# The Naked Scientists Forum

### Author Topic: Why is turbulence so difficult to study?  (Read 1097 times)

#### ijaz

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##### Why is turbulence so difficult to study?
« on: 10/12/2015 05:45:28 »
Turbulence is very difficult to model mathematically, Why??
« Last Edit: 10/12/2015 08:18:38 by chris »

#### evan_au

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##### Re: Why is turbulence so difficult to study?
« Reply #1 on: 10/12/2015 10:39:53 »
Turbulence involves large volumes of gas or liquid, whose behavior at large scales (meters to thousands of kilometers) is affected by the detailed behavior at nanometer scales (atomic/molecular).

Mathematically, this motion is described by the Navier-Stokes equations. Solving these is extremely difficult, and is eligible for a \$1 million Millennium Mathematics prize. So in practice, people use approximations and simulation.

To simulate turbulence, you need to simulate what is happening in large volumes where almost nothing is happening, but also at molecular scales, where lots is happening very quickly, and at every scale in-between.

Computer simulations work best if they can use a common measurement scale and timestep at all points in space. However, turbulence problems require very fine time steps and a very fine space grid for some areas, while the bulk of the simulation can use a coarse grid and coarse time steps. This makes simulation more difficult and less accurate.

#### wolfekeeper

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##### Re: Why is turbulence so difficult to study?
« Reply #2 on: 14/12/2015 18:30:23 »
Turbulence is very difficult to model mathematically, Why??
Turbulence is very chaotic; it's very sensitive to extremely small differences. So you can solve the maths with trivial differences, and it will come out completely different results. Plus the equations are nonlinear, which makes even solving the equations really hard.

#### evan_au

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##### Re: Why is turbulence so difficult to study?
« Reply #3 on: 14/12/2015 20:20:30 »
The chaotic nature is sometimes jokingly expressed as the "butterfly effect".
http://en.wikipedia.org/wiki/Butterfly_effect

Quote from: Edward Lorenz
a metaphorical example of the details of a hurricane (exact time of formation, exact path taken) being influenced by minor perturbations such as the flapping of the wings of a distant butterfly several weeks earlier

#### The Naked Scientists Forum

##### Re: Why is turbulence so difficult to study?
« Reply #3 on: 14/12/2015 20:20:30 »