all electron behavior is (or could be) collective. One thing that happens in CFD is that instead of dealing with atoms, you start seeing collective "objects" like eddies which interact with each other. That's something like the way that electrons in a field interact with each other except that the electron field is mostly linear hence much easier to deal with than CFD.

You start see the connections a bit more with things like superfluids.

Also most engineering specifically avoids "weird stuff" for good reason. If you are building a bridge you want to do it with time tested principles and you want to avoid as much "research" as possible. If you are using an 18th century physics model instead of a 21-st century one, and it matters, then you really have to ask whether you want to build the bridge that way.

The N/S equations are a fundamental recognition of fluid motion but numerically solving them seems to be a process of understanding collective behavior alone.

I don't see that sort of division. One thing that will also give people headaches are magnetic fields and GR, and you run into the same sorts of issues that you do with solving the NS equation.

One thing I love about the field is that you run into very practical problems. You have X CPU/GPU cycles and you have to make some decisions on what is the important physics that you want to simulate. You also get *very* *very* familiar with the computer architecture to squeeze out some more performance. For example, if you write a "for-loop" if you do it the wrong way, you are hosed because you want the CPU to pack those numbers in one bunch and execute them in one instruction. So you get familiar with things like the AVX instruction set, and what versions of what compilers will output that instruction

 

[MagnetoBLI]

Yes to be honest I have to agree, it does all seem great. The technical side complements the theory very nicely from the sound of it. Is it normal to focus on one particular area (application or theoretical issue) for a whole career or is it common to apply knowledge in many areas? It seems that fluid dynamics theory is very adaptable.

How soon will (likely to be) quantum computing play a significant role in fluid dynamics modelling? Is it likely to be a prerequisite to solving turbulence in your opinions?

 

[twofish-quant]

How soon will (likely to be) quantum computing play a significant role in fluid dynamics modelling?

At the very, very best case, ten years. Also, if you want my opinion right now, I can't possibly see how quantum computing would *ever* be useful to CFD. If I'm wrong about this, ten years is the minimum time it would take for someone show that I'm wrong.

Is it likely to be a prerequisite to solving turbulence in your opinions?

I think "solving" turbulence is the wrong way of describing what people are looking for. I wouldn't be surprised if it turns out that the NS-equations are "unsolvable" in the traditional sense.

Again going back to the limits of the clock work universe. Suppose I'm modelling a car with wind going over it. A "solution" of the problem would have me specify the exact initial conditions, run through the simulation, and then come up the exact trajectory of every atom. I strongly suspect that this sort of "solution" doesn't exist, because if I change the initial condition slightly, then the trajectories of the particles are going to be extremely different.

But I really don't want a "solution." What I want is to calculate drag coefficients, so I don't *need* an exact solution. I just need a model that replicates the physics that I'm interested in, that can be done with the computing power that I have. So I'm not interested in an "exact solution" but rather a "good enough approximation."

There's also an "artistic" element to this. When an artist paints with oil paints or water color, they are trying to get to the "artistic truth" of a situation. A painting of the sun isn't a real sun, but if you are a good artist, it's a good enough simulation. CFD works a lot of the same way. You use a palette of techniques to get to the "essential physical truth" of a situation.

 

[Studiot]

I take it my observations were not of interest|?

 

[MagnetoBLI]

Are there any areas in physics that are looking for exact solutions? It seems that for every application there is another fluid theory that applies to it, which intuitively seems like a job for an engineering-physicist rather than a pure physicist. What do you think?

I am unaware of the details of solar prominence, although they appear to be represent-able by a specific solution rather than a general underlying property.

 

[Studiot]

Are there any areas in physics that are looking for exact solutions? It seems that for every application there is another fluid theory that applies to it, which intuitively seems like a job for an engineering-physicist rather than a pure physicist. What do you think?

I have no idea how this relates to my comments.

I offered two areas of fundamental theory that have arisen recently from fluid dynamics.

We have barely scratched the surface of these phenomena to date. Much of our knowledge here is in the pure theory stage ('Faraday's what use is a newborn baby'), known applications are very limited.

I also offered two areas of applied theory that have not been solved to date, not to be sneered at but as examples of how little we know.

 

[MagnetoBLI]

Again going back to the limits of the clock work universe. Suppose I'm modelling a car with wind going over it. A "solution" of the problem would have me specify the exact initial conditions, run through the simulation, and then come up the exact trajectory of every atom. I strongly suspect that this sort of "solution" doesn't exist, because if I change the initial condition slightly, then the trajectories of the particles are going to be extremely different.

But surely this means all solutions that are true for initial condition changes are over simplified and provide an approximate solution in reality? Is it that fluids are so complex that this over-simplification is more pronounced when initial conditions are altered?

 

[twofish-quant]

But surely this means all solutions that are true for initial condition changes are over simplified and provide an approximate solution in reality?

