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Normalization of the energy spectrum and homogeneous turbulence

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Old   March 15, 2019, 04:40
Default Normalization of the energy spectrum and homogeneous turbulence
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luca mirtanini
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Hi,
I have two doubts:

1. I have not understood the scope of the Energy spectrum normalization. The only explanation that I found can be the comparison between more graph in order to align them in the inertial subrange, as done here at page 350 http://storm.colorado.edu/~jweiss/50...avalli1994.pdf

2. Someone can explain me the definition of homogeneous turbulence? I cannot understand why a turbulence can be defined homogeneous since, turbulence is always confined in an area as a wake or a jet.

Thank you
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Old   March 15, 2019, 06:03
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Quote:
Originally Posted by lucamirtanini View Post
Hi,
I have two doubts:

1. I have not understood the scope of the Energy spectrum normalization. The only explanation that I found can be the comparison between more graph in order to align them in the inertial subrange, as done here at page 350 http://storm.colorado.edu/~jweiss/50...avalli1994.pdf

2. Someone can explain me the definition of homogeneous turbulence? I cannot understand why a turbulence can be defined homogeneous since, turbulence is always confined in an area as a wake or a jet.

Thank you

1. Consider that making a variable non-dimensional is simple but does not guarantee that the non-dimensional values are of O(1). Normalization means you use the proper reference variables to get that,



2. there is a standard definition in terms of the property of the statistics, just see a statement on Wikipedia https://en.wikipedia.org/wiki/Homoge...pic_turbulence
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Old   March 15, 2019, 08:19
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1. I have asked why they decided to normalise
2. I ve already seen this wikipedia page. My question was: how can this theory work for turbulence which is confined only in particular area.
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Old   March 15, 2019, 08:40
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So you have the answer: if the statistics depend on the translated location, the flow is not homogeneous. This is what happens, for example, when you move along the normal direction to a wall.
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Old   March 15, 2019, 10:18
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When a flow can be approximated as homogeneous?
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Old   March 15, 2019, 10:58
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When a flow can be approximated as homogeneous?

for example, in channel flows one considers that at high Re number the flow is almost homogeneous in the center of the channel
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