# what does this mean? \nabla ^3U

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 October 13, 2013, 20:50 what does this mean? \nabla ^3U #1 Senior Member   Dongyue Li Join Date: Jun 2012 Location: Torino, Italy Posts: 742 Rep Power: 9 Thanks.

 October 16, 2013, 13:37 #2 Senior Member   Reza Join Date: Mar 2009 Location: Appleton, WI Posts: 116 Rep Power: 9 It should mean: Where did you see this term? Last edited by triple_r; October 16, 2013 at 13:37. Reason: formatting the equation correctly

October 16, 2013, 20:20
#3
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Dongyue Li
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Quote:
 Originally Posted by triple_r It should mean: Where did you see this term?
Thanks,

You mean its a scalar rite? Actually its a simple version of the regular one. Its an equation of a turbulence model.

"Partial-average-based equations of incompressible turbulent flow"

I attach a image. This equation is tough to handle. Right now I have no idea how to solve this equation.
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 October 17, 2013, 09:15 #4 Senior Member   Jonas T. Holdeman, Jr. Join Date: Mar 2009 Location: Knoxville, Tennessee Posts: 108 Rep Power: 10 It could also be interpreted as a tensor

October 17, 2013, 11:09
#5
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Filippo Maria Denaro
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Quote:
 Originally Posted by sharonyue Thanks, You mean its a scalar rite? Actually its a simple version of the regular one. Its an equation of a turbulence model. "Partial-average-based equations of incompressible turbulent flow" I attach a image. This equation is tough to handle. Right now I have no idea how to solve this equation.

I think is a simbolic power of the operator l.Grad therefore it must be applied n times on the function

 October 18, 2013, 10:30 #6 Senior Member   Reza Join Date: Mar 2009 Location: Appleton, WI Posts: 116 Rep Power: 9 Ignore my first answer please, I didn't see the dot product with l. As Filippo said, it is equal to application of n times in a row, and because of the dot product, it is a scalar operator. FMDenaro likes this.

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