What happens with turbulence and chaotic systems in general is that if your initial conditions change a little bit, then your final result becomes random. One way of thinking about this is imagine a particle near a turbulent field. If you change the initial conditions slightly, that particle could end up *anywhere*. If you care where all of the particles end up, you are stuffed, because where an individual particle ends up is random.

What this says is that the "reductionist" approach wouldn't work, you have to try something else.

You usually don't care about tracking every particle. What you care about are "generalized quantities" (i.e. if I put this shape in this gas, what's the drag coefficient). There are a number of techniques for figuring that out.

Is it that fluids are so complex that this over-simplification is more pronounced when initial conditions are altered?

It's not that fluids are particular complex, it's just undergraduate physics classes are deliberately oversimplified. The types of systems that you learn about in undergraduate physics are *deliberately* selected not to show complex behavior, and this is in part because engineers *deliberately* build systems that minimize weird behavior. So what happens is that physics undergraduates learn a "cookbook" of tools that work for certain rather simple systems. The mistake is thinking that you can use the cookbook for everything.

 

[MagnetoBLI]

Is anything truly random or is it just effectively random to today's computing power? But yes I understand what your saying about real systems being unique.

 

[twofish-quant]

The comment about 'similarity variables' is what I was most confused about; I knew relatively large scale properties were known but not the small scale properties, so that's interesting to hear.

The thing about similarity variables is that they let you show that one physical situation is basically the same as another, so you can run an experiment in one situation and scale it up to another.

For example, turbulence is controlled by the Reynolds number. So I can run water through a tube and get some numbers, and then apply them to some other physical situation. As long as the Reynolds number is the same, the behavior will be similar.

The problem is that there are some situations where you can't run an experiment. I can put a wing in a wind tunnel, but I can't drop gas down a black hole.

I was in general trying to target this issue; that properties are well understood and that focus is now on the phenomena/processes (collective behavior of properties and energy etc...)

I don't think that the bulk properties are well understood. Rather they are well defined.

However, I am intrigued by phenomena also. Out of interest, are there many other general solutions (rather than particular solutions) being devised or potential for existence for other fluid phenomena than turbulence?

One thing about this is that most of this is experimental/observationally driven. You see something, and you try to model it. Our understanding of the equations aren't good enough so that you can;t take the equations and *predict* some complex behavior.

You talk water, you run it through a tube. At some critical number, it turns turbulent. Now suppose you are a space alien that doesn't know about water and tubes. Someone gives you the NS equations. Looking at those equations, with the math techniques that we have, that space alien wouldn't be able to figure out that AHHH, at X situation, I see turbulence.

This matters for things like black holes and neutron stars. With GR, magnetic fields, and all sorts of quark phenonmenon, I'm sure that "something weird" happens.

Most of what I've read are particular solutions mainly focusing on, as you said, building up to something bigger, and there must be infinite particular solutions i.e. less pure feeling. I always thought more complex was not always better.

What usually happens in astrophysics is that people create particular approximations. For example, gravity works with GR, but GR is too hard to build bridges. However, by making some assumptions end up with Newtonian gravity which you can work with. Same thing happens in astrophysics. You find that with certain situations, magentic field lines get trapped with fluid, and you end up with the MHD approximation.

 

[MagnetoBLI]

Cheers for the replies, very useful. How does one go about choosing an area of fluid dynamics for a career? There seems to be select groups within uni departments that focus on specific areas (although maybe some overlap), presumably due to the time required to understand each area properly, and from reading over the next year (all I have until application time) I will barely scratch the surface.

 

[reasonableman]

This has been an interesting thread to read but I have to echo MagnetoBLI's view of the field. When you look at the literature it seems to, largely, be phenomenology (when you do this, this happens).

If a problem needs to be solved either a simple, soluble case is used, or it's modeled using CFD (yes, this can be an interesting challenge). Yes, it's led to new theories but there seems to be few fundamental ideas (NS equations describe everything, but are too complicated) that are used.

For example, take a simple problem of mixing milk in my tea. If I stir how long will it take to mix, if I stir twice how will that change the time? As far as I'm aware the answer to this question would be highly specific with no 'general principles'. Which is why it doesn't 'feel' like physics. This isn't necessarily a criticism, though.

 

[twofish-quant]

Cheers for the replies, very useful. How does one go about choosing an area of fluid dynamics for a career? There seems to be select groups within uni departments that focus on specific areas (although maybe some overlap), presumably due to the time required to understand each area properly, and from reading over the next year (all I have until application time) I will barely scratch the surface.

Usually someone specializes in a particular department that uses CFD in a certain way. There are some university centers for CFD and numerical programming.

One reason that it's subject focuses is that different departments look at different types of problems and those call for different techniques. For example aeronautical engineering typically looks at problems in which the fluid does do not weird things (i.e you have to worry about antimatter appearing near your airplane) but you have very complex shapes.

