# Normalization of the energy spectrum and homogeneous turbulence

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 March 15, 2019, 04:40 Normalization of the energy spectrum and homogeneous turbulence #1 Member   luca mirtanini Join Date: Apr 2018 Posts: 83 Rep Power: 3 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

March 15, 2019, 06:03
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Filippo Maria Denaro
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 Originally Posted by lucamirtanini 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

 March 15, 2019, 08:19 #3 Member   luca mirtanini Join Date: Apr 2018 Posts: 83 Rep Power: 3 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.

 March 15, 2019, 08:40 #4 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 4,658 Rep Power: 48 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. lucamirtanini likes this.

 March 15, 2019, 10:18 #5 Member   luca mirtanini Join Date: Apr 2018 Posts: 83 Rep Power: 3 When a flow can be approximated as homogeneous? arnie333 likes this.

March 15, 2019, 10:58
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Filippo Maria Denaro
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 Originally Posted by lucamirtanini 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