astrolabe wrote:Differences in temperature can cause turbulence resulting in pressure and density variables.
I partially agree. A consequence of turbulence are fluctuations in pressure and thus density. Differences in temperature cause a mass flow from warm to cold. That does not necessarily have to mean that the mass flow is turbulent.
Turbulence is (for me) next to the bigbang one of the least understandble phenomena. While the bigbang according to Weinberg can be modelled via a mathematical description, turbulence can only be approximated by statistical methods, which in some respect fail to do proper predictions. The chapter in Landau and Lifschitz "Fluid mechanics" gives a lot of clues. Nevertheless an image, a conceptual idea of turbulence is hard to find.
I use to compare mass flow with a toddler. It managed to do some steps. When it is slow and when it is not hampered by objects around him, distracted, it can walk. That is laminar flow. Now it gets distracted by the joy of an icecream or his favourite toy at the other side of the room. Its starts to run as fast as its small legs will allow it. In the process of running the legs get cluthered and it tumbles. Turbulent flow is a type of flow too fast for its surrounding and density. The flow tumbles over its own material and starts to spiral in vortices. I'm fully aware that the above description is an analogon which may not be precise and is absolutely of no use to do any prediction at all.
Turbulence is connected to too many degrees of freedom. When a block of aluminium moves very fast, (e.g. a airplane), the air around the aluminium is turbulent, the aluminium of the plane itself is not turbulent, not in the least to the enjoyment of those in the airplane. The intermolecular forces in the aluminium dominate the location of the atoms. In the air there more degrees of freedom, since intermolecular forces between the molecules of the air are too small to suppress the turbulence. These forces, to be precise the ability to withstand sheer forces, can be expressed into a macroscopic property: viscosity, the degree of "molasses-ability". (i know: this word is not correct english). There are two flavours of viscosity: dynamic viscosity (η) and kinematic viscosity (ν). The dynamic viscosity is the property used as in the famous Stokes law:
F = 6 π η r V
where r is the radius of a sphere, V is the velocity of the sphere with respect to the fluid (or gas) and F is the friction experienced by the sphere. As you might imagine, the density of the fluid or gas influences the dynamic viscosity. The kinematic viscosity corrects for effects of density, by normalizing the dynamic viscosity by the density of the fluid or gas:
ν = η / ρ
where ρ is the density.
The point of the concept as described above is that turbulence is bound to happen if the velocity of the flow is too fast. A dimensionless number has been introduced: the Reynolds number:
Re = v D / ν
If Re < 1, the flow is laminar. The shear forces are sufficiently low that any inclination to "tumble over its self" is suppressed. If Re > 1000 flow is turbulent. Viscosity no longer plays any role.
Turbulence can be initiated by sharp changes in geometry: the running toddler is bound to tumble over its legs, but still manages to stay upright. When it encounters the edge of a chair, it tumbles. Similarly an object in the path of flow can initiate turbulence.
A few examples of such geometrically triggered turbulence which not just
Astrolabe will like, are the
Von Kármán eddies,
orographic cloud bands and
orographic clouds as seen from below. The Von Kármán eddies are generated mostly by small islands in the ocean, like the Canarian islands, the Balearic islands, Ascension. The orographic structures are generated -as the word says- by moutains. The wingtips of an airplane are famous for its turbulence generating properties. Birds of prey have found a solution to minimize turbulence at their wingtips, by fingering their wingtips: these are divided into five separate feathers.
Summarizing:
- Turbulence is due to happen when the flow is too fast to be kept stable (laminar) by intermolecular forces or viscosity.
- Turbulence can be triggered by (sharp) changes in geometry
- Turbulence generates fluctuations in velocity
- Fluctuations in velocity generate fluctuations in density and thus pressure.
- When the fluctuations in density are levelled out, fluctuations in temperature can be generated
If we would know the circumstances in the Lagoon nebula, like kinematic viscosity, size ("D"), and velocity ("V") we can calculate the Reynolds number and figure out whether turbulence is likely or not.
[quote="astrolabe"]Differences in temperature can cause turbulence resulting in pressure and density variables.[/quote]
I partially agree. A consequence of turbulence are fluctuations in pressure and thus density. Differences in temperature cause a mass flow from warm to cold. That does not necessarily have to mean that the mass flow is turbulent.