In astrophysics you *do* have to worry about antimatter and tau neutrinos popup out in your fluid, but you have simple boundary conditions and shapes (i.e. stars are more or less spheres). What happens is that his why AE using finite element methods whereas astrophysicists use finite element models.

Then there are the CFD simulations of the entire universe.

http://www.mpa-garching.mpg.de/gadget/

where your grids are 100s kiloparsecs and your timesteps are tens of thousands of years.

 

[chiro]

I don't want to hi-jack this thread, but I was wondering if anyone can give some resources for CFD, in particular in relation to your own specific sub-area considering your own issues if you have them handy or in memory.

Getting a small insight into these intracacies has been very enlightening.

 

[MagnetoBLI]

Reasonableman: Yes, it's led to new theories but there seems to be few fundamental ideas (NS equations describe everything, but are too complicated) that are used.

From the below two quotes it seems that fundamental ideas in the current age of physics are based upon processes rather than intrinsic properties and that new found particles are systems of the same substance such as emergence phenomena. Is this the same with other ares of physics?

Robert Laughlin's Nobel Prize lecture on solid state physics mentions that his students feel betrayed when he tells them that fits to experiment/deductive techniques are perfectly valid , as the students are trained to think in reductionist terms and think non-amenable things are unimportant. He explains that 'emergent phenomena' can be described as a particle that has it's own characteristics and properties - like an eddy, which I thought was interesting.

Boneh3ad:
Experimental physics relies on observation of phenomena under highly controlled and specific conditions in the hopes of learning something that can later be broadened to a greater number of conditions until you have eventually described the more general phenomenon

And

Boneh3ad:
Even theoretical physics follows this pattern where most if not all the fundamental properties are known and it is a matter of proving our theories about those properties.

 

[AlephZero]

The types of systems that you learn about in undergraduate physics are *deliberately* selected not to show complex behavior, and this is in part because engineers *deliberately* build systems that minimize weird behavior.

You can't minimize weird behaviour in a rational way until you can predict something about it. Otherwise you may be dancing blindfold on the edge of a cilff, and of course there are plenty of examples in engineering (some from thousands of years ago) where engineering cliff-edges were discovered by falling off them.

I agrre that predicting the "details" (whatever that means) of a turbulent flow is probably not useful, but predicting the onset of turbulence, or the boundaries of turbulent regions in a flow pattern, would be a useful start. In mechanical engineering people are using nonlinear dynamics models to track how solutions depend on system parameters, to predict unstable or chaotic behavour, locate multiple solutions to the response of a system for the "same" conditions, etc. It hasn't yet been reduced to a black box method that anybody can use wthout understanding it, but it works in real-world situations, and on models with 200,000 DOF not two. But AFAIK, CFD hasn't got to that point yet.

As a simple CFD example, think about flow through a uniform pipe. The laminar flow solution of the NS equations is well known, and mathematicallly that solution exists for all Reynolds numbers. But experiment says there is some critical value Re* such that if Re > Re* this flow pattern doesn't physically happen. It would be very useful to have a way to compute the value of Re* from a simulation of the flow. And it might even be even more useful in the long term if somebody comes up with insight into why doing that calculation based on a continuum model of the fluid (i.e. NS) is impossible!

Probably doing "only" that wouln't earn you a Millennium Prize, but you have to start somewhere...

 

[twofish-quant]

From the below two quotes it seems that fundamental ideas in the current age of physics are based upon processes rather than intrinsic properties and that new found particles are systems of the same substance such as emergence phenomena. Is this the same with other ares of physics?

This is getting close to philosophy and one thing that I've found is that different people in physics can do physics basic on radically different philosophical foundations. I'd very strongly disagree with Reasonableman's quote, but I think its probably because we are looking at the world through fundamentally different philosophical lenses.

You can't answer the question of "is fluid dynamics a true physics subject?' without answering the question of "what is physics?" and that turns out to be a surprisingly difficult question to answer.

Robert Laughlin's Nobel Prize lecture on solid state physics mentions that his students feel betrayed when he tells them that fits to experiment/deductive techniques are perfectly valid , as the students are trained to think in reductionist terms and think non-amenable things are unimportant.

This gets to some pretty deep questions like "what are physicists trying to do?" It's quite fascinating philosophy, which gets you into sociology and history (so why *are* students trained to think in reductionist terms?)

One thing that is true in my case is that my thinking about physics comes from a Chinese Confucian background which gives a much different flavor them someone that comes from a Platonic reductionist background.

He explains that 'emergent phenomena' can be described as a particle that has it's own characteristics and properties - like an eddy, which I thought was interesting.

For that matter in quantum field theory, "particles" are Fourier transforms of fields. Things like the Higgs particle came out of solid state physics.