Turbulence is (for me) next to the bigbang one of the least understandble phenomena. While the bigbang according to Weinberg can be modelled via a mathematical description, turbulence can only be approximated by statistical methods, which in some respect fail to do proper predictions. The chapter in Landau and Lifschitz "Fluid mechanics" gives a lot of clues. Nevertheless an image, a conceptual idea of turbulence is hard to find.
I use to compare mass flow with a toddler. It managed to do some steps. When it is slow and when it is not hampered by objects around him, distracted, it can walk. That is laminar flow. Now it gets distracted by the joy of an icecream or his favourite toy at the other side of the room. Its starts to run as fast as its small legs will allow it. In the process of running the legs get cluthered and it tumbles. Turbulent flow is a type of flow too fast for its surrounding and density. The flow tumbles over its own material and starts to spiral in vortices. I'm fully aware that the above description is an analogon which may not be precise and is absolutely of no use to do any prediction at all.
Turbulence is connected to too many degrees of freedom. When a block of aluminium moves very fast, (e.g. a airplane), the air around the aluminium is turbulent, the aluminium of the plane itself is not turbulent, not in the least to the enjoyment of those in the airplane. The intermolecular forces in the aluminium dominate the location of the atoms. In the air there more degrees of freedom, since intermolecular forces between the molecules of the air are too small to suppress the turbulence. These forces, to be precise the ability to withstand sheer forces, can be expressed into a macroscopic property: viscosity, the degree of "molasses-ability". (i know: this word is not correct english). There are two flavours of viscosity: dynamic viscosity (η) and kinematic viscosity (ν). The dynamic viscosity is the property used as in the famous Stokes law:
F = 6 π η r V
where r is the radius of a sphere, V is the velocity of the sphere with respect to the fluid (or gas) and F is the friction experienced by the sphere. As you might imagine, the density of the fluid or gas influences the dynamic viscosity. The kinematic viscosity corrects for effects of density, by normalizing the dynamic viscosity by the density of the fluid or gas:
ν = η / ρ
where ρ is the density.
The point of the concept as described above is that turbulence is bound to happen if the velocity of the flow is too fast. A dimensionless number has been introduced: the Reynolds number:
Re = v D / ν
If Re < 1, the flow is laminar. The shear forces are sufficiently low that any inclination to "tumble over its self" is suppressed. If Re > 1000 flow is turbulent. Viscosity no longer plays any role.
Turbulence can be initiated by sharp changes in geometry: the running toddler is bound to tumble over its legs, but still manages to stay upright. When it encounters the edge of a chair, it tumbles. Similarly an object in the path of flow can initiate turbulence.
A few examples of such geometrically triggered turbulence which not just [b]Astrolabe[/b] will like, are the [url=http://upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Vortex-street-1.jpg/180px-Vortex-street-1.jpg]Von Kármán eddies[/url], [url=http://upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Wave_cloud.jpg/320px-Wave_cloud.jpg]orographic cloud bands[/url] and [url=http://ww2010.atmos.uiuc.edu/guides/mtr/cld/cldtyp/oth/gifs/org3.gif]orographic clouds as seen from below[/url]. The Von Kármán eddies are generated mostly by small islands in the ocean, like the Canarian islands, the Balearic islands, Ascension. The orographic structures are generated -as the word says- by moutains. The wingtips of an airplane are famous for its turbulence generating properties. Birds of prey have found a solution to minimize turbulence at their wingtips, by fingering their wingtips: these are divided into five separate feathers.
Summarizing:
[list=1][*]Turbulence is due to happen when the flow is too fast to be kept stable (laminar) by intermolecular forces or viscosity.
[*]Turbulence can be triggered by (sharp) changes in geometry
[*]Turbulence generates fluctuations in velocity
[*]Fluctuations in velocity generate fluctuations in density and thus pressure.
[*]When the fluctuations in density are levelled out, fluctuations in temperature can be generated[/list]
If we would know the circumstances in the Lagoon nebula, like kinematic viscosity, size ("D"), and velocity ("V") we can calculate the Reynolds number and figure out whether turbulence is likely or not.